Electronic, adsorption, and
transport properties of
diamondoid-based complexes
Von der Fakultät Mathematik und Physik und dem
Stuttgart Research Centre for Simulation Technology
(SRC SimTech) der Universität Stuttgart zur Erlangung
der Würde eines Doktors der Naturwissenschaften
(Dr. rer. nat.) genehmigte Abhandlung
Vorgelegt von
Bibek Adhikari
aus Jhapa, Nepal
Hauptberichter: Jun. Prof. Dr. Maria Fyta
Mitberichter: Prof. Dr. Siegfried Schmauder
Mitberichter: Prof. Dr. Udo Seifert
Tag der mündlichen Prüfung: 24.03.2017
Institut für Computerphysik der Universität Stuttgart
2017

Erklärung
Hiermit versichere ich, die vorliegende Arbeit selbstständig verfasst und keine
anderen als die angegebenen Quellen und Hilfsmittel benutzt, sowie die Zitate
deutlich kenntlich gemacht zu haben.
Stuttgart, den 24.03.2017
Bibek Adhikari
i

Acknowledgements
I would like to thank my advisor Jun. Prof. Maria Fyta for the opportunity
to work with her in the field of solid state physics and quantum chemistry.
She has been a great support during this time. This thesis would not have
been possible without her scientific and technical guidance. I would also like
to thank Prof. Siegfried Schmauder and Prof. Udo Seifert for being the co-
referees of this thesis.
I am very grateful to Prof. Sheng Meng for hosting me as a guest student
in his group at the Institute of Physics, Chinese Academy of Sciences and for
granting me the use of its computational resources. This thesis would have
been incomplete without the results obtained from my stay in China. Special
thanks go to Huixia Fu, Jin Zhang, and Zijing Ding for their invaluable coop-
eration and fruitful scientific discussions.
Many thanks to Dr. Christos Mathioudakis, Ganesh Sivaraman, and Balaji
Muthuraman who contributed and collaborated with me in different projects
which are a part of this thesis. I would like to thank Frank Maier for his kind
help in proof-reading the Zusammenfassung of this thesis, other colleagues and
the administrative staff from the Institute for Computational Physics for their
help and advice during my time at the institute. I would like to thank the
SimTech staff for the organization of the fun and refreshing Ph.D. weekends
and the annual Graduate School seminars.
I would also like to acknowledge the financial support from the Juniorprofes-
sorenprogramm funded by the Ministry of Science, Research, and the Arts
Baden-Württemberg (MWK) and from the collaborative network SFB 716
"Dynamic simulations of systems with large particle numbers" funded by the
German Funding Agency (Deutsche Forschungsgemeinschaft-DFG). This re-
search was supported in part by the bwHPC initiative and the bwHPC-C5
project provided through associated computing services of the JUSTUS HPC
facility at the University of Ulm.
Finally, I would like to thank my family in Nepal and my friends in Stuttgart,
especially Liana without whom I would have not been able to come this far.
iii

Summary
Quantum simulation is an invaluable tool to researchers from various fields of
scientific research. It allows the investigation of various complex condensed
matter in the regimes of physics, chemistry, and biology. In this work, we fo-
cused our attention in unraveling the physical, chemical, electronic, transport,
and optical properties of diamondoids and their complexes through quantum
simulations. We have implemented a bottom-up approach where we move from
the doping and functionalization of single diamondoids up to the diamondoid-
based molecular devices. Naturally, diamondoids have been extracted from
petroleum and also have been synthesized in the lab. These diamondoids are
hydrogen terminated carbon cage-like structures which have lattice structure
similar to diamond. As a result, they are found to be as rigid and stiff as dia-
monds and are comparable to the stiffness of graphite and carbon nanotubes.
In addition to their strong physical properties, they are also the building blocks
for important drugs. Furthermore, because they have a negative electron affin-
ity, they are potentially useful in molecular electronics and electron-emitting
devices.
Electronic properties were probed by modelling the doping and functional-
ization possibilities of diamondoids starting from adamantane up to hepta-
mantane. For the doped diamondoids, boron, nitrogen, silicon, oxygen, and
phosphorus were used. These dopants substituted a carbon site according to
an energy minimization criterion for the choice of the doping site. A single- and
double-functionalization using an amine- and a thiol-group involved the substi-
tution of a hydrogen site. The analysis started from the smallest adamantane,
while the effect of isomerization, using four isomers of tetramantane was also
investigated. The electronic properties of all these cases were probed through
the electronic density of states and the frontier orbitals, HOMO and LUMO.
The main goal of this study was the evaluation of the electronic band gap i.e.,
the conducting and optical properties of these modified diamondoids. We ob-
served a decrease in the band gap for all doped and functionalized diamondoids
as compared to the respective values of unmodified diamondoids. This decrease
was also evident in the double-functionalized molecules moving from the small-
est adamantane up to heptamantane. The band gap variation was found to be
related to a strong localization of the frontier orbitals on the modified diamon-
doids. In addition to showing the possibility of selectively tuning the electronic
properties of diamondoids, we also investigated the optical properties of these
complexes. The optical properties were only explored for adamantane and
v
diamantane which were modified through single and double-functionalization.
Different functional groups lead to different electronic and optical properties,
while a double-functionalization as compared to a single-functionalization de-
creases even further the electronic and optical band gap, moving it towards
the conducting region for the ground state and towards the visible region for
the excited state. We chose representative atoms and functional groups but
more can be tested.
Accordingly, synthesizing diamondoid-based complexes of specific size and
modification has the potential to tune their electronic and optical properties.
In terms of practical applications, the presence of functional groups provides
additional functional properties, as the diamondoids include sites that not only
tune their properties but also provide binding sites to other structures. The
fact that a double functionalization leads to a larger increase of the optical
properties provides the potential to form novel diamondoid-based emission de-
vices which include one functional group for the attachment of the diamondoid
on the substrate and another atomic group like the N-heterocyclic carbenes
(NHC)s molecules which provide the diamondoid with functionalities. The
NHCs can promote the selective binding or sensing of molecules in its vicin-
ity which was evident in the study of the adsorption of carbene-functionalized
diamondoids on metal surfaces. Keeping that goal in mind, we analyzed the
self-assembly of carbene- mediated diamondoids over Au(111), Ag(111), and
Pt(111) metal surfaces, respectively. The self-assembly of these complexes was
probed through the stability and adsorption, binding possibilities, and surface
morphology after adsorption. In our study, Au(111) and Pt(111) were the most
efficient metal surfaces for the adsorption of carbene-mediated diamondoid self-
assembled monolayers (SAM)s. Orbitals of d-symmetry are essential in order
to have orbital overlapping with carbon p-electrons and bond formation as in
the case of the Au(111) and Pt(111) surfaces. In Ag(111), the weaker bonding
was justified by the non-availability of the d-orbital of the metallic first layer
of the surface around the Fermi level. Calculation of the work functions of
carbene-mediated diamondoid SAMs on Au(111), Ag(111), and Pt(111) sur-
faces demonstrated that the modulation of the work function with respect to
the properties of clean metal surfaces and a dynamic tuning can be easily
achieved in NHC-ada/metal devices for organic electronic applications. The
charge re-distribution and the simulated STM images of the surfaces showed
that on Pt(111) the whole carbene ring of the NHC-ada molecule is associ-
ated with the SAM/metal bonding, increasing the adsorption energy of SAMs.
By comparing the molecular adsorption energies on reconstructed Au(111),
Ag(111), and Pt(111) surfaces, we found out that these geometries are stable
and of practical interest. However, it is essential to examine the thermal sta-
bility of these structures and the influence of environmental conditions on their
stability. Nevertheless, carbene molecules have proven to be a better alterna-
tive to the thiol-based bonding of diamondoids on metallic surfaces, opening
up the path for more stable and efficient SAMs/metal devices.
vi
In search of highly efficient diamondoid-based molecular devices, electronic
transport across molecular junctions made up of functionalized and doped di-
amondoids were investigated. A small diamondoid was placed in between the
two gold electrodes of the nano gap. The diamondoids were covalently bonded
to the gold electrodes through two different molecules, a thiol group, and an
N-heterocyclic carbene molecule. The transport properties of the diamondoid-
based molecular device were evaluated with respect to these two binding pos-
sibilities and the size of the diamondoid. We also investigated the influence of
doping the diamondoid on the properties of the molecular device. The com-
parison of the results was discussed based on the functionalization, the type of
dopants, and the diamondoid size. A di-thiol linker group was found to be effi-
cient compared to a carbene group attached to the Au(111) nano gap. Using a
nitrogen atom to dope the diamondoids lead to a considerable increase of the
electron transmission across the device. We showed the asymmetric feature
of the I-V curve applying the positive and negative bias, which indicates the
diode-like property resulting in rectification within a very small range of bias
voltages. The zero bias transmission function of undoped diamondoid systems
reveals that the highest occupied molecular orbitals (HOMO) peaks are away
from the Fermi level, which was beyond any practical voltage bias window.
In all the cases, the efficiency of the device was manifested and is discussed
in view of novel nanotechnological applications. We were able to selectively
tuned the electronic and transport properties of the diamondoid-based molec-
ular junctions by doping the molecules with boron and nitrogen. Doping with
nitrogen leads to an addition of a transmission peak very close to the Fermi
level leading to higher molecular conductance. Increasing the diamondoid size
leads to the slight decrease in the zero bias conductance. Such a decrease was
also observed when using the carbene molecules as the linker of the diamon-
doid on the nano gap surfaces. Bias dependent transport calculations revealed
that doping leads to a higher rectification ratio at very small applied bias volt-
ages. This behavior is the result of the energy shift of the HOMO peaks with
respect to the zero bias case. The rectifying effect in N-doped diamondoids is
related to the asymmetry in the structure when introducing the dopant. Since
a similar asymmetry is introduced by means of doping in the case of B and
B-N co-doping, we can assume that a similar rectifying behavior is observed
also for these latter cases.
vii

Zusammenfassung
Quantensimulation ist ein unschätzbares Werkzeug für Forscher aus verschiede-
nen Bereichen der Wissenschaft. Sie ermöglicht die Untersuchung verschied-
ener komplexer kondensierter Materie in der Physik, Chemie und Biologie. In
dieser Arbeit geht es um die Entschlüsselung der physikalischen, chemischen,
elektrischen, transport und optischen Eigenschaften von Diamantoiden und
deren Komplexen durch Quantensimulationen. Wir haben einen bottom-up
Ansatz implementiert, beginnend mit der Dotierung und Funktionalisierung
einzelner Diamantoiden bis hin zu Diamantoid-basierten molekularen Syste-
men. Diamantoide werden nicht nur natürlich aus Petroleum extrahiert, son-
dern auch im Labor synthetisiert.
Diese Diamantoide sind Wassersfoff-terminierte Kohlenstoffstrukturen, deren
Kohlenstoffgerüste denen von Diamanten gleichen. Aus diesem Grund sind sie
so starr und steif wie Diamanten und ihre Steifigkeit mit der von Graphit-
und Kohlenstoff-Nanoröhrchen vergleichbar. Abgesehen von ihrer Robustheit
dienen sie auch als Bausteine wichtiger Medikamente. Aufgrund der negativen
Elektronenaffinität von Diamantoiden weisen sie ein hohes Potential zum Ein-
satz in molekularelektrischen und Elektronen-emittierenden Systemen auf.
In dieser Dissertation wurden die elektrischen Eigenschaften durch Model-
lierung der Dotierungs- und Funktionalisierungsmöglichkeiten von Diaman-
toiden, ausgehend von Adamantan bis hin zu Heptamantan, untersucht. Für
die dotierten Diamantoide wurden Bor, Stickstoff, Silizium, Sauerstoff und
Phosphor verwendet. Diese Dotierungen ersetzen eine Kohlenstoffstelle auf-
grund eines Energieminimierungskriteriums bei der Wahl der Dotierungsstelle.
Die Einzel- und Doppelfunktionalisierung der Diamantoiden erfolgte durch
die Substituierung eines Wasserstoffatoms mit einer Amin- und einer Thiol-
Gruppe.
Die Untersuchung begann beim kleinsten Diamantoid, dem Adamantan, wobei
der Einfluss der Isomerisierung an vier Isomeren von Tetramantan ebenfalls er-
arbeitet wurde. Die elektrischen Eigenschaften aller dieser Strukturen wurden
mittels der Zustandichte, sowie den Grenzorbitalen HOMO (highest occupied
molecular orbital) und LUMO (lowest unoccupied molecular orbital) unter-
sucht. Das Hauptziel dieser Arbeit war die Auswertung der elektrischen Band-
lücke, d.h. die Leitfähigkeit und optischen Eigenschaften dieser modifizierten
Diamantoide. Wir haben eine Abnahme der Bandlücke für alle dotierten und
ix
funktionalisierten Diamantoiden beobachtet, im Vergleich zu den jeweiligen
Werten von nichtmodifizierten Diamantoiden. Diese Abnahme war auch in
den doppelfunktionalisierten Molekülen sichtbar, die sich vom Adamantan bis
hin zu Heptamantan erstrecken.
Es wurde festgestellt, dass die Bandlückenvariation auf eine starke Lokalisierung
der Grenzorbitale in den modifizierten Diamantoiden zurückzuführen ist. Dad-
urch wird eine gezielte Abstimmung der elektrischen Eigenschaften von Dia-
mantoiden möglich. Zusätzlich haben wir auch die optischen Eigenschaften
dieser Komplexe für Adamantan und Diamantan untersucht, die durch Einzel-
und Doppelfunktionalisierung modifiziert wurden. Dabei wurde beobachtet,
dass unterschiedliche funktionelle Gruppen zu unterschiedlichen elektrischen
und optischen Eigenschaften führen. Verglichen mit der Einzelfunktional-
isierung schiebt die Doppelfunktionalisierung die elektrische und optische Band-
lücke noch weiter in den leitenden Bereich des Grundzustandes und somit in
die Richtung des sichtbaren Bereichs des angeregten Zustandes. Wir wählten
repräsentative Atome und funktionelle Gruppen, um die Tendenz darzulegen,
wobei mehr noch getestet werden kann.
Dementsprechend könnte durch gezielte Herstellung von Diamantoid-basierten
Komplexen spezifischer Größe und Modifikation die elektrischen und optischen
Eigenschaften dieser Komplexe abgestimmt werden. Zusätzlich werden durch
funktionelle Atomgruppen weitere Bindungsmögligkeiten geschaffen, sodass
eine Bindung mit anderen Strukturen ermöglicht wird. Die Tatsache, dass
eine Doppelfunktionalisierung zu einer großen Zunahme der optischen Eigen-
schaften führt, bietet die Möglichkeit, neue diamantoid-basierte Emitter zu
bilden, wobei eine funktionelle Gruppe der Befestigung des Diamantoids auf
einem Substrat dient und eine weitere den Diamantoid mit Funktionalitäten
versorgt. Ein Beispiel einer solchen Atomgruppe wäre ein N-Heterocyclisches
Carbene (NHC) Molekül. NHC können die selektive Bindung oder Detek-
tion von naheliegenden Molekülen begünstigen, was bei der Untersuchung der
Adsorption von Carben-funktionalisierten Diamantoiden auf Metalloberflächen
deutlich wurde. In Anbetracht dieser Untersuchung haben wir die Selbstorgan-
isation von Carben-vermittelten Diamantoiden über Gold (Au(111))-, Silber
(Ag(111))-bzw. Platinum (Pt(111))-Metalloberflächen analysiert.
Die Selbstorganisation dieser Komplexe wurde durch die Stabilität, Adsorp-
tion, Bindungsmöglichkeiten und Oberflächenmorphologie untersucht. Wir
konnten zeigen, dass Au(111) und Pt(111) die effizientesten Metalloberflächen
für die Adsorption von carbenvermittelten Diamantoid-basierten selbstorgan-
isierten Monolagen (SAM) waren. Unsere Ergebnisse haben weiter gezeigt,
dass molekulare Orbitale der d-Symmetrie für die Orbitalüberlappung mit
Kohlenstoff-p-Elektronen und die Bindungsbildung wie im Fall der Au(111)-
und Pt(111)-Oberflächen essentiell sind. In Ag(111)-Oberflächen wurde die
schwächere Bindung durch die Nichtverfügbarkeit des d-Orbitales der metal-
lischen ersten Schicht der Oberfläche um das Fermi-Niveau gerechtfertigt. Die
x
Berechnung der Arbeitsfunktionen von Carben-vermittelten Diamantoid-SAMs
auf Au(111)-, Ag(111)-, und Pt(111)- Oberflächen zeigte auf, dass durch die
Modulation der Arbeitsfunktionen in Bezug zu den Eigenschaften einer reinen
Metalloberfläche, eine dynamische Abstimmung von NHC-ada/Metall-Bauele-
menten für organische elektrische Anwendungen möglich wird.
Die Ladungsverteilung und die simulierten STM-Abbildungen der Oberflächen
machten sichbar, dass auf Pt(111) der gesamte Carbenring des NHC-ada-
Moleküls mit der SAM/Metall-Bindung assoziiert ist, was die Adsorptionsen-
ergie von SAMs erhöht. Durch Vergleich der molekularen Adsorptionsenergien
auf rekonstruierten Au(111)-, Ag(111)- und Pt(111)-Oberflächen haben wir
herausgefunden, dass diese Geometrien stabil und von praktischem Interesse
sind. Es ist jedoch wichtig, die thermische Stabilität dieser Strukturen und den
Einfluss der Umweltbedingungen auf ihre Stabilität zu untersuchen. Durch
dieser Arbeit haben sich Carbenmoleküle als eine bessere Alternative zur thi-
olbasierten Bindung von Diamantoiden auf metallische Oberflächen erwiesen,
was den Weg für stabilere und effizientere SAMs/Metall-Bauelemente öffnet.
Auf der Suche nach hocheffizienten Diamantoid-basierten molekularen Syste-
men wurde der elektrische Transport innerhalb von molekularen Verbindungen
zwischen funktionalisierten und dotierten Diamantoiden untersucht. Dafür
platzierten wir einen Diamantoid zwischen zwei Goldelektroden, deren Ab-
stand wenige Nanometer betrug. Die untersuchten Diamantoide wurden durch
zwei unterschiedliche Moleküle, einer Thiolgruppe und einem N-heterocycli-
schen Carbenmolekül, kovalent an die Goldelektroden gebunden. Die Transport-
eigenschaften des diamantoidbasierten molekularen Systems wurden hinsichtlich
dieser beiden Bindungsmöglichkeiten und der Größe des Diamantoids ausgew-
ertet. Ebenso untersuchten wir den Einfluss der Dotierung des Diamantoids
auf die Eigenschaften des molekularen Systems. Der Vergleich der Ergebnisse
wurde anhand der Funktionalisierung, der Dotierung und der Diamantoidgröße
diskutiert. Eine Di-Thiol-Linkergruppe hat sich als effizienter erwiesen, im Ver-
gleich zu einer an den Goldelektroden gebundenen Carbengruppe. Die Verwen-
dung eines Stickstoffatoms zur Dotierung der Diamantoide führte zu einer er-
heblichen Verbesserung der Elektronenübertragung durch das molekulare Sys-
tem. Wir zeigten den asymmetrischen Verlauf der Strom-Spannungs-Kurve
(I-V) durch Anlegen einer positiven und negativen Vorspannung. Die Kurve
zeigte eine diodenartige Eigenschaft auf, die zu einer Gleichrichtung innerhalb
eines sehr kleinen Bereichs von Vorspannungen führt. Die Transmissionsfunk-
tion bei keiner Vorspannung für nicht dotierte Diamantoid-basierte Systeme
zeigte, dass die Peaks der höchst besetzten molekularen Orbitale (HOMO) vom
Fermi-Niveau entfernt sind und somit entfernt vom nutzbaren Bereich für eine
Vorspannung. In allen Fällen zeigte sich die Effizienz des Diamantoid-basierten
Systems und diese wurde im Hinblick auf neue nanotechnologische Anwendun-
gen erörtert. Wir konnten die Elektronen- und Transporteigenschaften der
Diamantoid-basierten molekularen Systeme durch Dotierung der Moleküle mit
Bor und Stickstoff selektiv abstimmen.
xi
Die Dotierung mit Stickstoff führt zu einer Vergrößerung eines Transmission-
speaks sehr nahe am Fermi-Niveau, was zu einer höheren molekularen Leit-
fähigkeit führt. Eine Erhöhung der Diamantoidgröße führt zu einer leichten
Abnahme der Leitungsleitfähigkeit bei keiner Vorspannung. Eine solche Ab-
nahme wurde auch beobachtet, wenn die Carbenmoleküle zur Verbindung des
Diamantoids an den Nano-Spaltflächen verwendet wurden. Vorspannungs-
abhängige Transportberechnungen zeigten, dass Dotierungen zu einem höheren
Gleichrichtungsverhältnis bei sehr kleinen angelegten Vorspannungen führt.
Dieses Verhalten ist das Ergebnis der Energieverschiebung der HOMO-Peaks
gegenüber denen bei keiner Vorspannung. Die gleichrichtende Wirkung in N-
dotierten Diamantoiden hängt mit der Asymmetrie in der Struktur zusammen,
wenn diese dotiert wird. Bei der B- und B-N-Dotierung kommt es zu einer ähn-
lichen Asymmetrie durch Dotierung, woraus wir folgern können, dass auch für
diese Fälle ein ähnliches Gleichrichtungsverhältnis beobachtet werden kann.
xii
Contents
Abbreviations xv
Nomenclature xvii
1 Introduction 1
1.1 Structure and nomenclature . . . . . . . . . . . . . . . . . . . . 1
2 Computational and theoretical background 7
2.1 Electronic structure and DFT . . . . . . . . . . . . . . . . . . . 7
2.1.1 The many-body problem . . . . . . . . . . . . . . . . . . 8
2.1.2 Hohenberg-Kohn theorem . . . . . . . . . . . . . . . . . 9
2.1.3 Kohn-Sham theory . . . . . . . . . . . . . . . . . . . . . 10
2.2 Solving the Kohn-Sham equations . . . . . . . . . . . . . . . . . 13
2.2.1 Plane wave method . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Localized atomic orbital method . . . . . . . . . . . . . 15
2.3 Electronic transport . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 Molecular junction . . . . . . . . . . . . . . . . . . . . . 16
2.4 Time-dependent density functional theory . . . . . . . . . . . . 19
2.4.1 Runge-Gross formalism . . . . . . . . . . . . . . . . . . . 19
2.5 Computational tools . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Modified diamondoids: doping and functionalization 22
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Electronic properties of diamondoids . . . . . . . . . . . . . . . 24
3.2.1 Adamantane . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Isomers of tetramantane . . . . . . . . . . . . . . . . . . 32
3.2.3 Band gap tuning . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Optical properties of lower diamondoids . . . . . . . . . . . . . 37
3.3.1 Adamantane . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 Diamantane . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.3 Optical band gap . . . . . . . . . . . . . . . . . . . . . . 47
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 Self-assembled monolayers 51
4.1 NHC mediated diamondoids . . . . . . . . . . . . . . . . . . . . 51
4.2 Diamondoid mediated SAMs . . . . . . . . . . . . . . . . . . . . 52
4.2.1 Structural analysis . . . . . . . . . . . . . . . . . . . . . 53
4.2.2 Adsorption Energies . . . . . . . . . . . . . . . . . . . . 55
xiii
CONTENTS
4.2.3 Isolated NHC-functionalized adamantane . . . . . . . . . 57
4.2.4 Work function . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.5 Surface morphology . . . . . . . . . . . . . . . . . . . . . 63
4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5 Diamondoid-based molecular junction 68
5.1 Molecular junction . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2 Diamondoid within a gold nano gap . . . . . . . . . . . . . . . . 72
5.2.1 Structural Characteristics . . . . . . . . . . . . . . . . . 73
5.2.2 Electronic properties . . . . . . . . . . . . . . . . . . . . 74
5.2.3 Electronic transport . . . . . . . . . . . . . . . . . . . . 75
5.3 Current-Voltage Characteristics . . . . . . . . . . . . . . . . . . 81
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6 Conclusions and outlook 85
Appendix 88
A Promoting assembly of carbon onions 88
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
A.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
A.3 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . 92
A.3.1 Introducing vacancies . . . . . . . . . . . . . . . . . . . . 92
A.3.2 Introducing dopants . . . . . . . . . . . . . . . . . . . . 95
A.3.3 Electronic properties . . . . . . . . . . . . . . . . . . . . 98
A.4 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . 102
List of Tables 105
List of Figures 107
Bibliography 111
xiv
Abbreviations
cam-B3LYP coulomb-attenuating method-Becke 3-parameter Lee Yang Parr
CI Configuration Interaction
CNT Carbon Nanotube
C/N Carbon Nitrogen ratio
CVD Chemical Vapour Deposition
DFT Density Functional Theory
DNA Deoxyribonucleic Acid
DOS Density Of States
DZP Double Zeta Polarization
EDOS Electronic Density Of States
EWF Eigenchannel Wavefunction
FEDs Field Emission Displays
GAMESS General Atomic and Molecular Electronic Structure System
GGA Generalized Gradient Approximation
HF Hartree-Fock
HK Hohenberg-Kohn
HOMO Highest Occupied Molecular Orbital
LAMMPS Large-scale Atomic/Molecular Massively Parallel Simulator
LCAO Linear Combination of Atomic Orbitals
LDA Local Density Approximation
LUMO Lowest Unoccupied Molecular orbital
MD Molecular Dynamics
xv
CONTENTS
MGGA Meta Generalized Gradient Approximation
NEGF Non-Equilibrium Green’s Function
NHC N-Heterocyclic Carbene
OPW Orthogonalised Plane Wave
PAW Projector Augmented Wave
PBE-GGA Perdew Burke Erzernhof-Generalized Gradient Approximation
PDOS Partial Density Of States
PW91 Perdew Wang 91
RR Rectification Ratio
SCF Self-Consistent Field
SAM Self-Assembled Monolayer
SIESTA Spanish Initiative for Electronic Simulations for Thousands of Atoms
STM Simulated Tunnelling Microscopy
S-matrix Scattering matrix
SZP Single Zeta Polarization
TDDFT Time-Dependent Density Functional Theory
TDOS Total Density Of States
UV Ultra Violet
VDW Van Der Waals
VASP Vienna Ab-initio Simulation Package
XC Exchange-Correlation
XPS X-ray Photoelectron Spectroscopy
xvi
Nomenclature
{t} Time
{α′} Polarization vector of the electromagnetic wave
{α} The exchange mixing parameter
{r} Position vector
{0} Dielectric Constant
{Chom} Correlation electron density
{Xhom} Exchange electron density
{ΓL} Energy level broadening of the left electrode
{ΓR} Energy level broadening of the right electrode
{Hˆ} Hamiltonian operator
{h¯} Planck Constant
{µ0} Surface dipole moment per area
{µL} Chemical potential of left electrode
{µL} Chemical potential with respect to the left electrode
{µR} Chemical potential of right electrode
{µR} Chemical potential with respect to the right electrode
{µz} Surface normal dipole moment per area
{ν1
(
r, t
)} Time-dependent potential
{νext(r, t)} Time-dependent external potential
{ω} Frequency of the electromagnetic wave
{Φ} Work function
{Ψ(r, t)} Total wave function of a many-body system
xvii
{ρ(r)} Ground state electron density
{ρ(r, t)} Time-dependent external density
{ρ↓} Densities of electrons with down spins
{ρ↑} Densities of electrons with up spins
{c(t)} Time-dependent constant term
{e} Charge of an electron
{f(t)} Envelope function the controls the electromagnetic wave
{fL/R} Fermi-Dirac distribution of the left and the right electrode
{G} Reciprocal lattice vector
{Ga} Advanced Green’s function
{Gr} Retarded Green’s function
{Heff} Effective Hamiltonian
{i} Imaginary unit
{Lm} Mean free path length
{Lφ} Phase relaxation length
{me} Mass of electron
{MI} Mass of nucleus
{rc} Cutoff distance
{T} Kinetic energy
{V } Potential energy
{Vb} Bias voltage
{Vext(r)} External potential
{ZI} Atomic number of the nucleus
Chapter 1
Introduction
Diamondoids are a series of perfectly defined, hydrogen-terminated nano-dia-
monds [1–3]. These diamondoids are available in various shapes and sizes
that can be extracted and isolated from petroleum products [4] and can be
organically synthesized [2] or nucleated from energetic species [3]. These nano-
diamondoids constitute a number of diamond cages which forms a diamondoid
family starting from adamantane (C10H16) and then diamantane (C14H20) and
so on. A self-assembly of diamondoids encapsulated inside carbon nanotubes
has also been investigated in the past [5–7]. In view of biotechnological appli-
cations, efficient site-specific incorporation of diamondoids on DNA [8], as well
as the use of diamondoids as biosensors for reading-out DNA molecules [9].
Diamondoids possess technologically interesting properties such as negative
electron affinity [10, 11] and are also used in CVD diamond growth [12]. The
chemical functionalization of diamondoids [10, 13, 14] has paved the way for
new diamondoid devices and various nanotechnological applications [15]. Dop-
ing and functionalization have opened various new possibilities for tailoring
the properties of diamondoids. Additionally, the exact understanding of the
structure of each diamondoid yields unique possibilities, such as investigating
shape and size effects in nanocrystals and the influence of single or multiple
doping with various impurity atoms. Diamondoids doped with boron and ni-
trogen atoms can be interlinked to form functional nanostructures in carbon
nanotubes [15], while lower diamondoids and their derivatives have also been
theoretically found to self-assembly into larger interlinked nanostructures [16].
In view of biotechnological applications, efficient site-specific incorporation of
diamondoids on DNA are possible [8], as well as the use of diamondoids as
biosensors for reading-out DNA molecules [9].
1.1 Structure and nomenclature
Diamondoids are found to form molecular van-der-Waals crystals at room tem-
perature and possess a large band gap [1–3, 17]. As a result, these crystals
are colorless and visually appear white due to the scattering of light. These
molecules have a high melting point around 200 ◦C and they also sublimate
at room temperature [17]. The partial pressure of the diamondoids depends
1
Chapter 1. Introduction
on their molecular weight and the shape of the diamondoid. The shape of
the diamondoid depends on the stacking order of the smallest molecular unit
which is known as adamantane. This order of stacking determines the strength
of these diamondoids. In Fig. 1.1, we can see the atomic structures of these
diamondoids starting from the smallest unit adamantane until heptamantane.
The diamondoid family is classified by the increasing number of crystal cages.
Adamantane is the smallest unit of the diamondoid family. It is composed
of a greek numeric prefix which resembles the number of cages by which a
diamondoid is constructed. Similarly, diamantane is the second member of
the diamondoid family which consist of two adamantane cages, triamantane
comprises of three and the series goes on. For the first three members of the
diamondoid family namely; adamantane, diamantane, and triamantane, no
isomers exist. However, as we go up increasing the number of adamantane
subunits, different isomers can be found for the same size of diamondoid start-
ing from tetramantane, which has four isomers.
In Fig. 1.2, all the diamondoid structures up to triamantane and isomers of
tetramantane structures are shown. Tetramantane possesses four structural
isomers. Similarly, for pentamantane there are ten different isomers and so
on. To differentiate between various isomers, Balaban and von Schleyer in-
troduced the nomenclature system that describes the structural arrangement
of the cages. The name of the diamondoid is usually preceded by a numeric
prefix in brackets. These brackets indicate the direction of the addition cages
along various axes of a tetrahedron [1]. This concept is schematically shown in
Fig. 1.2. Lower diamondoids from adamantane to tetramantane are built on
n-fused adamantane units which is followed by a general formula [C4n+6 H4n+12
], where n =1-4. However, several isomeric forms for n > 3 exist, and some
higher diamondoids of high symmetry do not necessarily follow this formula.
For the diamondoids like the diamantane and triamantane which possess ex-
plicit names, the full notation such as the [1] diamantane and [12] triamantane
are not used. There are three different ways to attach a fourth diamond cage
to a triamantane molecule which comprises a tetramantanes. These are shown
in the second row of Fig. 1.2. These isomers are classified as anti-, M skew-,
P skew-, iso- tetramantane and named as [121] tetramantane, M[123] tetra-
mantane, P[123] tetramantane and [1(2)3] tetramantane. Panel (d) of Fig. 1.2
depicts the sketches of the addition of a cage parallel to the first extension,
which generates [121] tetramantane. In Fig. 1.2(e), the additional cage is at-
tached in a different direction, therefore the resulting diamondoid is labelled
as [123] tetramantane. In Fig. 1.2(f), the fourth cage diverges off the main
axis. Such a diversion is indicated in the Balaban-Schleyer [1] nomenclature
using round brackets as [1(2)3] tetramantane. For larger diamondoids, another
adamantane sub-unit is added for each additional cage.
These nanometer-sized cages can also attach on metallic surfaces through a
thiol group [18,19] to form self-assembled monolayers (SAMs) with a negative
electron affinity and a strong monochromatic emission [10,20] as shown in Fig.
2
1.1. Structure and nomenclature
Diamantane C14H20 Triamantane C18H24 Tetramantanes C22H28
Pentamantane C26H32 Cyclohexamantane C26H30
[121] [1(2)3]
[123]
Heptamantane C30H34
[1212] [12312] [121321]
Adamantane C10H16
Figure 1.1: Diamondoids of different sizes and shapes are shown. The numerals
in the brackets indicate the structural arrangement of the cages in accordance
with the Balaban-Schleyer nomenclature.
(a) (b) (c)
(d) (e) (f)
Figure 1.2: When the diamond cages are fused along the tetragonal axes of a
bulk diamond, a diamondoid is formed. Three different tetramantane (d)-(f)
can be formed based on the structure of triamantane (c). These are classified
as (d) [121] tetramantane, (e) [123] tetramantane and (f) [1(2)3] tetramantane
with respect to the site of the fourth cage. The black arrows represent the
direction of the addition of the cages. [1]
3
Chapter 1. Introduction
1.3. These properties make diamondoids very promising for electronics applica-
tions. In the past, thiol-based SAMs on metal surfaces have led to significant
applications in the field of surface emission, sensing, electrochemistry, drug
delivery, and microelectronics [21–25]. However, thermal instability of these
thiol-based SAMs on gold in harsh environmental conditions has been a huge
hindrance in using them for industrial purposes [26–30]. Thiol-based SAMs
are found to be stable only when stored in an ultra high vacuum in the ab-
sence of light but tend to degrade after few weeks at room temperature [31–33].
The experimental shortcomings in the preparation of SAM’s usually include an
unknown surface reconstruction, undefined particle shape and interactions of
the sample with its environment. The present vacuum phase investigations on
diamondoids allow us to get rid of these experimental hindrances and produce
data of atomically defined neutral particles.
Figure 1.3: Schematic illustration of a self-assembled monolayer of [121]-
tetramantane-6-thiol on a noble metal surface.
The goal of the present study is the theoretical investigation of the influence
of different variables that define the electronic, transport, and optical proper-
ties of diamondoids. We implemented a bottom-up approach to studying the
properties of diamondoids, the influence of structural modification (doping and
functionalization) on their electronic and optical properties. The fundamental
aim of our research is to computationally develop modified diamondoid-based
complexes and transition metals structures in view of their nanotechnological
applications. We examined their stability, metal-carbon, and metal-thiol elec-
tronic properties keeping in mind the long-term applications as the growth of
diamond-like films over various metal surfaces. Our investigation is based upon
various parameters such as the size of diamondoid, its shape and the chemical
alteration that we induce by doping and functionalization. Ideal or unmodi-
fied diamondoids of different sizes and shapes are examined to determine the
impact of size and shape on the electronic and optical properties. Diamon-
4
1.1. Structure and nomenclature
doids with functional groups like thiol, carbene, and diamondoids doped with
various atoms are studied to learn about the influence of different kinds of
chemical modifications on transport properties of diamondoid-based molecu-
lar junctions. Quantum chemical calculations under the framework of Density
Functional Theory DFT are used to help interpret and analyze the results.
The content of this thesis is the following:
In Chapter 2, the theoretical background and methodology used in this thesis
is explained.
In Chapter 3, we study the stability, structural alterations as well as the effect
on the electronic and optical properties of the modified (doped, single-, and
double-functionalized) diamondoids with respect to the properties of ideal un-
modified diamondoids. The electronic and optical properties in all cases are
probed through the frontier orbitals, namely the highest occupied (HOMO)
and lowest unoccupied (LUMO) molecular orbitals, as well as the electronic
and optical band-gap. We also compare the structural modification, localiza-
tion, and delocalization of orbitals and also look at the excited state geometry
and make comparisons to the absorption spectra.
In Chapter 4, we aim to study the structural and electronic properties of
carbene-functionalized diamondoid monolayers on metal surfaces. For the lat-
ter, we consider gold, silver, and platinum surfaces. We study the structural
and electronic properties of the diamondoid SAMs on these surfaces, their
morphology, and work function in view of their nanotechnological applications
as potential electron emitters and sensors.
In Chapter 5, we study the influence of the diamondoid size, the type of
dopants, and the diamondoid functionalization on the properties of molecu-
lar devices, that is a metallic break-junction in which a diamondoid is inserted
and bonded through the functionalization group on the metallic surfaces. For
the electrodes, two Au(111) surfaces are taken. For tetramantane, one of the
isomers, the [121] tetramantane molecule was chosen. Different dopants and
functional groups were chosen to separately dope and functionalize the dia-
mondoids.
In Chapter 6, we summarize and discuss the outcomes of this work and provide
an outlook on the possible future work.
Finally, in Appendix A, we probe the binding possibilities of the smallest
multi-shelled concentric fullerenes, known as carbon onions, which is also an-
other type of carbon-cages. We focus on the binding behavior of adjacent
carbon onions and promote their binding through the addition of vacancies,
as well as through doping with boron and nitrogen atoms.
5
Chapter 1. Introduction
Publications
The following publications are related to this thesis:
1. Adhikari B., Uhlig F., Meng S., and Fyta M.– "Optical properties of
modified diamondoids: influence of carbene" (in preparation)
2. Adhikari B., Sivaraman G., Fyta M.– "Diamondoid-based molecular
junctions: a computational study" Nanotechnology 27, 485207, 2016
3. Natterer A., Adhikari B., Fyta M.– "Complexes of carbene-functionali-
zed diamondoids and metal atoms: Electronic properties" J. Organomet.
Chem, pp. 8-15, 2016
4. Adhikari B., Meng S., Fyta M.–"Carbene-mediated self-assembly of
diamondoids on metal surfaces" Nanoscale 8, 8966 - 8975, 2016
5. Adhikari B., Fyta M.– "Towards double-functionalized small diamon-
doids: selective electronic band-gap tuning"Nanotechnology 26, 035701,
2015
6. Adhikari B., Muthuraman B., Mathioudakis C., Fyta M. –"Promoting
assembly of carbon onions: an atomistics approach" Phys. Status Solidi
A 211, 277-287, 2014
6
Chapter 2
Computational and theoretical
background
In this chapter, a brief introduction is given into the theoretical background of
the electronic structure calculations and the theoretical tools that are used in
this work for the interpretation of the results. In section 2.1 the basics of quan-
tum chemical electronic structure computations along with density functional
theory (DFT) are introduced. Next, we discuss the many body problems,
basics of density functional theory, Born-Oppenheimer approximation, and
various methods used in solving the Kohn-Sham formalism. In section 2.3, we
discuss the methods implemented in the modelling of a molecular junction for
the calculation of transmission spectra. Finally, in the section 2.4, we describe
the computational background behind the time-dependent density functional
theory calculations.
2.1 Electronic structure and DFT
Electronic structure theory has evolved a great deal in the recent past lead-
ing to the characterization of materials into insulators, semiconductors, and
metals. Several methods have been proposed till date; namely the Hartree-
Fock (HF) method [34], plane wave (PAW) method [35], orthogonalized plane
wave (OPW) method [36], and the pseudopotential method [37] etc. Elec-
tronic structure calculations made rapid developments after the density func-
tional theory (DFT) was introduced in 1960’s. DFT is mainly based on the
Hohenberg-Kohn [38] theorem which states that all the properties of a many-
body system can be completely determined by the ground state charge density.
Since the 1990’s, electronic structure calculations based on density functional
theory became more and more popular in the field of quantum calculations.
Density functional theory has been by far the most widely used method to in-
vestigate the electronic properties of materials and solids. It is also referred as
an ab initio method, because of its simplicity which allows to understand the
properties of a very complex system just by providing some basic structural
information as an input parameter which is usually the spatial coordinates.
7
Chapter 2. Computational and theoretical background
Depending upon the system and the properties we would like to investigate,
it has been proven time and again to be an accurate alternative to other com-
putationally inefficient methods. On the basis of results obtained from DFT
one can also make predictions of experimental properties and help further in
designing and synthesizing interesting and novel materials. DFT describes the
properties of condensed matter systems in an accurate manner ranging from
standard bulk metals to molecules, proteins, surfaces, and interfaces. The sole
idea of DFT is to describe a many-body interacting system in terms of its par-
ticle density instead of the many-body wavefunction. The efficiency of DFT is
because of the fact that it reduces the 3N degrees of freedom of a many-body
system to merely three spatial coordinates. Its basis is the well known as the
Hohenberg-Kohn theorem [38], which is based on the formalism that all the
properties of a system can be considered to be unique functionals of its ground
state density.
The Born-Oppenheimer approximation [39] and Kohn-Sham formalism [40]
combine to produce DFT calculations provided that the approximations for
the exchange-correlation (XC) potential are accurate enough. However, they
cannot be accurate but a good approximation. The XC potential describes
two basic properties of the electrons which are namely: exchange term and
the correlation term. These two terms describe the effects of the Pauli prin-
ciple and the Coulomb potential of a particular system. Some of the well
known approximations that have been widely used are: the local density ap-
proximation (LDA) [38], generalized gradient approximation (GGA) [41], meta
generalized gradient approximation (metaGGA) [42], hybrid functionals [43],
nonlocal functionals [44] etc.
LDA is one the commonly used approximations. It substitutes the XC energy
density of an inhomogeneous system by a homogeneous electron gas at the local
density. Generalized gradient approximation (GGA) [45] is another popularly
used approximation which is a generalization of the LDA that includes also
the contributions from electron density gradient. With these approximations,
the results of DFT calculations for various systems usually agree quite well
with the experimental data. Also, the computational efficiency with DFT
has been relatively high compared to solving the many-electron wavefunction,
such as the Hartree-Fock method [34, 46]. However, various shortcomings of
DFT include inaccuracy in the band gap of semiconductors. It also fails to
accurately describe the charge transfer [47], transition states [48], and shows
inconsistencies when it comes to strongly-correlated systems because of the
errors in the standard DFT approximations [49,50].
2.1.1 The many-body problem
The basic aim of all the electronic structure methods is to solve the Schrödinger
equation. The equation can be given in a general time-dependent form as fol-
lows:
8
2.1. Electronic structure and DFT
ih¯
∂
∂t
Ψ
(
r, t
)
= HˆΨ
(
r, t
)
(2.1)
where Ψ(r, t) is the total wavefunction and Hˆ is the Hamiltonian operator,
r, t are the positions and time, respectively. A general description of the
Hamiltonian of a many-body system can be written as:
H = − h¯
2
2MI
∑
I
∇2R −
h¯2
2me
N∑
i
∇2r +
1
2
∑
I 6=J
ZIZJe
2∣∣∣RI −RJ ∣∣∣2 (2.2)
+
e2
2
∑
i 6=j
1∣∣∣ri − rj∣∣∣2 − e2ZI
∑
I,i
1∣∣∣RI − ri∣∣∣ (2.3)
where the first and second terms in the above equation is the kinetic energy
(KE) of the nuclei and of the electrons, the third term is the potential energy
(PE) of the nucleus-nucleus Coulomb interaction, the fourth term is the PE
of electron-electron Coulomb interaction and the last term is the PE of the
nucleus-electron Coulomb interaction. The indices {I}, {J} and {i} and {j}
run over the electrons and nuclei respectively, {ri} and {me} represent the
positions and the masses of electrons, {RI} and {MI} are positions and masses
of the nuclei and {ZI} is the atomic number of the nucleus and {e} is the
electronic charge. The time-independent Schrödinger equation can be written
as:
HΨ
(
RI , ri
)
= EΨ
(
RI , ri
)
(2.4)
where {Ψ
(
RI , ri
)
} is the total wavefunction of the system. In order to simplify
the solution scheme of Schrödinger equation, Born-Oppenheimer approxima-
tion was introduced by Born and Oppenheimer [39]. The nuclei are heavier
and move much slower than the electrons. When we consider the movement
of electrons, we consider that the positions of nuclei are fixed, the total wave-
function {Ψ} only depends on the electronic degrees of freedom. This implies
that the potential and the kinetic energy of the nuclei are constant. Taking
these approximations into consideration, we can simplify 2.2 as the following:
H = − h¯
2
2me
N∑
i
∇2r +
e2
2
∑
i 6=j
1∣∣∣ri − rj∣∣∣2 +
∑
i
Vext(r) (2.5)
In equation 2.5, the external potential
∑
i Vext(r) can be formulated as:∑
i
Vext(r) = −
i∑
I
e2ZI
|RI − ri| (2.6)
2.1.2 Hohenberg-Kohn theorem
DFT is based upon is based upon two variational Hohenberg-Kohn (HK) the-
orems [40] as the following;
9
Chapter 2. Computational and theoretical background
• The first theorem states that for the ground state electron density {ρ(r)},
an external potential {Vext(r)} determines the external potential {Vext(r)}.
That is, two different potentials can generate different ground state den-
sities. That also means the states including ground and excited states
of the many-body wavefunctions can be calculated and the ground state
particle density can be used to determine all the properties of the system.
• The second theorem states that the universal functional {F [ρ(r)]} of the
density is independent of the external potential {Vext(r)} acting on the
interacting system in which the non-interacting particles move. The min-
imum of the energy functional {E
[
ρ(r)
]
=
∫
ρ(r)Vext(r)dr + F
[
ρ(r)
]
}
is the exact ground state energy of the system and the exact ground
state density {ρ0(r)} minimizes this functional. Thus, the ground state
energy and density are determined by the functional {E
[
ρ(r)
]
}.
2.1.3 Kohn-Sham theory
The Kohn and Sham (KS) [40] theory is merely an extension of the Thomas-
Fermi (TF) model [51]. In the Thomas-Fermi method, the electron density ρ(r)
is the basic variable instead of the wavefunction. As a result, the TF theory
fails to describe bonding between atoms and the formation of molecules and
solids. In contrast, KS method obtains the ground-state kinetic energy from
a non-interacting system. A non-interacting system of reference can also be
called as an auxiliary particle system or the fictitious non-interacting system.
The auxiliary Hamiltonian {HˆS} for a non-interacting particle system can be
written as:
HˆS = T + VS (2.7)
where {VS(r)} is the effective Kohn-Sham single-particle potential where the
interacting electrons are treated as non-interacting electrons in presence of an
effective potential. Next, we can write the density functional as follows:
Es[ρ] = Ts[ρ] +
∫
Vs(r)ρ(r)dr (2.8)
where ρ(r) and Ts is the KE of the non-interacting electron gas of the system.
Then the energy functional {E
[
ρ(r)
]
} can be rewritten as:
E
[
ρ(r)
]
= Ts
[
ρ(r)
]
+ EH
[
ρ(r)
]
+ EXC
[
ρ(r)
]
(2.9)
where for the kinetic energy term {Ts
[
ρ(r)
]
} is given by:
Ts
[
ρ(r)
]
= −1
2
N∑
i=1
∫
ψ∗i (r)∇2ψi(r)dr (2.10)
10
2.1. Electronic structure and DFT
and {EH
[
ρ(r)
]
} is the electrostatic Hartree energy of the electrons which can
be formulated as:
EH
[
ρ(r)
]
=
1
2
∫ ∫
ρ(r)ρ(r′)
|r − r′| drdr
′ +
∫
Vext(r)ρ(r)dr (2.11)
and lastly the exchange-correlation term {EXC
[
ρ(r)
]
} can be written as:
EXC
[
ρ(r)
]
= F
[
ρ(r)
]
− Ts
[
ρ(r)
]
+ EH
[
ρ(r)
]
(2.12)
Next, the ground state energy of a many-body system can be obtained by
minimizing the energy functional {E
[
ρ(r)
]
} through a variational approach.
Exchange-correlation functional
The Kohn-Sham theory is still an approximation because of the unknown XC
energy functional {EXC [ρ
(
r
)
]} which can be defined as:
EXC
[
ρ(r)
]
= T
[
ρ(r)
]
− Ts
[
ρ(r)
]
+ Eelec
[
ρ(r)
]
− EH
[
ρ(r)
]
(2.13)
where {T [ρ(r)]} and {Eelec[ρ(r)]} are the exact kinetic and electron-electron
interaction energies. The XC energy in an integral over the whole space with
XC energy at {r} is considered to be the same as in a homogeneous electron
gas of that electron density at the point {r}. The total exchange-correlation
functional {EXC
[
ρ(r)
]} can be written as:
EXCLDA
[
ρ(r)
]
=
∫
ρ(r)XChom
(
ρ(r)
)
dr =
∫
ρ(r)
[
Xhom
(
ρ(r)
)
+ Chom
(
ρ(r)
)]
dr
(2.14)
= EXLDA
[
ρ(r)
]
+ ECLDA
[
ρ(r)
]
(2.15)
Similarly, for a spin polarized system, it can be written in such a way:
EXCLSDA
[
ρ↑(r), ρ↓(r)
]
=
∫
ρ(r)XChom
(
ρ↑(r), ρ↓(r)
)
dr (2.16)
where {ρ(r)} is the total electronic density at {r}, {hom} denotes the homo-
geneous electron gas and {ρ↑}, {ρ↓} are the densities of electrons with up and
down spins respectively. XChom
(
ρ(r)
)
is the function of density which is further
expanded into the exchange density Xhom
(
ρ(r)
)
and the correlation density
Chom
(
ρ(r)
)
. LDA is the cheapest form of approximations in terms of compu-
tational time but it tends to underestimate the atomic ground state energies
and ionization energies while overestimating binding energies. It also makes
large errors in predicting the energy band gaps of some semiconductors. Its
success and limitations lead to approximations of the XC energy functional
11
Chapter 2. Computational and theoretical background
beyond the LDA, through the addition of gradient corrections to incorporate
longer range gradient effects (GGA). The generalized gradient approximation
(GGA) is another form of approximation used in electronic structure calcula-
tions which are simply an improvement to LDA. It includes density gradient
corrections and the magnitude of the gradient of the electron density. A general
form of GGA for a spin polarized case can be written as:
EXCGGA
[
ρ↑(r), ρ↓(r)
]
=
∫
ρ(r)XC
(
ρ↑(r), ρ↓(r), |∇ρ↑|, |∇ρ↓|
)
dr (2.17)
GGA has higher complexity than LDA but can lead to better results but is
not always as efficient as LDA. GGA can lead to bad results where it might
overestimate the lattice constants of ionic crystals. LDA performs better for
covalently bonded systems and GGA for magnetic and metallic systems. How-
ever, both GGA and LDA might fail to reproduce accurate results in the
case of transitions and rare earth compounds. Meta generalized gradient ap-
proximation (MGGA) [42] go beyond the regular GGAs to include additional
semi-local information beyond the first-order density gradient contained in the
GGA, such as higher order density gradients, or more popular is the inclusion
of the kinetic energy density {τ(r)} which involves derivatives of the occupied
Kohn-Sham orbitals. The hybrid functionals [43] combine the exact (Hartree-
Fock) exchange with conventional GGAs, the general form as:
EhybridXC = α(E
HF
X − EGGAX ) + EGGAXC (2.18)
where {α} is the exchange mixing parameter, {HFX } is the Hartree-Fock ex-
change. There are other approximations such as the fully nonlocal average
density approximation [44] and weighted density approximation which uses an
exact density functional and directly models the exchange-correlation hole us-
ing the analytic functions. However, these functionals are not commonly used
because they are computationally expensive.
Pseudopotentials
The pseudopotentials [37] are an approximation where we generate a univer-
sal pseudopotential so that the chemical properties of a particular system is
determined entirely by the outermost valence electrons keeping the core elec-
trons chemically inert. This simplification is connected with a corresponding
replacement of the true valence wavefunctions with pseudo-wavefunctions that
lead to a major reduction in the number of wavefunctions which have to be
handled as shown in the sketch of Fig. 2.1. In the process, the core electrons
are ignored and the core states are frozen. Most widely used pseudopoten-
tials nowadays include norm-conserving pseudopotentials [52] and ultrasoft
pseudopotentials [53]. There are three important aspects in pseudopotential
theory.
• The pseudopotential should be consistent with the XC functionals and
eigenvalues of an isolated atom should be accurately reproduced by the
pseudopotential.
12
2.2. Solving the Kohn-Sham equations
• The wavefunctions or also called the pseudo-wavefunctions should coin-
cide with the valence wavefunctions.
• The pseudo-wavefunction charge within the core should be equal to the
corresponding charge of the valence wavefunction, which is also called as
norm-conserving pseudopotentials.
 Pseudo
VPseudo
r
rc
Figure 2.1: Comparison of a pseudo wavefunction (Ψpseudo) and the pseu-
dopotential (Vpseudo) is presented. The real and the pseudo wavefunction and
potentials should match with each other certain cutoff radius rc.
The equation for the pseudopotential that considers only the valence electrons
is given by: [
− h¯
2
2me
∇2 + V pseudoeff
]
Ψpseudoi = 
pseudo
i Ψ
pseudo
i (2.19)
here, the effective potential {Veff} and the wavefunction {Ψi} is replaced by
the pseudopotential {V pseudoeff } and {Ψpseudoi }. Since the core states are frozen
and core electrons are ignored the valence electrons are represented by pseudo-
wavefunctions which have fewer nodes resulting in lesser computation time.
2.2 Solving the Kohn-Sham equations
Solving the Kohn-Sham equations leads to the exact density and ground state
energy of a system under investigation. Since the Kohn-Sham effective po-
tential {VKS} and the electron density {ρ
(
r
)
} are closely related to each
13
Chapter 2. Computational and theoretical background
other, the equations are solved with the self-consistent field method (SCF). In
the SCF method, the calculations are done iteratively where an approximate
Hamiltonian is first chosen, then the Schrödinger equation is solved to obtain
a more accurate set of orbitals until the results converge. In other words, this
process generally starts with an initial guess of the electron density, which is
usually a superposition of the atomic electron densities of the system. After
that the effective Kohn-Sham potential {VKS} is calculated and the Kohn-
Sham equation is solved with eigenvalues and wave functions obtained from
the iterations. Next, a new electron density is calculated from the wavefunc-
tions. After that, the self-consistency condition is analyzed, which depends on
the convergence criteria. This criterion could be the change of total energy or
total density or the total force acting on atoms which are usually a threshold
for the successful convergence. If the self-consistency criteria are not achieved,
the mixing of the electron density with electron density from previous itera-
tions takes place to obtain a new electron density. Hence, a new iteration will
start with the new electron density. This process is continued until the self-
consistency criteria is reached. After the system is fully relaxed at the ground
state, other quantities can also be calculated including total forces, stress ten-
sors, eigenvalues, orbitals, the density of states, band structure, etc. Some of
the methods that are used in solving the Kohn-Sham equations are discussed
below. The self-consistency algorithm for solving the density functional theory
is depicted in Fig. 2.2.
Figure 2.2: The SCF algorithm implemented in DFT.
14
2.2. Solving the Kohn-Sham equations
2.2.1 Plane wave method
In this method, the wavefunctions or the eigenfunctions of the Kohn-Sham
equations are expanded in a complete set of plane waves {eik.r}. Pseudopoten-
tials are used to replace the external potential of the nucleus. Plane waves have
played an important role in the early orthogonalized plane wave calculations
and are generalized to modern projector augmented wave (PAW) method [35].
In this method, forces can be easily calculated and it can be easily developed
to quantum molecular dynamics simulations as well as response to external
perturbations. However, results from plane wave methods using pseudopo-
tentials are usually less accurate than results from all-electron full potential
methods. Great care should be taken when one generates a pseudopotential
and it should be tested to match results from all-electron calculations. The
most widely used codes using plane waves and pseudopotentials are VASP [54],
Quantum ESPRESSO [55], ABINIT [56], etc. By using Bloch’s theorem [57]
one can simplify the system from an infinite number to a finite number of
electrons within a single primitive unit cell. In the case of a periodic system
the expansion of the of the wave function in the form of discrete plane wave
basis set in such a manner:
φ(k,j)
(
r
)
=
∑
G
C(
j,k+G
)e
[
i
(
k+G
)
.r
]
(2.20)
where {G} is the reciprocal lattice vector, {k} is restricted to the first Brillouin
zone [58] and {j} is the band index. The energy cutoff is given by:
Ecutoff =
h¯2
2m
∣∣∣K +G∣∣∣2 (2.21)
By enlarging {Ecutoff} one can control the quality of the calculations. The
cutoff energy is not the only parameter which influences the convergence. Also,
the size of the supercell is an important factor. The reason is that the plane
wave basis set is periodic in all three space directions. If the super cell is too
small neighboring molecules interact strongly with each other. Hence, a high-
energy cutoff, adequate number of k-points and a large box size is required so
that the system is converged.
2.2.2 Localized atomic orbital method
Plane waves are not the most effective approach when it comes to accurately
describing molecular systems. The most common way to solve the problem is
to the expand the one-electron wavefunctions as molecular orbitals in terms
of atomic orbitals. These atomic orbitals can be represented in terms of basis
functions in various functional forms. These basis functions when used in a
large number improves the accuracy and hence the electronic properties. One
of the most well-known methods in this category is the linear combination of
atomic orbitals (LCAO). SIESTA [59] is also a band structure DFT program
employing periodic boundary conditions in all three directions. It employs a
15
Chapter 2. Computational and theoretical background
linear combination of atomic orbitals (LCAO) basis set, which in turn pro-
vides us with the information of orbitals that we are most interested in. It also
provides us with the molecular orbital density of states, which contains the
contributions of each of the molecular orbital to the total electronic density of
states (DOS). By integrating these states up to the Fermi energy, the occupa-
tion of each orbital can be obtained. The result yields the occupation of these
orbital in electrons where we can distinguish the occupied and the unoccupied
orbitals from each other. It also allows the use of localized linear combinations
of the occupied orbitals like the valence-bond, or Wannier-like functions [60],
scaling linearly with the number of atoms making each and every calculations
computationally efficient.
2.3 Electronic transport
Similar to the electronic structure calculations, the theoretical description of
quantum electron transport through molecular systems is also a very compli-
cated many-body problem to solve. Different methods and approaches have
been proposed ranging from solving the exact many-body problems to semi-
empirical models. Among all these available methods we use the so-called
ab initio method, also often known as the first principle calculations that only
requires the geometry of the system, to begin with. Later on, the transport
properties can be calculated using the Green’s functions and the DFT. In this
section, we demonstrate how the transport formalism can be combined with
standard electronic structure method to provide a first-principle description of
electron transport in a molecular junction. The method is solely based upon
the non-equilibrium Green’s function (NEGF) method [61].
2.3.1 Molecular junction
A molecular junction is a geometrical setup where a finite scattering region also
called as the central region is connected to two semi-infinite periodic systems or
lead. Schematic diagram of a molecular junction is depicted in Fig. 2.3. Here,
{L} and {R} are the two semi-infinite left and right metallic leads or electrodes
and {C} is the central region which comprises of the molecule. When we apply
a bias voltage the charge carriers flow from the left lead to the right one through
the molecule. It is very important not to have a very short molecule to avoid
tunneling between the electrodes. Molecular orbitals play a very important
role in transport calculations. The alignment of these molecular orbitals with
respect to their Fermi level of the electrodes is important for conductance in
between the electrodes. The conductance is observed as the result of the charge
transfer to or from the molecule and the electrodes. The total Hamiltonian of
the system usually comprises of the Hamiltonian of the central region {HC}, of
the left electrode {HL} and the right electrode {HR} and lastly the interaction
of the molecule and the electrodes {Vint} respectively. This is illustrated in a
16
2.3. Electronic transport
CL R
Figure 2.3: Here we show a diagram of a diamondoid based molecular junction
where (C) is the central region between the two semi-infinite left (L) and right
(R) leads.
form of an equation below:
H = HL +HC +HR + Vint (2.22)
We need to keep in mind that the Hamiltonian for each of the electrodes
denoted by {HL/R} has infinite dimension. As a consequence, we introduce a
screening approximation. In doing so, we now reduced the infinite dimension
of the Hamiltonian to just the dimension of the Hamiltonian of the molecule.
However, the semi-infinite behaviour of the electrode is taken into account by
using self-energy. This is how we construct an effective Hamiltonian:
Heff =
∑
L
+
∑
R
+HC (2.23)
where {∑L/R} is the self-energy term for the left and right electrodes and
{HC} is the Hamiltonian of the molecule.
The size and the length scale {L} of the molecular junction plays a very im-
portant role in defining the transport regimes. Basically, the regimes depend
on two different parameters namely: the mean free path {Lm}, where the
electrons travel until their momentum relaxes and the other one is the phase
relaxation length {Lφ}, where the electrons travel until they achieve phase
relaxation. Hence the length {L} has to be small enough to avoid classical
conductance behaviour. Various kinds of transport regimes on the basis of the
length scale of L, Lφ, and Lm can be listed which are described below:
• If {L} is very small than {Lm}, there is no scattering during the transport
process in the device and it belongs to the ballistic transport regime.
Carbon-based materials and metallic nanowires show ballistic transport
behaviour.
17
Chapter 2. Computational and theoretical background
• In the case of the short molecules where {L} is smaller than {Lm}, the
electron transport is elastically scattered. Reason being that the electron
transport is quick enough to not react with other molecular vibrations.
This kind of regime is known as the coherent or elastic regime.
• If we are dealing with long molecules, electron transport take long enough
to interact with another electron in the system. This results in inelastic
scattering and hence it is named as an incoherent or inelastic regime.
In order to describe the transport mechanism for the elastic transport regimes,
one uses DFT coupled with NEGF formalism. The Hamiltonian in terms of
{L,C,R} is formulated as:
H =
HLL HLC 0HCL HCC HCR
0 HRC HRR
 . (2.24)
Similarly, the overlap matrix {S} is defined as:
S =
SLL SLC 0SCL SCC SCR
0 SRC SRR
 . (2.25)
Next step is to calculate the self-energy term of the left and right electrode
including the molecule. After we construct the self-energy matrix, we can
substitute and obtain the effective Hamiltonian {Heff} from equation 2.23.
Now the retarded Green’s function {Gr} matrix is formulated which is based
upon electron density and is written as follows:
Gr(E) =
[
ES −Heff
]
(2.26)
where {Heff} is the effective Hamiltonian {S} is the overlapping matrix and
{E} is the self-energy term. Finally, since the effective Hamiltonian {Heff}
and the retarded Green’s function {Gr} are functional of electron density, a
self-consistent calculation is performed to obtain the final electron density.
Next, using the Landauer-Buttiker [62] formula, the transmission coefficient is
calculated as a function of energy and current {I(V )} at a certain bias voltage
{Vb} which is given as follows:
T (E, Vb) = Tr
[
ΓL(E, Vb)G
a(E, Vb)ΓR(E, Vb)G
r(E, Vb)
]
(2.27)
where {Ga} is the advanced and {Gr} is the retarded Green’s function, {E}
is the self-energy term, {ΓL} and {ΓR} denotes the energy level broadening
of the left and the right electrode, respectively. The current {I(V )} can be
written as:
I(V ) =
e
pih¯
∫ [
T (E, Vb)fL(E, Vb)− fR(E, Vb)
]
dE (2.28)
=
e
pih¯
∫
T (E, Vb)
[
fL(E, µL)− fR(E, µR)
]
dE (2.29)
18
2.4. Time-dependent density functional theory
where {fL/R} is the Fermi-Dirac distribution of the left and right electrodes
and {µL} and {µR} are the chemical potential with respect to the left and the
right electrode.
2.4 Time-dependent density functional theory
In this section, we describe an extension of DFT where the potential and
the electron density of the system vary in time. We begin by introducing
the Runge-Gross theorem which forms the basis of time-dependent density
functional theory. Next, we discuss the application of time-dependent density
functional theory (TD-DFT) to the problem of calculating electronic excitation
energies of molecules.
2.4.1 Runge-Gross formalism
Runge gross theorem [63] states that for a many-body system that is evolving in
time from a fixed initial state there is a one-to-one correspondence between the
time-dependent external potential νext(r, t) and the electronic density ρ(r, t).
This implies that we only need the density of a system in order to obtain an ex-
ternal potential which can be used to the solve the time dependent Schrödinger
equation. According to the Runge-Gross theorem proved that two potentials
{ν1
(
r, t
)} and {ν2(r, t)} which differ from each other by a time-dependent con-
stant term {c(t)} cannot produce the same time-dependent electron density
{ρ(r, t)}:
ν1
(
r, t
)
6= ν2
(
r, t
)
+ c
(
t
)
(2.30)
ρ1
(
r, t
)
6= ρ2
(
r, t
)
(2.31)
As a result, with the help of the Runge-Gross theorem, we can formulate the
time-dependent Kohn-Sham scheme. Similar to the time-independent case,
we introduce an auxiliary system of non-interacting electrons to an external
potential {νKS}. The external potential is chosen in such a way that the density
of the Kohn-Sham electrons is the same as the density of the original interacting
system. Hence in this manner, with the help of Kohn-Sham and Runge-Gross
theorems the time-dependent Schrödinger equation can be written as:
i
∂
∂t
φ
(
r, t
)
= HˆKS(r, t)φi(r, t) (2.32)
Now the Hamiltonian can be expressed as:
HˆKS(r, t) =
∇2
2
+ νKS[ρ](r, t) (2.33)
Next, we formulate the time-dependent electron density in terms of square
moduli of the Kohn-Sham orbitals {φi}:
ρ
(
r, t
)
=
N∑
i=1
∣∣∣φi(r, t)∣∣∣2 (2.34)
19
Chapter 2. Computational and theoretical background
As in the time-independent case, it breaks down into a sum of three terms:
νKS
[
ρ
](
r, t
)
= νExt
(
r, t
)
+ νHartree
[
ρ
](
r, t
)
+ νxc
[
ρ
](
r, t
)
(2.35)
The first term {vExt
(
r, t
)
} on the right-hand side of equation 2.35 is the
external potential acting on the electrons, which contains the electrostatic
potential of the nuclei as well as the time-dependent external potential that
is assumed to act on the electrons. If the time-dependent part of the external
potential is subjected to the electric field component of the electromagnetic
radiation, then {vExt(r, t)} will be given by:
vExt
(
r, t
)
= Ef(t)sin
(
ωt
)
r · α′
Nnuc∑
a=1
Za
|r − ra| (2.36)
where {α′} is the polarization vector of the electromagnetic wave, {E} is the
amplitude of its electric field component and {ω} is its frequency. {f(t)} is an
envelope function that controls the shape of the electromagnetic wave. Simi-
larly, the second term {vHartree
[
ρ
](
r, t
)
} on the right-hand side of Eqn. 2.35
is the Hartree term {vHartree} that describes the instantaneous self-interaction
energy of the electron density.
vHartree
[
ρ
](
r, t
)
=
∫ ρ(r, t)∣∣∣r − r′∣∣∣d3dr′ (2.37)
The third term {vxc
[
ρ
](
r, t
)
} is the time-dependent exchange-correlation po-
tential. It contains the quantum-mechanical many-body effects that are miss-
ing from the Hartree term and also corrects the kinetic energy that is being
calculated for the Kohn-Sham spin-orbitals which describe the auxiliary system
of non-interacting electrons.
2.5 Computational tools
The SIESTA [59] package was used to investigate the electronic and transport
properties of diamondoid-based complexes. Spanish Initiative for Electronic
Simulations with Thousands of Atoms or SIESTA is a very efficient tool to
execute electronic structure calculations and also an ab initio molecular dy-
namics simulations. SIESTA uses localized basis sets which scales linearly and
hence can be implemented over all kinds of the system under study. A very
important feature of the code is that it is very accurate and computationally
efficient producing results that are of the same quality as of other approaches,
such as plane-wave or all-electron methods. Some of the main characteristics
of SIESTA is the use of Kohn-Sham self-consistent density functional method
with LDA and GGA approximation with the inclusion of van der Waal’s inter-
action. It uses norm-conserving pseudopotential with atomic orbitals as basis
20
2.5. Computational tools
sets.
Electronic transport calculations were performed using DFT combined with
the non-equilibrium Green’s functions (NEGF) formalism, as implemented in
the TranSIESTA [64] code. TranSIESTA facilitates the modelling and sim-
ulation of electronic molecular junctions or devices. The tranSIESTA calcu-
lation usually involves three parts. First, the electronic structure of the leads
is calculated with a DFT calculation and then the Hamiltonian for the infi-
nite leads which are saved for the subsequent steps. Next, a periodic SIESTA
calculation is performed for a system that includes the central region and the
leads. This yields the Hamiltonian and density matrix for the central region.
Next, the Hamiltonian for the leads and the central region is used to calculate
the retarded Green’s function. The density is calculated by integrating over
the retarded Green’s function using an efficient contour integration technique
that requires only a few energy points. This yields a Hamiltonian for the cen-
tral region. A separate self-consistent iteration for the Green’s function makes
it possible to calculate the electronic structure for a system with a finite bias
voltage between the electrodes. Finally, the transmission calculation is per-
formed by a utility knows as TBTrans.
Vienna ab initio simulation package or VASP [54] was used under the frame-
work of DFT in order to self-assemble the monolayer of diamondoid-based
complexes over the metal surfaces. In addition to the electronic structure cal-
culation, it also performs quantum-mechanical molecular dynamics from the
first principles. Unlike SIESTA, in VASP, the one-electron orbitals, the elec-
tronic charge density, and the local potential are expressed in plane wave basis
sets. The electron-electron and the ion-ion interactions are described using
norm-conserving or ultrasoft pseudopotentials, or the projector-augmented-
wave method. Its basic aim is to compute an approximate solution to Schrödinger
equation, either with DFT by solving the Kohn-Sham equations or within the
Hartree-Fock (HF) approximation.
General Atomic and Molecular Electronic Structure System or GAMESS-
US [65] package was used to compute the excited state properties of func-
tionalized diamondoids. GAMESS-US is a program for ab initio molecular
quantum chemistry. Correlation corrections to the SCF wavefunctions is not
only implemented by the density functional theory approximation but with
additional configuration interaction (CI) [66], second order perturbation the-
ory [67], and coupled-cluster approaches [68]. Excited states can be computed
by CI or TDDFT procedures.
21
Chapter 3
Modified diamondoids: doping and
functionalization
In this chapter, we focus on the structural alterations and the effect of doping
and functionalization on the electronic and optical properties of diamondoids,
from the smallest adamantane to heptamantane. In section 3.1, we present
a brief introduction of diamondoids and their possible application after dop-
ing and functionalization. Next, we present the analysis of the results for
doped diamondoids using boron, nitrogen, silicon, oxygen, and phosphorus as
dopants. In view of the diamondoid-based devices we mainly focus on a double-
functionalization of diamondoids up to heptamantane using both these atomic
groups with amine and thiol groups. We discuss the higher efficiency of a
double-functionalization compared to doping or a single-functionalization of
diamondoids in tuning the electronic and optical properties, such as the elec-
tronic and optical band gap of modified small diamondoids in view of their
novel nanotechnological applications. Finally, in section 3.4, a short discus-
sion based on the work is presented. Some of the sections of this chapter are
also the part of our published article "Bibek Adhikari and Maria Fyta 2015
Nanotechnology 26 035701 c© IOP Publishing. Reproduced with permission.
All rights reserved”.
3.1 Introduction
The variety of sizes and modifications diamondoids can assume have shown
their great potential for novel nanotechnological applications [10,13,14]. Differ-
ent production methods of diamondoids exist: these can be found in petroleum
[4], be organically synthesized [2] or also nucleated from energetic species
[3]. Diamondoids are expected to play a significant role as suitable building
blocks for functional nanostructures [15]. These nanometer-sized cages can
be attached on metallic surfaces through a thiol group [18, 19] and form self-
assembled layers which have a negative electron affinity [10, 11] and a strong
monochromatic emission [10, 69], being thereby promising for electronics ap-
plications. Lower diamondoids and their derivatives have been theoretically
observed to self-assemble into larger interlinked nanostructures [16] also with
22
3.1. Introduction
the possibility of self-assembly of diamondoids encapsulated inside carbon nan-
otubes [5–7]. Diamondoids doped with boron and nitrogen atoms can be inter-
linked to form functional nanostructures in carbon nanotubes [15], while lower
diamondoids and their derivatives have also been theoretically found to self-
assembly into larger interlinked nanostructures [16]. In view of biotechnological
applications, efficient site-specific incorporation of diamondoids on DNA are
possible [8], as well as the use of diamondoids as biosensors for reading-out
DNA molecules [9].
The possibility of chemical modification of diamondoids [2] has opened a new
dimension in nanotechnology [10]. The size, the art of doping, and func-
tionalization of diamondoids can tune their properties, such as optical and
electronic [70, 71]. Amine functionalized diamondoids have good conductance
properties [16], while thiolated diamondoids attached to the gold surface show
excellent electron emission properties [18]. Studies have shown that the band
gap of these nano diamonds decrease with the increase in their size and push-
pull doping is believed to be the most effective way to tune the band gap
of these diamondoids [72]. Modified diamondoids also show alterations in
their optical properties as compared to those of unmodified diamondoids [18].
Amine-derivatives [73] of the lower diamondoid, adamantane, are already in
use in pharmaceutical applications [74] as anti-viral [75] and anti-Parkinsons
agents [76]. These derivatives have also been found to have good conduc-
tance properties depending on their relative orientation between two metallic
electrodes [77]. In view of their nanotechnological applications, these doped
and functionalized diamondoids can be excellent electron emitters, better than
carbon nanotubes for field-emission displays (FEDs) [10]. These diamondoid-
based FEDs as electron emitters could be seen as the future of flat-panel dis-
plays, microwave telecommunications and microelectronics [10,78–80]. Recent
research has also shown that these diamondoids combined with buckyballs
form to show faster and powerful device as the unimolecular rectifier [81].
We aim to extend previous studies on modified diamondoids and the alteration
of their electronic properties in view of the novel nanotechnological application.
Along these lines, we focus on doping and functionalization of diamondoids
with five different dopants and the use of a single- and double-functionalization
with atomic groups on the same diamondoid. The investigation of a pathway
to selectively tune the conduction properties of the modified diamondoids is
the main goal of this work. The novelty of this study is related to the double-
functionalization, which to our knowledge has not been studied before. The
purpose of the double-functionalization is based on the nanotechnological ap-
plications of diamondoids: the first functionalization (usually a thiol group)
can be used to attach diamondoids on surfaces, while the second (the amine
group) has been widely used in drug industry and can tune the electronic prop-
erties of the diamondoid-functionalized surface or promote the attachment of
other species on this surface.
23
Chapter 3. Modified diamondoids: doping and functionalization
3.2 Electronic properties of diamondoids
We have implemented SIESTA [59] code under the framework of DFT for the
analysis of the electronic properties of doped and functionalized diamondoids.
Using Siesta scheme, the Kohn-Sham eigenstates are expanded using a linear
combination of atomic orbitals. The local density approximation (LDA) [82]
was used in modelling the exchange-correlation functional together with norm-
conserving Troullier-Martin type pseudopotentials [83] a split valence double
zeta polarized basis set. A mesh cutoff parameter of 200 Ry has been used
for the calculations. The geometry optimization was performed using the con-
jugate gradient algorithm and the structure was relaxed until forces on the
atoms were lower than 0.04 eV/Å.
For computational efficiency, the smaller diamondoids adamantane (C10H16)
up to heptamantane (C30H34) were modelled. The ideal diamondoids include
only carbon atoms which form the diamond-like cages and the hydrogen atoms
which passivate the cages. Our investigation is being carried out as follows:
First, we choose a diamondoid site, remove one of its carbon atoms and replace
it with a dopant. As representative dopants, also due to their proximity to
carbon in the periodic table, we choose boron (B), nitrogen (N), silicon (Si),
phosphorous (P), and oxygen (O). At a second step, we study the selective
functionalization of the lower diamondoids. We begin with a single functional-
ization, by replacing one of the hydrogen atoms of the diamondoid with a thiol-
(SH-) or amine- (NH2-) atomic group. At a final step, we double functionalize
the diamondoids with both the thiol- and amine groups. We use some of the
dopants which have been studied before for diamondoids, in order to provide a
consistent study towards the double-functionalized diamondoids, which is the
main interest of this work.
Specifically, for the doped diamondoids, we have followed previous studies
which indicated the dopant site [72], but also performed a "dopant-site scan"
through a comparison of possible doping sites for each dopant based on an
energy minimization. Accordingly, the single site for each dopant which cor-
responded to the minimum energy was chosen as the doping site for a further
investigation of the electronic structure of the respective doped diamondoid.
Note, that the dopant site is not the same for each doped diamondoid. In
the single-functionalized diamondoids, the functional (amine- or thiol-) group
was attached to an apical site (which is not the same for the two groups) of
the diamondoid substituting the hydrogen atom at that site. We have per-
formed simulations for three different functionalization cases: amine-, thiol-,
and amine-,thiol-functionalized diamondoids. For the first two, we refer to
single-functionalization, while for the last as double-functionalization. For the
former, the functionalization sites were taken from the literature [18]. In the
double-functionalization, the same site as in the single-functionalization was
used for attaching the amine group. The thiol group functionalization site
was based on a scan based on an energy minimization corresponding to struc-
24
3.2. Electronic properties of diamondoids
tures with different functionalization sites. The two substitutional sites for the
amine- and thiol groups are the opposite apical tips of a diamondoid. Along
the above lines, we probe the possibilities of tuning the band gap through
modifications of the diamondoids using the dopants or functional groups men-
tioned above.
Along these lines, we study the stability, structural alterations as well as the
effect on the electronic properties of the modified (doped, single-, and double-
functionalized) diamondoids with respect to the properties of ideal unmodified
diamondoids. The electronic properties in all cases are probed through the
electronic density of states (eDOS), the frontier orbitals, namely the highest
occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO), as well
as the electronic band gap. The electronic band gap is defined as the difference
between the HOMO and LUMO levels.
a) b) c)
d) e) f)
g) h) i)
Figure 3.1: (a) Ideal adamantane. In (b)-(f) the relaxed doped structures
for B-adamantane, N-adamantane, O-adamantane, Si-adamantane, and P-
adamantane are shown, respectively. In (g) and (h) the single-functionalized
adamantane with an amine- and a thiol- group are depicted, respectively, while
in (i) the double- functionalized amine-, thiol- adamantane is sketched.
25
Chapter 3. Modified diamondoids: doping and functionalization
Results and Discussion
We begin our analysis with doped diamondoids and choose the lowest one,
adamantane, as a representative case. The aim is to provide a proof of princi-
ples as to the effect of doping and it is expected that doping other diamondoids
should show similar qualitative trends. We continue with a single- and double-
functionalization of adamantane and move on to the effect of isomerization.
For this, we choose the three isomers of tetramantane and double-functionalize
these. In the end, we focus on the double-functionalization of the lower dia-
mondoids up to heptamantane.
3.2.1 Adamantane
All the modified adamantane structures considered in the following analysis
are depicted in Fig. 3.1 in which the ideal adamantane is also shown for
comparison. In order to qualitatively evaluate this picture, the corresponding
structural properties are plotted in Fig. 3.2. On the two panels of this figure,
the bond-angle and bond-length variations in the doped adamantane cases
are shown. A first observation is related to the deviation from the almost
perfect tetrahedral arrangement in ideal adamantane. The bond lengths for
Si- and P-doped adamantane have been stretched whereas for the N- and O-
doped cases the bond lengths are shorter than 1.53 Å, which is the C-C bond
length for ideal adamantane. This implies a stronger bonding between the
C-N, C-O and C-B atom-pairs than in C-Si or C-P. Accordingly, as expected,
N, B, and O are better dopants for the diamond-like cages, in terms of their
structural properties and the deviation from the tetrahedral symmetry. The
same trend was found in the bond-angle variation with the dopant type as
evident in the lower panel of Fig. 3.2. The C-C-C bond angle in the ideal
adamantane is found to be 109.7◦. The bond angles in case of N- and O-
doped adamantane do not change much as compared to Si -, B -, P-doped
adamantane. A different trend is observed for the B-doped adamantane as
the C-B-C bond-angle deviated more from the ideal case as in the Si-doped
adamantane, though the reversed was observed for the respective bond lengths.
In order to investigate the stability of these modified adamantanes, we calcu-
lated the substitution energy of these newly formed molecules and the energy
values are shown in Fig. 3.3. The substitution energy Es of these doped and
functionalized structures was calculated by using the formula
Es = Edoped/func + Esubs − Eadamantane − Eadded (3.1)
where Edoped/func is the total energy of the doped or functionalized molecule,
Esubs is the total energy of replaced or substituted units; CH4 in case of doped
structures and H2; in case of functionalization, Eadamantane is the total energy
of a pure adamantane molecule, Eadded is the total energy of the added units;
namely BH3, NH3, OH2, SiH4, PH3, H2S for different dopants and functional
groups mentioned above. In Fig. 3.3 the variation of energy with different
dopants is given. A lower substitution energy according to the definition cor-
responds to an easier substitution reaction. In the case of doped diamondoids,
26
3.2. Electronic properties of diamondoids
1.4
1.5
1.6
1.7
1.8
1.9
B
on
d-
le
ng
th
 (A
ng
.)
Dopants in adamantane90
95
100
105
110
115
B
on
d-
an
gl
e 
(de
g.)
Si
P
B
ideal
N
O
adamantane
N O
ideal
Si B P
(a)
(b)
Figure 3.2: Variation of (a) the bond length and (b) bond angle with the type
of dopant in adamantane.
the energy is lowest for the B-doped case with a higher negative value indi-
cating natural substitution reaction whereas for functionalization thiols show
lesser substitution energies as compared to amine and thiol plus amine func-
tionalized cases. Next, we move on to the electronic density of states (eDOS)
of the doped adamantane molecules which are sketched in the upper panel
of Fig. 3.4. The eDOS of the doped structures are considerably altered by
the presence of dopants as compared to the ideal adamantane. Although in
most cases, the HOMO and LUMO levels are similarly occupied, the doping
introduces electronic states in the band gap of the ideal case, decreasing in
this way the band gap of doped-adamantane. This shrinking of the band gap
is different for different dopants. Regarding the occupation of the HOMO and
LUMO levels, these deviate from ideal adamantane in the P- and Si-doped
adamantane, which actually shows a larger deviation in the strength of the
C-dopant bond as discussed above.
In order to provide a better qualitative understanding of the differences in the
electronic structure of doped-adamantane, the frontier orbitals, HOMO and
LUMO are sketched in Fig. 3.5(b)-(f). In the ideal adamantane, the HOMO
or the occupied states are localized over the C-C bonds whereas the unoccupied
states are more delocalized and spread out over the whole molecule [13]. These
orbitals become less delocalized in the doped-adamantane, in which the HOMO
state becomes almost localized on the dopant site. Deviations were observed
27
Chapter 3. Modified diamondoids: doping and functionalization
Dopants and functionalization groups in adamantane
-2
-1.6
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
1.6
S
u
b
st
it
u
ti
o
n
 e
n
e
rg
y
 (
e
V
)
B
Si
P
ideal
SH-
NH
2
-
ON
NH
2
-, SH-
Figure 3.3: Variation of the substitution energies for doped and functionalized
adamantane compared to its ideal case. Lower substitution energy values imply
easier substitution reaction than the higher ones.
eD
O
S
ideal
B
N
O
Si
P
-8 -6 -4 -2 0 2 4
Energy-E
LUMO-adamantane
(eV)
eD
O
S
ideal
NH
2
-
SH-
NH
2
-,SH-
doped-adamantane
funct.-adamantane
Figure 3.4: Electronic density of states (eDOS) for doped and functionalized
adamantane. All data have been shifted with respect to the LUMO level of
ideal adamantane, as denoted in the x-axis.
28
3.2. Electronic properties of diamondoids
in the B-doped adamantane, while the less localized orbitals were observed
in the O-doped case, though this case had shown a larger deviation from the
ideal case as discussed above. The total charge density contours of the doped
and functionalized adamantanes as shown in Fig. 3.6. We can clearly observe
the qualitative difference in charge distribution over the surface of diamon-
doid with respect to different dopants and functional groups. This difference
is based on the fact that these dopants posses different electro-negativities. In
addition, the variation in the bonding behaviour of the dopants at the doping
site also plays a significant role in the distribution of charge densities. These
differences correspond to the HOMO and LUMO depicted in Fig. 3.5.
Next, we turn to single- and double-functionalized adamantane. The eDOS
data of these cases with respect to ideal adamantane are shown in Fig. 3.4(lower
panel). Similarly to the doped-adamantane cases, the eDOS are altered com-
pared to the eDOS of ideal adamantane. Again, the presence of one or two func-
tional groups is related with the addition of electronic states in the band gaps
of ideal adamantane decreasing the band gap of functionalized-adamantane.
The occupation of the LUMO levels is similar to the ideal case, while in the
double-functionalization the occupation of the HOMO level differs. The re-
spective HOMO and LUMO states are sketched in Fig. 3.5(g)-(i), from which
it is evident that these are much more localized than in the doped-adamantane
cases. Both HOMO and LUMO levels are associated and localized on the func-
tional groups. In the double-functionalized adamantane, only the HOMO level
is associated with the amine group similar to the amine-functionalized adaman-
tane in which mainly the HOMO level is located on the functional group. In
all three functionalized cases the HOMO state is more pronounced than the
LUMO at the doping sites.
The variations in the electronic band gaps in both doped- and functionalized
adamantane is shown in Fig. 3.7 as compared to the ideal adamantane. As
evident from the previous analysis, the substitution of an atom in the ideal
adamantane with another atom or atomic group, changes the band gap, hence
the conducting properties, of the modified adamantane molecules. The band
gap for ideal adamantane from our simulations was found equal to 6.82 eV
whereas for B-doped adamantane the value decreased to 4.79 eV, which was the
lowest value from all doped-adamantane cases studied here. A similar decrease
in the band gaps was observed in the functionalized-adamantane. Interestingly
the SH-adamantane has the same band gap as B-doped adamantane (4.79
eV), denoting that different modifications of the same molecule can result in
very similar conducting properties. However, a double-functionalization of
adamantane reduces the band gap even further to 4.63 eV. In this respect,
an additional scanning of possible functional groups would make a further
tuning of the electronic band gap of adamantane, and diamondoids in general,
possible. Nevertheless, our findings underline the importance of a double-
functionalization for a further shrinking of the band gap in diamondoids.
29
Chapter 3. Modified diamondoids: doping and functionalization
(a) (b) (c)
(f)(e)(d)
(g) (h) (i)
Figure 3.5: The frontier orbitals, HOMO (in blue) and LUMO (in red)
for the (a) ideal and doped adamantane. In (b)-(f) these orbitals for the
doped B-adamantane, N-adamantane, O-adamantane, Si-adamantane, and P-
adamantane are shown, respectively. In (g) and (h) the HOMO and LUMO
levels for single-functionalized adamantane with an amine- and a thiol group
are depicted, respectively, while in (i) the double-functionalized amine-, thiol-
adamantane is sketched.
30
3.2. Electronic properties of diamondoids
a) b) c)
d) e) f)
g) h) i)
Figure 3.6: The 2-D contours are shown where the contours are sliced along
X-direction for all the doped and functionalized adamantane. (a) Ideal
adamantane. In (b)-(f) the charge densities contours for B-adamantane, N-
adamantane, O-adamantane, Si-adamantane, and P-adamantane are shown,
respectively. In (g) and (h) the single-functionalized adamantane with an
amine- and a thiol- group are depicted, respectively, while in (i) the charge
density of double-functionalized amine-, thiol- adamantane is sketched.
31
Chapter 3. Modified diamondoids: doping and functionalization
Dopants in adamantane
4.5
5
5.5
6
6.5
7
B
an
d
-g
ap
 (
eV
)
Functionalized adamantane
Si
O
P
N
B
Ideal Ideal
NH
2
-
SH-
NH
2
-,SH-
(b)(a)
Figure 3.7: Electronic band gaps for (a) doped- and (b) single-, as well as
double-functionalized adamantane.
3.2.2 Isomers of tetramantane
In the following, the effect of isomerization in double-functionalized diamon-
doids is being investigated. As a representative case, the four isomers of tetra-
mantane are being considered. Diamondoids vary in size by the number of
diamond cages they include. In tetramantane, four of these diamond-like cages
form the diamondoid, producing thereby four different isomers. These isomers
are named using the Balaban and von Schleyer notation [1]. This notation
depends solely upon the orientation of the respectively bonded diamond cages
along their respective axes. According to this notation, different ways of at-
taching a fourth diamond cage to triamantane exist, leading to the four tetra-
mantane isomers. These isomers are classified as anti-, M skew-, P skew-, iso-
tetramantane and named as [121] tetramantane, M[123] tetramantane, P[123]
tetramantane and [1(2)3] tetramantane.
The eDOS of the double-functionalized isomers of tetramantane are summa-
rized in Fig. 3.8 and compared to the ideal tetramantane isomer in each
case. The double-functionalized tetramantane molecules include an amine-
and a thiol-group as in the respective case of double-functionalized adaman-
tane. The amine- and thiol-groups are attached on the two opposite apical
sites of the tetramantane structures. The presence of the functional groups
again introduces electronic states in the band gaps of the ideal cases, shrink-
ing the band gap. The HOMO and LUMO states are similarly occupied in the
32
3.2. Electronic properties of diamondoids
eD
O
S Ideal
Functionalized
eD
O
S
eD
O
S
-8 -6 -4 -2 0 2 4
Energy-E
eD
O
S
[121]tetramantane
[1(2)3]tetramantane
M[123]tetramantane
P[123]tetramantane
LUMO-tetramantane
(eV)
Figure 3.8: The electronic density of states (eDOS) for the ideal and double-
functionalized tetramantane isomers. In all panels, the data are shifted with
respect to the LUMO level of the ideal tetramantane in each panel, as denoted
in the x-axis.
double-functionalized and ideal cases. As expected, the eDOS of the ideal iso-
mers also differ leading to different band gaps for tetramantane in its different
isomer structures. In this sense, the relative orientation of the diamond-like
cages in these isomers plays a role in defining the band gap and the electronic
structure overall. The variation in these band gaps for all isomers, ideal and
double-functionalized are given in Fig. 3.9. It is clearly evident that a double
functionalization can decrease the band gap approximately 20% compared to
the ideal cases. Interestingly, the trend in the band gap variation of the isomers
is reversed in the double-functionalized case. [1(2)3] tetramantane has a higher
band gap than [121] tetramantane when these are double-functionalized. This
order is reversed in the ideal tetramantane cases.
In Figure 3.10, the frontier orbitals (upper panel) and 2D contour plot (lower
panel) of all four double-functionalized tetramantane isomers are sketched.
These show a clear localization of the HOMO and LUMO on the functional
groups denoting an increased role of the functional groups in defining the
electronic properties of these structures. Both HOMO and LUMO levels are
associated with the thiol group, while only the HOMO is localized at the amine
site. Different behvaiour of the charge re-distribution over the functionalized
surface is observed in the 2D contour plots of the double functionalized tetra-
33
Chapter 3. Modified diamondoids: doping and functionalization
Tetramantaneisomers
3.5
4
4.5
5
5.5
6
6.5
B
an
d
-g
ap
(e
V
)
ideal
doublefunctionalized
[121]
P[123]M[123][1(2)3]
[121]
[1(2)3]
M[123]
P[123]
Figure 3.9: The electronic band gaps for the ideal and double-functionalized
tetramantane structures as denoted by the labels in the graph.
Tetramantane isomers
[1(2)3] [121] M[123] P[123]
Figure 3.10: The HOMO (in blue) and LUMO (in red) levels (upper panel)
and 2D contour density plot (lower panel) of four double functionalized tetra-
mantane isomers are shown.
34
3.2. Electronic properties of diamondoids
mantane isomers.
3.2.3 Band gap tuning
In the previous analysis, it was shown that it is possible to alter the electronic
properties and tune the electronic band gap of small diamondoids through
selective doping or functionalization. A double-functionalization using the
amine- and thiol- atomic groups shows a larger decrease in the band gaps
moving these closer to the semiconducting region. As a final case, we turn to
the effect of the diamondoid size. Accordingly, double-functionalized lower dia-
mondoids from adamantane up to heptamantane are being investigated. In the
ideal cases, the band gap decreases with the size, i.e. number of diamond-like
cages, as shown in the literature [72] and also confirmed through our calcula-
tions (see the upper panel in the graph in Fig.3.11). Again, at this point, the
qualitative trend is important and not the exact values of the band gaps. Using
a double-functionalization (with an amine- and a thiol group) of these small
molecules can further decrease the band gap as evident from the lower panel
of the graph in Fig. 3.11. As in the previous sections, both functional groups
have substituted a hydrogen atom of the ideal diamondoids on their two oppo-
site apical sites. A comparison of the ideal and double-functionalized cases in
Diamondoid size
4.7
4.75
4.8
4.85
B
an
d
-g
ap
 (
eV
) 6
6.3
6.6
6.9
adaman
tane
diaman
tane
triaman
tane
[121]te
traman
tane h
ex
am
an
tan
e
hep
tam
ant
ane
[12
(1)
3]p
en
tam
an
tan
e
ideal
double-functionalization
Figure 3.11: The variation of the band gaps for double-functionalized (with a
thiol and an amine group) diamondoids with respect to their size (graph, lower
panel). For comparison the respective variation for the ideal diamondoids is
shown in the upper panel of the graph.
this graph underlines a more abrupt decrease in the latter structures. This de-
35
Chapter 3. Modified diamondoids: doping and functionalization
crease is more evident moving from double-functionalized diamantane to the
double-functionalized pentamantane isomer. The decrease in the band gap
with respect to the ideal cases is close to 15% in adamantane and almost 20%
in heptamantane. Int the ideal cases, the respective relative decrease is 5% and
15%. Nevertheless, the decrease in the band gap in the double-functionalized
molecules becomes smoother going from pentamantane to heptamantane. An
additional study of higher double-functionalized diamondoids remains to show,
whether this trend saturates or not. Note, though, that the variation in the
band gap of the ideal diamondoids is larger (a difference of almost 1 eV be-
tween adamantane and heptamantane) than in the double-functionalized cases
(a respective difference of about 10% of the ideal cases). Finally, a sketch of
a) b) c) d) e)
Figure 3.12: In the upper panel relaxed structures for the double-functionalized
(a) diamantane, (b) triamantane, (c) [12(1)3] pentamantane, (d) hexamantane,
and (e) heptamantane are shown together with their frontier orbitals (HOMO
in blue, LUMO in red) are shown. In the lower panel 2D contour of the same
systems are depicted.
the frontier orbitals of the double-functionalized diamondoids in Fig. 3.12 (up-
per panel) and 2D contour plots Fig. 3.12 (lower panel) shows a very strong
localization of the HOMO and LUMO at the functionalized sites as opposed to
the ideal cases, where the frontier orbitals are more delocalized. The HOMO
and LUMO in most of the double-functionalized cases are mainly located on
the thiol-group, while no LUMO is associated with the amine group, as also
shown in the previous analysis. Accordingly, the thiol group plays a larger role
in the electronic properties of these functionalized molecules and could pro-
vide a stronger binding site to other structures for practical applications. The
eDOS of the double-functionalized diamondoids starting from adamantane up
to heptamantane has been summarized in Fig. 3.13. The process of function-
alization is the same as discussed in the previous section where the amine-
and thiol- groups are attached on the opposite apical sites of the diamondoids.
These functional groups influence the electronic properties by inducing elec-
tronic states in the band gaps as we increase the number of diamondoid rings.
In doing so, the band gap of these higher diamondoids is reduced as compared
36
3.3. Optical properties of lower diamondoids
-6 -4 -2 0 2 4 6
Energy - EF
eD
O
S
adamantane
diamantane
triamantane
[12(1)3]pentamantane
hexamantane
heptamantane
double-functionalization
Figure 3.13: The electronic density of states (eDOS) for the double-
functionalized higher diamondoids. The Fermi energy is set to zero.
to adamantane. This decrease of the band gap towards the conducting region
is a very important attribute in view of its application in potential electronic
devices.
3.3 Optical properties of lower diamondoids
In order to unravel the optical properties of ideal, single- and double- func-
tionalized diamondoids, quantum chemical calculations were performed using
the Gamess-US [65] quantum chemical software package. Both ground state
and excited state geometry optimization were performed under the framework
of DFT with a gradient convergence tolerance of 10−5 Hartree/Bohr. We
use a hybrid functional (cam-B3LYP) [84] with 6-311+G(d,p) basis sets [85]
where the diffuse s shells were added to hydrogens to describe the exchange-
correlation. The hybrid exchange-correlation functional mentioned above uses
the Coulomb-attenuation method [86], which is found to be very accurate in
the description of the polarizability of long chains, excitations to Rydberg
states and charge transfer excitations [87]. All the excited state calculations
were performed using the Tamm/Dancoff approximation [88] which compares
very well to the full TDDFT calculations.
In view of the nanotechnological applications of diamondoid based complexes,
we explore the excitation properties of diamondoids. We compare the optical
properties of functionalized diamondoid molecules with their pristine counter-
37
Chapter 3. Modified diamondoids: doping and functionalization
parts. As previously discussed, thiolated diamondoids have been proven to be
promising building blocks for hybrid systems such as SAMs on metal surfaces
as a highly effective electron emitting system. We move on to comparatively
study the alteration in structure, absorption spectra, and the distribution of
occupied and unoccupied molecular orbitals at the first excited state. Further-
more, we also investigate the trends in the optical band gap of these diamon-
doids as a function of their size and the effect of functionalization. In the end,
we discuss the application of these diamondoid-based complexes as potential
emission devices.
Results and discussion
As in the ground state S0 calculations, smallest diamondoids adamantane
(C10H16) and diamantane (C14H20) shown in Fig. 3.14 and Fig. 3.17 respec-
tively, were chosen for functionalization. We study the optical properties as
a function of selective functionalization of these two lower diamondoids. We
begin with a single functionalization, by replacing one of the hydrogen atoms
of the diamondoid with a thiol- (SH-) or amine- (NH2-) atomic group. The
method of single functionalization and the choice of the site is consistent with
the ground state calculations discussed above. At the next step, we double
functionalize the diamondoids with both the thiol- and amine-groups. In the
single-functionalized diamondoids, the functional (amine- or thiol-) group was
attached to an apical site of both adamantane or diamantane substituting the
hydrogen atom at that particular site. We have performed simulations for
three different functionalization cases: amine-, thiol-, as well as amine-, thiol-
functionalized diamondoids along with the ideal cases. For the first two, we re-
fer to single-functionalization, while for the third as double-functionalization.
The two substitutional sites for the amine- and thiol-groups are the opposite
apical tips of a diamondoid.
We study the stability, structural alterations as well as the effect on the ex-
cited state properties of these modified (single-, and double-functionalized)
diamondoids in comparison to the properties of ideal unmodified diamondoids
as investigated previously in this chapter. The optical properties in all the
cases are probed through the frontier orbitals, namely the highest occupied
(HOMO) and lowest unoccupied molecular orbitals (LUMO), absorption spec-
tra, as well as the trend in the optical band gaps. The optical band gap
is simply the measure of the difference between the HOMO and the LUMO
energies derived from the quantum chemical calculations at the first excited
state S1. We also probe the possibilities of tuning the optical band gap through
modifications of the diamondoids using the functional groups mentioned above.
3.3.1 Adamantane
We begin with the structural analysis of all the functionalized adamantane
cases depicted in Fig. 3.14 in which the upper panel (a)-(d) represents the
38
3.3. Optical properties of lower diamondoids
fully relaxed ground state geometries and the lower panel (e)-(h) show the op-
timized excited state geometries obtained from TDDFT calculations. We can
observe a qualitative difference in the structure of ground state and excited
state geometries after relaxation. The deviation from the perfect tetrahedral
structure is the result of the stretching, shrinking, and tilting of the bonds in
a different manner in different systems. In the case of the ideal adamantane,
substantial change of the geometry upon excitation is observed where the C-H
bond on the apical top slightly deviates towards the left as seen in Fig. 3.14
(a and e).
a) b) c) d)
e) f) g) h)
Figure 3.14: The optimized geometries at the ground state S0 (upper panel)
and excited states S1 (lower panel). Upper panel (a-d) a view of the re-
laxed ideal view of the adamantane, amine-functionalized adamantane, thiol-
functionalized adamantane, and amine+thiol functionalized adamantane are
shown. Similarly, the lower panel (e-h) depicts the fully relaxed excited state
geometries corresponding to the same system shown in the upper panel. All
the simulations are performed within cam-B3LYP level of theory. The C, H,
S, and N atoms are shown in black, white, yellow, and blue, respectively.
Quantitatively, the difference in terms of the bond length and bond angle at the
ground state and excited state geometries are listed in Table 3.1. For the ideal
case, we see that the C-H bond length and the C-C-H angle at the top apical
doping site were found to be 1.09 Å and 109.59◦. These numbers tend to change
at the excited state where the C-H bond length is elongated to 1.13 Å and the
C-C-H bond angle also changes to 113.85◦ which is almost a difference of 4◦
for the ground and the excited state. For the single functionalization case, we
move on to SH- functionalization. We also find considerable changes in the
geometries for the functionalized case. The C-S and S-H bonds are elongated
to 1.85 Å and 1.88 Å, respectively, which also brings deviation in the H-S-C
39
Chapter 3. Modified diamondoids: doping and functionalization
Table 3.1: Structural properties of ideal and functionalized adamantane. Bond
lengths are given in Å and angles in degrees.
Adamantane Ground State Excited State
Ideal
C-H 1.09 1.13
C-C-H 109.59 113.85
SH-
C-S 1.83 1.85
S-H 1.34 1.88
H-S-C 96.74 88.40
C-C-S 111.20 109.06
NH2
C-N 1.46 1.41
N-H 1.01 1.07
H-N-H 106.65 120.91
C-C-N 108.67 112.44
SH-,NH2-
C-S 1.84 1.86
S-H 1.34 1.88
C-N 1.46 1.45
N-H 1.01 1.01
H-N-H 106.78 106.82
C-C-N 108.78 108.83
H-S-C 96.25 84.63
C-C-S 109.94 114.14
and C-C-S bond angles. These elongations of the bonds at the apical site of
the thiolated adamantane compares well with the literature values and indicate
weaker bonds which results in lower transition energies [18, 19]. Similarly, in
the case of the amine- (NH2-) atomic group which is the second column of Fig.
3.14 (b and f) we observe the deviation in the C-N bond length decreases to
1.41 Å and the N-H bond length elongated to 1.07 Å at the excited states.
H-N-H bond angle is drastically increased from 106◦ to 120.91◦ which is an
increase of almost 15◦ as compared to its ground state geometry. In the case
of the amine- and thiol- (NH2-, SH-) atomic groups which are depicted in the
two right columns of Fig. 3.14, we see that the S-H bond length has been
stretched to 1.88 Å. However, we do not observe any major deviation in the
bond length or the bond angle at the amine site for double-functionalization.
Bond lengths of C-N, N-H, and the bond angle H-N-H are almost identical to
each other on both the ground and the excited state as listed in Table 3.1.
Optical properties
Next, we move on to the optical properties of these modified adamantanes. In
order to have a proper understanding of the difference in the electronic struc-
ture before and after excitation, we present the HOMO and the LUMO levels
as sketched in the second and third column of Fig. 3.15 along with their struc-
tures. We know from our previous investigations, that in the ground state,
40
3.3. Optical properties of lower diamondoids
HOMO LUMO
a)
b)
c)
d)
Structure
Figure 3.15: Calculated excited state geometrical structures (left column) of
the ideal and doped functionalized adamantane and the corresponding iso-
surfaces of the HOMO (middle column) and the LUMO (right column). The
positive (in red) and negative (in blue) orbitals are shown for an isovalue of
0.013.
41
Chapter 3. Modified diamondoids: doping and functionalization
0 2 4 6 8 0 2 4 6 8
ab
so
rp
tio
n 
cr
os
s-
se
ct
io
n 
(ar
b. 
un
its
)
Energy (eV)
Ideal NH2-
SH- NH2-,SH-
Figure 3.16: Absorption spectra for ideal adamantane (a), amine-
functionalized adamantane (b), thiol-functionalized adamantane (c), and
amine- and thiol- functionalized adamantane (d) are shown in red, blue, or-
ange, and green respectively. In the x-axis, we have the excitation energies in
eV obtained after the TDDFT calculations using cam-B3LYP functional and
the y-axis represents the absorption cross-section or the oscillator strength in
arbitrary units.
the HOMO states of the ideal adamantane are localized over the C-C bonds
whereas the unoccupied states LUMO are more delocalized and spread out
over the whole molecule [13]. As per out expectations, these orbitals show
slightly different localization in case of the excited state. As we can see in the
top-most panel of Fig. 3.15, the occupied orbitals (HOMO) are not confined to
just the C-H bond and there is a significant variation in the LUMO states. In
accordance with the slight deviation in the bond angle of C-H at the apical site
of the ideal adamantane, the LUMOs are altered which results in a slight gap
in its spread over the surface. In case of the thiol- (SH-) and amine- (NH2-)
single functionalized cases (second and third row in Fig. 3.15), the HOMO
becomes less delocalized and is concentrated only on the dopant site similar to
the ground state orbitals, whereas the gap in the LUMO widens as compared
to the ideal case in Fig. 3.15(c).
Similarly, in the case of the double-functionalization, the HOMO is associated
with the thiol group as the orbitals are localized more on the thiol functional
site than the amine site and the LUMO is associated with the amine func-
tional group as it shows a similar LUMO pattern as seen in the last column
of Fig. 3.15(b). The reason behind these differences is the excitation between
42
3.3. Optical properties of lower diamondoids
orbitals, which also provides the main contribution to the S0 - S1 transition
in adamantane, where S0 is the ground state and S1 is the first excited state.
These orbitals are symmetric in the ground state, while they get distorted at
the fully relaxed excited state. In Fig. 3.16, we show the absorption spectra
of the ideal, single, and double functionalized adamantane obtained from the
gas phase TDDFT calculations. In the case of ideal adamantane, we can see
the first excitation energy at 6.15 eV while the highest peak is at 8.32 eV. Sim-
ilarly, in amine-functionalized case, the first peak is observed at 4.85 eV with
the highest peak at 8.7 eV which lies in ultra-violet (UV) range. These excita-
tion energies are found to shift drastically in case of the thiolated adamantane.
In the thiol-functionalized case, the first excitation energy is found to be at
2.81 eV, which lies in the visible range, while in the double-functionalized thiol-
and amine- case, it is found to be at 2.74 eV. However, it has to be noted that
the first prominent peak for both of these cases are found to be at 5.11 eV and
5.31 eV. The shift in the spectra for different molecules occurs due to different
excitation energies. The effect of single- and double-functionalization in the
absorption spectra is clearly evident by the shift of these peak points towards
the visible region from the UV region.
3.3.2 Diamantane
a) b) c) d)
e) f) g) h)
Figure 3.17: The optimized geometries at the ground state S0 (upper panel)
and excited states S1 (lower panel). Upper panel (a-d) a view of the re-
laxed ideal view of the diamantane, amine-functionalized diamantane, thiol-
functionalized diamantane, and amine-, thiol- functionalized diamantane are
shown. Similarly, the lower panel (e-h) depicts the fully relaxed excited state
geometries corresponding to the same system shown in the upper panel. All
the simulations are performed within the cam-B3LYP level of theory. The C,
H, S, and N atoms are shown in black, white, yellow, and blue, respectively.
43
Chapter 3. Modified diamondoids: doping and functionalization
Table 3.2: Structural properties of ideal and functionalized diamantane. Bond
lengths are given in Å and angles in degrees.
Diamantane Ground State Excited State
Ideal
C-H 1.09 1.11
C-C-H 109.70 107.84
SH-
C-S 1.83 1.85
S-H 1.34 1.90
H-S-C 96.55 87.70
C-C-S 106.52 110.82
NH2
C-N 1.45 1.41
N-H 1.01 1.07
H-N-H 106.11 121.00
C-C-N 108.76 112.45
SH-,NH2-
C-S 1.83 1.85
S-H 1.34 1.90
C-N 1.46 1.46
N-H 1.01 1.01
H-N-H 106.76 106.74
C-C-N 108.77 108.77
H-S-C 96.81 87.63
C-C-S 111.40 109.14
Next, we performed TDDFT calculations with diamantane which is a slightly
larger molecule than adamantane. Since diamantane comprises of two fused
cages of adamantane, it is a symmetric structure resulting in a zero dipole
moment. This property of diamantane would affect the excitation behaviour
in its ideal state which refers to no functional groups attached to its apical tip.
However, the effect of dopants would induce a dipole moment in the structure
resulting in interesting characteristic features which are discussed below. First
of all, the structural analysis of all the functionalized diamantane cases is de-
picted in Fig. 3.17 in which the upper panel (a)-(d) represents the fully relaxed
ground state geometries and the lower panel (e)-(h) show the optimized ex-
cited state geometries obtained by TDDFT calculations. We can observe that
there are very qualitative differences in the structure of the ground state and
excited state geometries after relaxation in the case of ideal diamantane. A
slight deviation in the amine- functionalized case is observed with elongation
and tilting of the N-H bonds in the second column of Fig. 3.17(b and f). A
substantial distortion is observed in the cases of the thiol- functionalization
which is depicted in the third column of Fig. 3.17. The S-H bond length has
clearly been stretched. Finally, for the double functionalized case, shown in
the last column (d) in Fig. 3.17, we observed distortion in both the amine
and thiol sites leading to the deviation of the hydrogen atom from its initial
ground state geometry.
Similar to adamantane, we also present the quantitative differences in terms
44
3.3. Optical properties of lower diamondoids
of the bond length and bond angle at the ground state and excited state
geometries for functionalized diamantane. The differences in the bond length
and bond angle of the functionalized structures as listed in Table 3.2. For
the ideal case, we see that the C-H bond length and the C-C-H angle at the
top apical doping site were found to be 1.09 Å and 109.70◦. These numbers
tend to change at the excited state where the C-H bond length is elongated
to 1.11 Å and the bond angle also changes to 107.84◦. We notice that the
excited state behaviour of diamantane in terms of C-C-H bond angle is not
comparable to adamantane. In the case of ideal adamantane, the bond angle
was found to be larger at the excited state while for ideal diamantane the C-
C-H bond angle tend to become smaller than the ground state. We also found
changes in the geometries for the single-functionalized cases. The S-H bond is
elongated to 1.90 Å which while the C-S bond also elongates to 1.85 Å which
also brings deviation in the H-S-C and C-C-S bond angles. These elongations
result in the lower transition energies of modified diamantane [18]. Similarly,
in case of the amine- (NH2-) functionalization, we observe the deviation in the
C-N bond length which decreases to 1.41 Å and the N-H bond length gets
elongated to 1.07 Å at the excited states which are exactly same as in case of
adamantane. H-N-H bond angle is drastically increased from 106◦ to 121.00◦
which is again the same as adamantane. In case of the amine- and thiol- (NH2-
, SH-) functionalization, which are depicted in the two right columns of Fig.
3.14, we see that the S-H bond length have been stretched to 1.90 Å. However,
we do not observe any major deviation in the bond length or the bond angle
at the amine site for double-functionalization. Bond lengths of C-N, N-H, and
the bond angle H-N-H are almost identical to each other on both the ground
and the excited state.
Optical properties
Next, we move on to the optical properties of modified diamantane molecules.
We present the HOMO and the LUMO levels as sketched in Fig. 3.18. Sim-
ilar to the adamantane cases, the HOMO states of the ideal diamantane are
localized over the C-C bonds whereas the unoccupied states LUMO are more
delocalized and spread out over the whole molecule [13]. However, in contrast
to adamantane, these orbitals do not show any different behaviour in case of
the excited state properties. The reason behind this is the zero dipole moment
of diamantane, which results in very less distortion of the molecular structure
leading to an identical spread of the frontier orbitals in both the ground and
excited states. As we can see in the top-most panel of Fig. 3.18, the occupied
orbitals HOMO are confined to the C-H bond and the LUMO states spread all
over the surface showing no difference between the ground state or the excited
state properties. In the case of the thiol- (SH-) and amine- (NH2-) single func-
tionalized cases (second and third row in Fig. 3.18), the HOMO becomes less
delocalized and is concentrated only on the dopant sites, whereas the spread
of the LUMO differs from its ideal counterpart in Fig. 3.18(c). Similarly, in
the case of the double-functionalization, the HOMO is mostly associated with
45
Chapter 3. Modified diamondoids: doping and functionalization
Structures HOMO LUMO
a)
b)
c)
d)
Figure 3.18: Calculated excited state geometrical structure (left column) of
ideal and double functionalized diamantane and the corresponding iso-surfaces
of the HOMO (middle column) and the LUMO (right column). The positive
(in red) and negative (in blue) orbitals are shown for an isovalue of 0.013.
46
3.3. Optical properties of lower diamondoids
the thiol group as the orbitals are localized mostly close to that. Interestingly,
the LUMO pattern in Fig. 3.18(c) is abruptly different as compared to the
other single functionalized cases. We can observe the difference in the orbital
where the positive (in red) have a larger surface area where the negative (in
blue) is diminished. Note that we implemented the same level of theory and
methodology for all cases. The reason behind these differences is the excitation
between these orbitals which also provides the main contribution to the S0 - S1
transition in diamantane. These orbitals are symmetric in the ground state
while they get distorted at the fully relaxed excited state.
In the next step, we show the absorption spectra of the ideal, single- and
double- functionalized diamantane in Fig. 3.19 as obtained from the gas phase
TDDFT calculations. In the case of ideal diamantane, we can see the first
excitation energy at 6.99 eV. Similarly, in the amine-functionalized case, the
first peak is observed at 4.87 eV with the highest peak at 7.8 eV which lies
in the UV range. As in the case of adamantane, these excitation energies are
found to shift drastically in case of the thiolated diamantane. In the thiol-
functionalized case, the first excitation energy is found at 2.78 eV and in the
double-functionalized case, the first excitation energy lies at 2.77 eV, which
is also in the visible range. However, as observed in the case of adaman-
tane, the first prominent peak for the thiol-functionalized case and the double-
functionalized case is observed at 5.03 eV and 5.08 eV, respectively. The shift
in the spectra for different molecules is because of the different excitation en-
ergies. These results suggest the effect of single- or double- functionalization
in the absorption spectra clearly evident by the shift of these peak positions
towards the visible region. These results show the other possible functional
groups could be used to shift the spectra from the deep UV region towards the
visible region.
3.3.3 Optical band gap
In our previous analysis, it was shown that it is possible to alter the electronic
properties and tune the electronic band gap of small diamondoids through se-
lective doping or functionalization. As a result, double-functionalization using
the amine- and thiol- atomic groups showed a larger decrease in the band gaps
moving these closer to the semiconducting region. Similar to that, in this sec-
tion, we compare the optical band gap of single- and double-functionalized-
adamantane and diamantane to its ideal case. The electronic and optical band
gap decreases with the size for the ideal cases in both the ground state and
excited state cases with the increasing number of cages. The optical band gap
corresponds to the energies from S0 - S1 transitions. For ideal adamantane and
diamantane S1 was found to be 6.15 eV and 6.99 eV, respectively as seen in
Fig. 3.20. Note that the optical band gap is generally lower than the electronic
band gap (refer to [89, 90]). Although, the increase in the optical band gap
of ideal diamantane within the framework of TDDFT has also been observed
in the literature [91]. Again, at this point, the qualitative trend is important
47
Chapter 3. Modified diamondoids: doping and functionalization
0 2 4 6 8 0 2 4 6 8
ab
so
rp
tio
n 
cr
os
s-
se
ct
io
n 
(ar
b. 
un
its
)
Energy (eV)
Ideal NH2-
SH- NH2-,SH-
Figure 3.19: Absorption spectra for ideal diamantane (a), amine-functionalized
diamantane (b), thiol-functionalized diamantane (c), and amine- and thiol-
functionalized diamantane (d) are shown in red, blue, orange, and green re-
spectively. In the x-axis, we have the excitation energies in eV obtained after
the TDDFT calculations under the theory of cam-B3LYP functional and the
y-axis represents the absorption cross-section or the oscillator strength in ar-
bitrary units.
Functionalized adamantane
5
6
7
O
pt
ic
al
 b
an
d-
ga
p 
(eV
)
Functionalized diamantane
(a) (b)
NH2-NH2-
SH-
SH-
NH2-, SH-
Ideal
NH2-, SH-
Ideal
Figure 3.20: The variation of the optical band gaps for single and double-
functionalized (with a thiol and an amine group) diamondoids with respect to
their ideal cases.
48
3.3. Optical properties of lower diamondoids
Adamantane Diamantane
g
ro
u
n
d
e
x
c
it
e
d
HOMO LUMO HOMO LUMO
HOMO LUMO HOMO LUMO
Figure 3.21: Comparison of the frontier orbitals at the ground state and ex-
cited state of the double-functionalized adamantane and diamantane. All the
simulations are performed within cam-B3LYP level of theory. The positive (in
red) and negative (in blue) orbitals are shown for an isovalue of 0.013.
and not the exact values of the band gaps which are quantitatively not well
reproduced with the method used. Using a double-functionalization (with an
amine- and a thiol-group) of these small molecules can further decrease of the
optical band gap.
As evident from the previous analysis, the substitution of an atom in the ideal
adamantane with another atom or atomic-group, changes the optical band
gap, hence the optical properties, of the functionalized diamondoid molecules.
Interestingly, the NH2-adamantane and NH2-diamantane has an almost same
optical band gap (approx. 4.85 eV), which relates to the similar optical proper-
ties for both the molecules. For the SH-adamantane and SH-diamantane cases,
the optical band gap was found to be 5.11 eV and 5.03 eV which is in reasonable
agreement with the experimental optical band gap of thiolated adamantane,
i.e 5.85 eV [19]. The double-functionalization also lowers the optical band gap
as compared with the ideal cases to 5.31 eV and 5.08 eV. However, these values
are higher than the single-functionalized cases. In this respect, an additional
functional group would make it possible to further tune the optical band gap of
diamondoids in general. Nevertheless, our findings underline the importance
of a functionalization for a further shifting of the optical band gap towards the
visible region. In Fig. 3.21, we show the frontier orbitals of the ground state
and excited state of double- functionalized adamantane and diamantane. As
we already know that the localization and delocalization of the HOMO and
LUMO over the surface of the molecule plays a very important role in defining
their optical properties. As seen in Fig. 3.21, the HOMOs are mostly localized
to the thiol group which is at the bottom tip of the functionalized diamantane
49
Chapter 3. Modified diamondoids: doping and functionalization
while the LUMO spreads all over the surface. We also found out that the
interesting functional properties of both the diamondoid molecules are mainly
induced by the functional groups rather than the size of diamondoids [18].
3.4 Conclusions
Overall, we have shown the possibility to selectively tune the electronic and
optical properties of modified diamondoids through single- and double- func-
tionalization. We found out that different dopants and functional groups lead
to different electronic and optical properties. Double-functionalization as com-
pared to a single-functionalization decreases even further the electronic band
gap towards conducting region and the optical band gap towards the visible
region. Selectively synthesizing diamondoid complexes of a specific size and
modification has the potential to tune their electronic and optical properties
as molecular devices. In order to probe the possibilities of constructing di-
amondoid based devices, we discuss the self-assembly of diamondoid based
complexes over different metal surfaces in the next chapter.
50
Chapter 4
Self-assembled monolayers
In this chapter, we analyze the electronic properties of self-assembly of diamon-
doids on metal surfaces. In section 4.1, we introduce N-heterocyclic carbenes
(NHC)s which are emerging as an alternative class of molecules to thiol-based
self-assembled monolayers (SAMs), making carbene-based SAMs much more
stable in harsh environmental conditions. Next, we present the results and
analysis where we have functionalized tiny diamondoids using NHCs in order
to prepare highly stable carbene-mediated diamondoid SAMs on metal sub-
strates. We focus on binding characteristics, stability, and adsorption of the
NHC mediated diamondoid SAMs on the metal surfaces. The surface morphol-
ogy of all NHC-based diamondoid SAMs was revealed through simulated STM
images, which show characteristic features for each surface. The conclusion of
this work is summarized in the final section 4.3. Some of the sections of this
chapter are also the part of our published article "B. Adhikari, S. Meng and
M. Fyta, Nanoscale, 2016, 8, 8966 - Reproduced by permission of The Royal
Society of Chemistry. All rights reserved".
4.1 NHC mediated diamondoids
N-heterocyclic carbenes [92] are the ring-like structures made up of carbon
and nitrogen. One of the simplest forms of carbene is Imidazolylidene which is
shown in Fig. 4.1. Unlike typical carbene molecules, which are highly reactive
and have very limited stability, NHCs usually have two hetero-atoms adjacent
to the carbene carbon. The partial aromaticity at the backbone of the car-
bene ring is another reason for its high stability. In addition, NHCs can be
prepared on the industrial scale, can be crystallized, distilled, and stored for
long period of time in order to become commercially available reagents [93–95].
Bulky NHC ligands have also theoretically been shown to stabilize the main
group compounds [96]. In the past, thiol-based SAMs on metal surfaces have
led to significant applications in the field of surface emission, sensing, elec-
trochemistry, drug delivery, and microelectronics [21–25]. However, thermal
instability of these thiol-based SAMs on gold in harsh environmental condi-
tions has been a huge hindrance in using them for industrial purposes [26–30].
Thiol-based SAMs are found to be stable only when stored in an ultra high
51
Chapter 4. Self-assembled monolayers
C
N N
R1 R2
R3R4
Figure 4.1: General structural formula of imidazolylidene-structures
vacuum in the absence of light but tend to degrade after few weeks at room
temperature [31–33]. Accordingly, an alternative molecule which mediates the
formation of diamondoid SAMs on substrates is needed. For this, we propose
the use of N-hetero-cyclic carbene (NHC) molecules to promote binding of di-
amondoids on metal surfaces. This feature increases the NHC stability. In
this work, we aim to study the structural and electronic properties of carbene-
functionalized diamondoid monolayers on metal surfaces. For the latter, we
consider gold, silver, and platinum surfaces. We also study their morphology
and work function in view of their nanotechnological applications as potential
electron emitters and sensors.
4.2 Diamondoid mediated SAMs
The smallest diamondoid adamantane (C10H16) was chosen to model a free
radical self-assembled monolayer absorbed on the metal substrates. Two varia-
tions of carbene molecules were chosen and attached to adamantane to prepare
two different diamondoid SAMs, namely (C13N2H18) and (C23O1N2H32) [97].
To these, we refer in the following as NHC1, and NHC2, respectively. The for-
mer is chosen on a purely theoretical basis, while the latter has already been
used in experiments. We chose both as representative carbene candidates in
order to extend the search for potential carbene-mediated diamondoid-based
SAMs. (C23O1N2H32) has been investigated experimentally and (C13N2H18)
is a molecule with less complexity and could be easier manipulated. Before
structural relaxation, the NHC-mediated diamondoid-SAMs were placed on
the on-top site of the surfaces and at a distance larger than 2.20 Å. Preferen-
tial site binding of the NHC2 on the surfaces is not considered in this work
taking into account the experimental evidence that the lowest carbene-C atom
(for NHC2) is bonded on the on-top site on an Au(111) surface [97]. Our
52
4.2. Diamondoid mediated SAMs
initial calculations also showed that the on top site is also preferred by the
NHC1-mediated adamantane. Two different molecules chosen to self-assemble
on the metal surfaces are shown in Fig. 4.2. The figure shows adamantane
functionalized with the carbene molecules NHC1 and NHC2. In the following,
we refer to these functionalized diamondoids as NHC1-ada and NHC2-ada,
respectively. The notation NHC-ada/metal (or modified metal surfaces) refers
to the NHC-mediated adamantane SAMs on one of the metal surfaces.
NHC1-ada NHC2-ada
Figure 4.2: The NHC1-functionalized adamantane (left) and the NHC2-
functionalized adamantane (right).
4.2.1 Structural analysis
We begin the discussion with the analysis of the structural characteristics of
all carbene-mediated diamondoid surfaces. All structurally relaxed SAMs are
depicted in Fig. 4.3. The distance of the carbene-functionalized diamondoid
from the surface is also denoted by the arrows which is calculated based on
the bond-length of the lowest carbon atom of the carbene-functionalized di-
amondoid to the closest metal atom of the surface. We observe a variability
in the ’C-metal ’bond-length for the different molecules and metal surfaces
in the range of 1.97 - 2.28 Å. An overall closer arrangement is evident for
the diamondoid-SAMs on Pt(111), followed in trend by the diamondoid-SAMs
on Au(111) evident due to the shorter bond (1.97 Å for the NHC1-ada case
and 2.02 Å for the NHC2-ada case) of the functionalized diamondoid with the
Pt surface. For the Au(111) surface, these values are 2.08 Å for NHC1-ada
and 2.12 Å for NHC2-ada. As discussed in the literature [97], despite various
53
Chapter 4. Self-assembled monolayers
NHC structures are available, the C/N ratios for the films and nanoparticles
investigated using X-ray photoelectron spectroscopy (XPS) were compared to
previous experimental studies and were found to be optimal for the NHC with
the C3H7 ligand. The NHC coverage for this case was also found dense enough
to prevent other impurities from binding to other sites not covered by the
NHC. This is the same molecule (NHC2) we chose in our investigations due to
the previous experimental evidence. As implied in the introduction, the family
of NHC molecules can assume a number of variations, other than the C3H7.
Additional ligands have not been investigated here. The aim of this work was
not an extensive study of such ligands and NHC members, rather provide a
proof of principles of the efficiency of such molecules in promoting the bind-
ing of diamondoids on metal surfaces in order to form self-assembled layers of
diamondoids. The larger bond-length in both Ag SAMs is an indication of a
less stable SAM, which will be further evaluated in the following. For the Ag
surface, the respective bond lengths are 2.19 Å for NHC1-ada and 2.28 Å for
the NHC2-ada case. The shorter bonds of the diamondoid-SAMs on Au(111)
and Pt(111) denote a stronger bonding compared to the Ag(111) surfaces. In
Figure 4.3: (a)-(c): adsorption of the NHC1-mediated adamantane SAMs on
Au(111), Ag(111), and Pt(111), respectively. (d)-(f): adsorption of the NHC2-
mediated adamantane SAMs on the same surfaces. The black arrows indicate
the C-metal bond-lengths in each case.
the case of NHC2-ada, two of the hydrogen atoms of the carbene molecule
come close to the metal surfaces. Note, that these H atoms are all bonded to
secondary C atoms in the ligand. One of these secondary C atoms is bonded
to the N atom of the carbene ring. The distance of the H atom bonded to
54
4.2. Diamondoid mediated SAMs
the secondary C atom (close to the nitrogen) and the metal surface was found
to be 2.86, 2.80, and 2.05 Å for the Au, Ag, and Pt surfaces, respectively. In
the case of Pt(111), these distances are quite small indicating that two of the
hydrogen atoms attached to a secondary carbon atom of the carbene C3H7
ligands could also bind to the metal surface. This will be confirmed by the
HOMO re-distribution analysis below. The distance of the H atoms bonded to
the other two secondary C atoms in the ligand which is closest to the metal is
3.18, 3.22 and 3.11 Å for H-Au, H-Ag, H-Pt, respectively. For the NHC1-ada
case, the distances of the lowest hydrogen atoms of the carbene ring are 3.32,
3.16, and 2.75 Å for H-Au, H-Ag, and H-Pt, respectively. Another important
structural detail is the relative orientation of the adsorbed NHC-adamantane
with respect to the metal surfaces. Close inspection of all structures in Fig.
4.3 reveals that for each NHC-ada its vertical arrangement with respect to
all three surfaces is almost the same. In order to prove this, we have calcu-
lated the angle between the carbene carbon atom which is closer to the surface
(the one involved in the ’C-metal’ bond mentioned above), the closest metal
atom and one of its nearest neighbors. These angles lie in the range 93-96◦ for
NHC1-ada and 100-106◦ for NCH2-ada for all three surfaces. The values de-
note an orthonormal arrangement of the carbene-mediated adamantane-SAMs
on the metal surfaces which is observed for both NHC1-ada and NHC2-ada.
In the latter case, though, and for all three metal surfaces, the metal atom
bonded to the carbene-functionalized adamantane was slightly pulled off the
metal surface in order to stronger bond to the molecule. Hence, the respective
angles are about 10◦ larger than for NHC1-ada. This higher "attraction" of
the closest metal atom from the NHC2-ada was also reported in a relevant
experimental work [97]. This behavior was not observed for the NHC1-ada
case on any of the surfaces. The most important structural characteristics
for the NHC-mediated adamantane-SAMs investigated here are summarized
in Table 4.1.
4.2.2 Adsorption Energies
In order to assess the quality of the SAM binding on the metal surfaces, we
investigate adsorption energies. The adsorption energy Eads, for a molecule ad-
sorbed on a surface is the difference between the total energy of the molecule/me-
tal system (Etotal) and the sum of the total energies of the two components.
This sum includes the total energy of the clean metal surface (Eclean) and the
total energy of the isolated molecule (Emol). The following equation holds for
the adsorption energy:
Eads = Etotal − Eclean − Emol (4.1)
The adsorption energies for both NHC-ada on the gold and platinum surfaces
are found in the range -1.70 to -1.92 eV. Accordingly, no significant qualita-
tive difference in their stability can be inferred for these cases. For the silver
surfaces, these energies are about 30-45% higher compared to the NHC-ada ad-
sorption on gold and platinum. In this respect, the SAMs can be easily formed
55
Chapter 4. Self-assembled monolayers
Table 4.1: Structural properties and adsorption energies (Eads) for the carbene-
mediated diamondoid SAMs on metal surfaces depicted in Fig. 4.3. Energies
are given in eV, angles in degrees, and bond-lengths in Å.
SAMs NHC1-ada NHC2-ada
Gold (111)
Eads -1.819 -1.700
C-Au 2.08 2.12
C-Au-Au 95 103
H-Au 3.32 2.86
Silver (111)
Eads -1.190 -1.067
C-Au 2.19 2.28
C-Au-Au 96 105
H-Au 3.16 2.80
Platinum (111)
Eads -1.843 -1.921
C-Au 1.97 2.02
C-Au-Au 93 100
H-Au 2.75 2.05
on Au(111) and Pt(111) than on Ag(111). The fact that for the same metal
surface, both SAMs lead to similar adsorption energies, can be understood as
a similar efficiency of the metal surface in adsorbing both the NHC1- and the
NHC2-functionalized adamantane. This similarity is evident despite the fact
that NHC1-ada does not contain the C3H7 ligand attached to nitrogen as in the
NHC2-ada case. The stability of NHC2-ada has already been observed experi-
mentally revealing the practical interest of NHC2-ada SAMs [97]. Accordingly,
due to the similarity in the adsorption energies, we can argue that the theoret-
ical molecule NHC1-ada considered here could be an additional potential can-
didate in forming carbene-mediated SAMs on metal surfaces. All adsorption
energies as calculated through Eq.4.1 are summarized in Table. 4.1. According
to the above analysis, the bonding of the carbene-mediated diamondoid-SAMs
on metal surfaces is stronger compared to thiol-mediated diamondoid-SAMs
on the same surfaces. Specifically, our calculations lead to longer bonds in the
latter case. For thiol-functionalized adamantane molecules, the S-Au, S-Ag,
S-Pt bond-lengths (which correspond to the SAM-surface bonding) were found
to be 2.56, 2.55, and 2.33 Å, respectively. The respective adsorption energies
are -2.16, -2.18, and -3.15 eV, respectively. At a first sight, these denote a bet-
ter adsorption of sulfur-bonded adamantane on the metal surfaces. For thiol,
the preferred adsorption site on the metal surfaces is the fcc site, while for the
NHC-ada the preferred adsorption site is the on-top site. This is confirmed by
our initial calculations and experiments [98].
According to recent theoretical investigations, DFT simulations with common
GGA functionals incorrectly favor adsorption sites with a high coordination,
such as the fcc site, rather than a low coordination site, such as the on top site
[99]. Note, that though the fcc site for thiol-mediated adsorption is preferred
in the experiments [98], the DFT-derived adsorption energies for the fcc site
56
4.2. Diamondoid mediated SAMs
have not always been in good agreement with experiments. This was evident
in the case of CO adsorption on Pt(111) [100]. Due to this possible discrepancy
between experimental and theoretical data on the preferable binding sites, we
focus on the comparison of bond lengths rather than binding sites. Accordingly,
we compare the bond lengths between the S-mediated and NHC-mediated
SAM adsorption on the metal surfaces. These bond lengths are significantly
shorter in the latter case and differ about 11-19% between the two cases. This
finding indicates a stronger bonding of the NHC-diamondoid SAMs than thiol-
diamondoid SAMs on the metal substrates.
4.2.3 Isolated NHC-functionalized adamantane
For the analysis of the electronic properties of the structures studied here, we
begin with the projected electronic density of states (PDOS) and the frontier
orbitals of the free-standing (no metal surface) carbene-functionalized adaman-
tane. The latter are the highest occupied (HOMO) and lowest unoccupied
molecular orbitals, HOMO and LUMO, respectively. The charge density of
the frontier orbitals of the free standing SAMs was sketched in Fig. 4.4. We
observe that the charge density for the HOMO is quite delocalized over the
whole molecule, including the adamantane and NHC parts (for both NHC1
and NHC2). On the other hand, the charge density for the LUMO is more lo-
calized on the carbene ring and the lower N-C-N atoms, the tip of the carbene
ligand. This ligand promotes binding of the molecule to the metal surface.
These features differ from the ideal adamantane case, as expected. For the
ideal adamantane, the charge density for the HOMO is localized in between
the carbon-hydrogen bonds and the charge density for the LUMO is delocal-
ized and spread out over the molecule’s surface [101]. The respective PDOS
of the isolated NHC-ada molecules shown in Fig. 4.5 are considerably altered
by the presence of the carbene as compared to the ideal adamantane [101].
For both molecules, the s-orbitals contribute more to the electronic density
of states in both the HOMO and the LUMO levels. A comparison of both
carbene variations, NHC1 and NHC2, reveals that the s- and p- distributions
in the PDOS are similarly broad. The functionalization introduces electronic
states in the band gap of the ideal adamantane, decreasing in this way the
electronic band gap of carbene-functionalized adamantane. This band gap
reaches 3.62 eV for NHC1-ada and 3.37 eV for NHC2-ada which is a decrease
of almost 50 % compared to the value for ideal adamantane [101]. Note, that
the results for the electronic band gaps were obtained with DFT without any
correction for the band gap calculation. Accordingly, these values are expected
to be off with respect to experimental values. However, our simulations can
capture the trends in the modification of the electronic band gap due to the
carbene-functionalization and this trend is of interest here.
Adamantane modified metal surfaces
The adsorption of the NHC-ada molecules on the metal surfaces alters the
electronic properties of the clean surfaces and the isolated NHC-ada. The
57
Chapter 4. Self-assembled monolayers
Figure 4.4: The charge density of its highest occupied molecular orbital
(HOMO) (top-left; in blue), and the charge density of the lowest unoccupied
molecular orbital (LUMO) (top-right; in red) are shown. Charge density of
the HOMO (bottom-left; in blue), and that for the LUMO (bottom-right; in
red) are also given.
electronic features of the adsorbed SAMs mapped through the PDOS are shown
in Fig. 4.6 and reveal the qualitative influence of the SAM adsorption of
the surfaces. For all substrates, we observe that the HOMO of the molecule
is slightly shifted towards the Fermi energy which indicates the bonding to
the surface. The occupied levels become more spread out. The unoccupied
levels become less peaked and slightly more broad for the adsorbed molecules.
The trend in the height of the peaks in the p-orbital contribution for the
occupied electronic levels is altered in the adsorbed cases, as the third peak
before the Fermi energy is more pronounced compared to the fourth peak
in the non-adsorbed cases. This again denotes the tendency to ’move’ the
electronic levels in order to promote binding to the surface. According to the
total density of states shown in Fig 4.7, all occupied electronic levels enter the
band gap region of the free standing carbene-functionalized adamantane before
adsorption. In order to reveal the binding characteristics and the reactivity
of the metal surfaces, we calculated the PDOS of the first layer of the metal
substrates and the PDOS of the carbon atom of the carbene ring which is the
closest and binds to the surface. For a better qualitative understanding of the
nature of bonding and the hybridization of the electrons, the contributions
with respect to the angular momentum (s-,p-, and d-orbitals) in the PDOS
are plotted in Fig. 4.8. A covalent bond between the molecule and the surface
can be formed when d-orbitals are contributing more to the density of states
58
4.2. Diamondoid mediated SAMs
s-orbital
p-orbital
-6 -4 -2 0 2 4 6
E - E
F
(eV)
NHC1-ada
NHC2-ada
P
D
O
S
Figure 4.5: Projected density of states (PDOS) for both carbene-functionalized
adamantane molecules before adsorption. The contributions from the s- and
p-orbitals are depicted in black and red, respectively. The Fermi energy in
each case was shifted to 0 eV.
near the Fermi energy. In such a case, the p-electrons of the molecules can
coordinate with the hybrid orbitals of the metal surface and promote bonding
of the two structures. Inspection of the left panels in this figure reveals that
the contribution of the d-orbitals in the PDOS for the first layer of the Au
and Pt surfaces at the Fermi level is very large compared to the respective
contributions of the s- and p-orbitals. The contributions of the carbene carbon
atom in the PDOS (right graphs in each panel of Fig. 4.8) reveals a peak in the
p-orbital contributions around the Fermi energy. Accordingly, the p-orbitals
of the lowest carbene atom are available to overlap with the d-orbitals of the
metal and share electrons to form bonds. The overlapping is not so evident
in Ag(111); a difference possibly assigned to its higher reactivity compared
to gold and platinum. Since the p-orbital contribution to the PDOS for the
NHC1-ada/Au and the NHC2-ada/Pt is more peaked at the Fermi level, it
can be inferred that the bonding in these two cases should be slightly stronger
compared to NHC2-ada/Au and NHC1-ada/Pt. For the latter structures, the
p-orbital contribution of the carbene-C atom is slightly off the Fermi level. This
is in agreement with the shorter C-Au bond for NHC1-ada/Au compared to
NHC2-ada/Au in Table 4.1. For Pt(111), though, we see a reverse behavior:
the p-orbital contribution for NHC2-ada/Pt is peaked exactly at the Fermi
level, but the C-Pt bond according to Table 4.1 is 2% longer than in NHC1-
ada/Pt for which the p-orbital contribution in the PDOS shows a peak slightly
off the Fermi level. Nevertheless, the adsorption energy for NHC2-ada/Pt is 4%
higher than in NHC1-ada/Pt, denoting stronger adsorption in the former case.
A possible explanation lies in the existence of the C3H7 ligand in NHC2-ada and
59
Chapter 4. Self-assembled monolayers
-6 -4 -2 0 2 4 6
E - E (eV)
F
NHC1-ada on Au
NHC2-ada on Au
NHC1-ada on Ag
NHC2-ada on Ag
NHC1-ada on Pt
NHC2-ada on Pt
P
D
O
S
Figure 4.6: Projected density of states (PDOS) for both carbene-functionalized
adamantane molecules after adsorption. The contributions from the s- and p-
orbitals are depicted in black and red, respectively. The Fermi energy in each
case was shifted to 0 eV.
the attraction of the nearest hydrogen atoms on Pt(111) as will be revealed
through the analysis of the surface morphologies in the next sections. The
calculated dipole moments of the NHC-ada/metal structures were extracted
from our calculations. The x- and y-coordinates of the dipole moments of all six
structures was zero. Only the z-component of the dipole moments was found
nonzero, and are for the NHC1-ada/metal on Au(111), Ag(111), and Pt(111),
-6.532, -5.519, -6.340 Debye, respectively. For NHC2/ada on the same metals,
the dipole moment values are -7.224, -5.735, -6.912 Debye, respectively. Note,
that the z-axis was taken normal to the modified surfaces. All dipole moments
are negative indicating that in all cases, the dipole moment vector points from
the adsorbed molecule towards the metal surface. Overall, the modified gold
substrates show higher dipole moments. The NHC2-mediated adamantane
SAM also corresponds to a larger dipole moment compared to the NHC1-ada
adsorbed structures.
4.2.4 Work function
As a measure of the efficiency of carbene-mediated adamantane SAMs on
metal surfaces for practical applications, we performed the analysis of their
work functions Φ. We expect these to be modulated with respect to the work
function of the clean metal surfaces, in a way that charge transfer from the
modified surfaces becomes more efficient. This feature would be valuable for
potential electronics applications of the NHC-ada/metals. An adsorbate layer
contributes to the charge transfer in the adsorption procedure, significantly
60
4.2. Diamondoid mediated SAMs
e D
O
S
NHC*
NHC*-ada-Au
NHC*-ada-Ag
NHC*-ada-Pt
-8 -6 -4 -2 0 2 4 6
Energy - ELUMO-NHC* (eV)
e D
O
S
NHC1-ada
NHC2-ada
Figure 4.7: Total density of states (TDOS) of the NHC1 molecules (upper
panel) and NHC2 molecules (lower panel) before and after adsorption over the
metal surfaces. The energy has been shifted to LUMO level of the respective
NHCs in all the cases. The color black denotes NHCs without adamantane
attached to it apical region while red, green and blue represents the NHCs
after adsorption over Au, Ag, and Pt respectively. The symbol * denotes
either NHC1 or NHC2 molecule.
modulating the work function of the metal surface. The electrons leaving the
metal surface will have to pass through the interface dipole layer. The orien-
tation of the dipole influences the efficiency in the removal of electrons. The
electrostatic potential at each point of the unit cell in our simulations is used to
create an electrostatic profile along the z- direction normal to the surface. The
work function is obtained from the electrostatic profile value in the vacuum
area. The relationship of the work function and the surface dipole moment is
given by:
∆Φ = − e
0
(µz − µz,0) = − e
0
∆µ (4.2)
where µ0 is the surface dipole per unit area, µz is the surface-normal dipole per
unit area for the SAM adsorbed surface, e is the charge, and 0 is the dielectric
constant. A positive value of µ indicates a dipole that is pointing away from
the bulk, which leads to a decrease of the work function. A negative value
of µ corresponds to a dipole pointing to the bulk, thus increasing the work
function and hindering the charge transfer. The calculated work functions of
61
Chapter 4. Self-assembled monolayers
s
p
d
-6 -4 -2 0 2 4 -4 -2 0 2 4 6 -12 -8 -4 0 4
P
D
O
S
E - E
F
(eV)
Au
Ag
Pt
Au
Ag
Pt
NHC1-ada
NHC2-ada
NHC1-ada
NHC1-ada
NHC2-ada
Au-bulk
Ag-bulk
Pt-bulk
Au-bulk
Ag-bulk
Pt-bulkNHC2-ada
Figure 4.8: The contributions of the s-, p-, and d-orbitals to the PDOS of the
metal surfaces are depicted for the first layer of the metal surface for Au(111),
Ag(111), and Pt(111) on the left. For the same surfaces, the middle graphs
depict the PDOS contribution of the s- and p-orbitals of the carbene carbon
atom which is closest and binds to the metal surface. The right panels depict
the PDOS for the bulk metals before adsorption. The Fermi energy has been
shifted to 0 eV in all cases. The contributions of the s-, p-, and d-orbitals are
shown in black, red, and blue, respectively.
the clean Au(111), Ag(111), and Pt(111) surfaces according to our calculations
are 5.25, 4.5, and 5.73 eV, respectively. We have found that the adsorption
of the NHC-ada SAMs lowers the work function considerably. To assess the
two contributions from the molecule and the metal surface, we must consider
two additional systems. We first remove the molecular layer and compute
the electrostatic profile of the relaxed free gold surface. At a second step, we
remove the gold surface and compute the electrostatic profile of the free radical
SAM. We then superpose the electrostatic profile of these two systems after
aligning the vacuum level on the right part as shown in Fig. 4.9. In this figure,
the modulation of the work function due to the adsorption of the carbene-
mediated adamantane monolayers is reported. The work function of the metal
surface modified with the NHC1-functionalized adamantane was found to be
3.80 eV for Au(111), 3.26 eV for Ag(111), and 4.18 eV for Pt(111), respectively.
For the NHC2-ada molecule, the work function was 3.82 eV for Au(111), 3.30
eV for Ag(111), and 4.30 eV for Pt(111), respectively. For both SAMs, we find
a significant decrease in the work function of the order 37-38 % for Au(111),
36-38% for Ag(111), and 33-37 % for Pt(111). Overall, the work functions
62
4.2. Diamondoid mediated SAMs
-10
-5
0
5
metal
SAM/metal
SAM
-10
-5
0
5
-5
0
5
-5
0
5
-12
-6
0
6
0 5 10 15 20 25
normal axis z (Å)
-12
-6
0
6
E
 -
 E
 
(e
V
)
F
NHC1-ada/Au
NHC1-ada/Ag
NHC1-ada/Pt
NHC2-ada/Au
NHC2-ada/Ag
NHC2-ada/Pt
Figure 4.9: Plane averaged electrostatic profiles of the two different configura-
tions of carbene-functionalized adamantane SAMs on all three surfaces. The
labels denote the specifically modified surface for each panel. The zero energy
is set at the Fermi level of each system. In orange, pink, and cyan are shown
the electrostatic potentials of the bare metal substrate, the free molecule SAM,
and the whole system, respectively. The black arrows between the cyan and
the orange lines point to the work function shifts after adsorption.
for both SAMs and all three surfaces are very similar and differ only about
1-3%. For the NHC2-ada/metals the work functions are slightly higher and
can presumably be assigned to the presence of the additional two C3H7 ligands
in NHC2.
4.2.5 Surface morphology
In order to reveal the electronic and structural morphology of the metal sur-
faces, we looked into two additional features, the localization of the highest
occupied orbitals close to the surface and the simulated scanning tunneling
microscope (STM) images. In Fig. 4.11, the charge density distributions for
the HOMO after adsorption reveal the re-arrangement of the total electronic
charge due to the adsorption of the NHC-ada SAMs on the metal substrates.
From this figure, it is clearly evident that the occupied orbitals after adsorp-
63
Chapter 4. Self-assembled monolayers
Table 4.2: Bader charge analysis comparing the charges on the SAM and the
metal surfaces before and after adsorption. The first line denotes the modified
system. All values are given in electrons.
SAMs NHC1-ada NHC2-adaAu Ag Pt Au Ag Pt
NHC-ada +0.47 +0.31 +0.52 +0.48 +0.26 +0.51
metal -0.28 -0.10 -0.34 -0.25 -0.03 -0.31
tion are mostly localized next to the bonding sites of the carbene lower tip and
the surface of the metal. Qualitatively, no significant differences in the orbitals
for the Au and Ag modified surfaces were found. Nevertheless, the orbitals
tend to occupy the upper part of the carbene ring close to the adamantane in
the case of the modified Pt(111). We also observe that the charge in the case
of Pt(111) is spread over the whole carbene ring, which is not the case in the
modified Au(111) and Ag(111) surfaces. In the latter two cases, the charge
re-arrangement occurs mainly around the carbene atoms which are closer to
the metal surface and are involved in the bonding.
A Bader charge analysis was performed in order to reveal the effect of SAM
adsorption on the modified surfaces [102]. Specifically, we calculate the change
in the total charge in the molecule and the surface after the adsorption of the
molecule on the metal surfaces, compared to its total charge before adsorption.
All results are summarized in Table 4.2. The changes in the total charge due
to adsorption are given separately for the adsorbed molecule only (’NHC-ada’
in the Table) and the substrate only (’metal’ in the Table). Overall, the
surfaces have a negative change in their charge after adsorption, while the
NHC-ada molecules a positive change. This finding indicates that the charge
re-arrangement in the NHC-ada/metal structures is being done in a way to
move charge towards the molecule, an important property towards applications
like field-emission displays.
STM images
The application of a bias voltage between the tip and the NHC-ada/metal
when these are brought close to each other at a distance of a few angstroms
will enable the electrons to tunnel through the vacuum space between the two
surfaces. The electron flow is usually referred as tunneling current and is de-
pendent on three parameters: the distance of vacuum between the surfaces,
the applied bias voltage, and the local density of states. We keep the distance
of an STM tip at about 10 Å above the NHC-ada/metal surface along the
normal z-axis while scanning with the tip the XY-plane of this surface to pro-
duce a constant current. We consider a negative surface bias of -1 V in order
to sample all occupied surface states from this energy value up to the Fermi
level. This enables the measurement of the topography of the NHC-ada SAM
surfaces and reveals the STM images of all modified metal surfaces studied
here. In Fig. 4.10, we show the simulated STM images of all SAM-modified
64
4.2. Diamondoid mediated SAMs
Figure 4.10: In (a)-(c) the simulated STM images of the systems after adsorp-
tion of NHC1 on Au(111), Ag(111), and Pt(111), respectively are shown. Pan-
els (d)-(f) correspond to the simulated STM images of the NHC2 on Au(111),
Ag(111), and Pt(111), respectively. For the STM simulations, a negative bias
of -1 V was applied to the surface at a height of 10 Å above the surface.
metal surfaces. These images are produced by calculating the contour plots
of the tunneling current density on the plane parallel to the surface. From
this analysis, distinct bright spots corresponding to the carbene-functionalized
adamantane adsorbed to the surface are seen. A brighter spot is observed
in all STM panels on the atoms which are more involved in the bonding to
the surface. A similar behaviour to the charge re-distributions is evident in
Fig. 4.11 in terms of the molecular orientation of the carbene-functionalized
adamantane on the metal substrate.
The more extensive structure of the NHC2-ada is clear in the lower panels
of Fig 4.10. This feature is based on the additional C3H7 ligand in NHC2.
A slightly different orientation of both NHC1-ada and NHC2-ada on Pt(111)
compared to their orientation on the gold and silver surfaces is evident. Note,
that before structural relaxation all NHC-ada SAMs were placed with the same
orientation on all metal surfaces. Small differences in the bright spots in the
case of Pt(111) also denote different binding characteristics compared to the
Au(111) and Ag(111) cases. This is in agreement with the observation we
made based on Fig. 4.11(c) and (f), that the charge on Pt(111) involves the
whole carbene ring and not only the lower N-C-N atoms closer to the surface
as in the modified gold and silver surfaces. The different charge re-distribution
65
Chapter 4. Self-assembled monolayers
(a) (b) (c)
(d) (e) (f)
Figure 4.11: In upper panel (a)-(c) the re-distribution of the charge density of
the HOMO after adsorption of NHC1 on the metal surfaces Au(111), Ag(111),
and Pt(111), respectively are shown. Lower panels (d)-(f) depict the charge
re-distribution of the HOMO after adsorption of NHC2 on Au(111), Ag(111),
and Pt(111), respectively.
of the molecule on Pt(111) is also clear by comparing panel (f) to panels (d)
and (e) of Fig. 4.11. The shorter distance of the H atoms of the NHC2 ligand
to Pt(111) surface given in Table 4.1, link to a bonding of these H atoms to
the Pt surface. The adsorbate (NHC2-ada) orientation on Pt(111) changes
in order to facilitate this bonding. This is not the case in NHC1-ada/Pt for
which we also observe a different orientation with respect to NHC1-ada/Au and
NHC1-ada/Ag. The difference here is based on the observation in Fig. 4.11(c)
that the charge re-distribution in NHC1-ada/Pt involves the whole carbene
ring. Accordingly, the charge of the whole ring promotes (or is involved) in
the bonding and again the NHC1-ada needs to re-orient to account for this
additional attraction.
4.3 Discussion
In summary, we have successfully modelled the adsorption behaviour of carbene-
functionalized diamondoids on different metal surfaces. Au(111) and Pt(111)
were found to be the most efficient metal surfaces for adsorbing carbene-
mediated diamondoid SAMs than the Ag(111) surfaces. The weaker bonding
of Ag(111) was justified by the non-availability of the d-orbital of the metallic
first layer of the surface around the Fermi level. By comparing the molecular
66
4.3. Discussion
adsorption energies on reconstructed Au(111), Ag(111), and Pt(111) surfaces,
we conclude that these geometries are stable and of practical interest. Nev-
ertheless, carbene molecules have proven to be a better alternative to the
thiol-based bonding of diamondoids on metallic surfaces, opening up the path
for more stable and efficient SAMs/metal devices. Dynamic tuning of the work
function was easily achieved in NHC-ada/metal devices for organic electronic
applications. Finally, in this chapter we have demonstrated the possibility to
use small diamondoids to coat metal surfaces and assessed the search for opti-
mal anchoring of molecules on surfaces. Based on these findings and in view of
its electronic applications, we present a theoretical study of the diamondoid-
based molecular device in the next chapter.
67
Chapter 5
Diamondoid-based molecular
junction
In this chapter, we deal with the computational investigation of diamondoid-
based molecular conductance junctions and their electronic transport proper-
ties. A small diamondoid is placed between the two gold electrodes of the
junction and is covalently bonded to the gold electrodes through two different
molecules, a thiol group, and an N-heterocyclic carbene molecule. In sec-
tion 5.2.2, the transport properties of these devices and the influence on these
of different functionalizations, dopants, and diamondoid sizes are discussed.
Next, we perform a comparative study of various devices based on their elec-
tronic transport properties. We also present their structural and electronic
characteristics. In the end, we discuss the implications of our results on novel
nanotechnological applications of diamondoid-based molecular devices. Some
of the sections of this chapter are also the part of our published article "Bibek
Adhikari et al 2016 Nanotechnology 27 485207 c© IOP Publishing. Reproduced
with permission. All rights reserved".
5.1 Molecular junction
A molecular junction is simply defined as a system where a molecule or a col-
lection of molecules is embedded in between two probes or electrodes [103] as
sketched in Fig. 5.1. The major component of a particular junction is the
molecule that is embedded in between. The stability, conductance, transmis-
sion, and efficiency of the junction depends on the properties of molecules.
These molecules affect the bulk properties of the whole system. The fact
that diamondoids are used as building blocks and can be efficiently attached
on metal surfaces can naturally suggest their use in molecular conductance
junctions [2, 104–106]. The field of molecular electronics was introduced four
decades ago with the proposal of using a single organic molecule as a recti-
fier [107]. Since then, the idea that a molecule sandwiched between a metal
junction could be used as a sub-nanometer electronic component has been
vigorously pursued with the hope of replacing the existing silicon technology
in electronics applications as they approach device scaling limits [108–113].
68
5.1. Molecular junction
Z
Y
 Lead L
X
 Lead RScattering region
Figure 5.1: The setup for the transport calculations: the dithiol-diamantane
and the inner ten layers of the Au(111) (five on each side of the molecule
along the z-direction) determine the scattering region. This is in turn coupled
to semi-infinite leads (made of 3 layers of gold) on both sides. Electronic
transport occurs along the z-direction.
Doping and functionalization using boron and nitrogen have always been used
in the past to tune the electronic properties of such devices [114–118]. The
alteration and modification of transmission spectra are mainly due to the shift
in the energy levels of the electrode which resulted in the rectifying behavior
with respect to the applied source and drain voltage. [119–125] In our in-
vestigation, we study the influence of two different diamondoids (diamantane
and tetramantane), the type of dopants, and the diamondoid functionalization
on the properties of a metallic break-junction [126]. In such a device, a dia-
mondoid is inserted and bonded through the functionalization groups on the
metallic surfaces. For the electrodes, two Au(111) surfaces are taken. In order
to evaluate the effects mentioned above, we pick two representative lower di-
amondoid cases, diamantane, and tetramantane to vary the diamondoid size.
For tetramantane, one of the isomers, the [121]-tetramantane molecule was
chosen [1]. Boron (B), nitrogen (N) and boron with nitrogen (BN) are chosen
to separately dope the diamondoids. Accordingly, in the doping cases, one of
the carbon atoms of the diamondoid cages are replaced by one of the dopants.
For the functionalization molecules, we have used (a) a thiol group (commonly
used to attach diamondoids on a metal surface) and (b) the N-hetero-cyclic
carbene (NHC) molecule, a member of the carbene family [127].
Overall, we have considered a set of sixteen different diamondoid-based devices,
which differ in the diamondoid size (2 variations), the doping (4 variations -
3 doped and one undoped case), and the functionalization molecules (2 varia-
tions). These functionalized diamondoids chosen to be placed within the gold
junction are shown in Figs. 5.2,5.3. In the following, we use the notation ’diam’
and ’tetra’ for diamantane and (121)-tetramantane, respectively. ’X-doped’,
with X=B, N, and BN, denotes the doping of the diamondoid, while the term
’undoped’ is used for the undoped diamondoids. Note, that the diamondoids
are functionalized on both sides in order to bind to the Au(111) surfaces on
69
Chapter 5. Diamondoid-based molecular junction
a)
g) h)
e) f)
c) d)
b)
Figure 5.2: The relaxed atomic structures of the dithiol-molecules which will
be inserted in the gold nano gap. (a) dithiol diamantane, (b) dithiol tetra-
mantane, (c) dithiol B-doped diamantane (d) dithiol B-doped tetramantane
(e) dithiol N-doped diamantane (f) dithiol N-doped tetramantane (g) dithiol
BN-doped diamantane (h) dithiol BN-doped tetramantane. The color coding
for the atoms is set as follows: carbon(grey), hydrogen(cyan), nitrogen(blue),
boron(green), and sulphur(orange). This color coding will be used in the fol-
lowing.
70
5.1. Molecular junction
a)
g) h)
f)
d)c)
b)
e)
Figure 5.3: The relaxed atomic structures of the dicarbene-molecules which will
be inserted in the gold nano gap. (a) diNHC diamantane, (b) diNHC tetra-
mantane, (c) diNHC B-doped diamantane, (d) diNHC B-doped tetramantane
(e) diNHC N-doped diamantane (f) diNHC N-doped tetramantane (g) diNHC
BN-doped diamantane (h) diNHC BN-doped tetramantane. The color coding
for the atoms is set as follows: carbon(grey), hydrogen(cyan), nitrogen(blue),
boron(green), and oxygen(red).
71
Chapter 5. Diamondoid-based molecular junction
each side of the nano gap. Accordingly, the notations ’dithiol’, and ’diNHC’
denote the double functionalization using a thiol or a carbene (NHC) group.
The molecules are placed within the Au(111) junction and then relaxed. Five
5×5 Au(111) layers are used as the screening layer at each side of the surface
between the electrode and the molecule as depicted in Fig. 5.1. These Au(111)
surfaces together with the inserted molecule consist the scattering region (de-
vice). The device is coupled on either side to three outer layers of Au(111)
which form the semi-infinite leads. For the device relaxation, two inner atomic
layers of the Au(111) surface on either side of the molecules was also allowed
to relax to enable preferential binding. The other three outer layer of the de-
vice Au(111) were fixed at their bulk positions. Finally, for the fully relaxed
devices, electronic transport calculations were performed by means of coupling
to semi-infinite leads on either side, the results of which are discussed in the
next section. There is no direct tunneling across the Au(111) nano gaps for a
capacitor distance of 6 Å or more [128].
5.2 Diamondoid within a gold nano gap
Simulations based on the density functional theory (DFT) [129,130] as imple-
mented in the code SIESTA [59] were carried out. We have used the generalized
gradient approximation of Perdew-Burke-Erzernhof (PBE-GGA) [45], and the
norm-conserving Troullier-Martins pseudopotentials [52]. For the basis set, we
have considered a double-ζ with polarization basis set (DZP) for the molecules,
and a single-ζ with polarization (SZP) for the gold atoms (5d10, 6S1) which has
been proven efficient for similar setup [128]. An energy shift of 0.01 Ry with a
real space sampling grid (mesh cutoff) of 200 Ry. A Monkhorst-Pack k-points
mesh of 5× 5× 1 for the scattering region and 5× 5× 40 for the semi-infinite
leads were used. The Au(111) unit cell was fully relaxed and we obtained the
lattice constant of 4.186 Å which compares well with the data reported in lit-
erature [58]. The geometry optimization of the length of the scattering region
was performed using the conjugate gradient algorithm and the structure was
relaxed until the net forces on each component were lower than 0.01 eV/ Å.
The electronic transport calculations are performed using DFT combined with
the non-equilibrium Green’s functions (NEGF) formalism, as implemented in
the TranSIESTA [64] code. Bias dependent self-consistent calculations were
performed to obtain the current-voltage characteristics ranging from −0.9 V
to +0.9 V in steps of 0.1 V. The current (I) through the scattering region at
a bias (Vb) is calculated by integration of the transmission spectrum using the
Landauer-Büttiker formula [62]:
I(Vb) =
2e
h
∫ µL
−µR
T (E, Vb)[fL(E − µL)− fR(E − µR)]dE (5.1)
where T (E, Vb) is the bias dependent transmission probability of an electron
with energy E, and fL(E − µL), fR(E − µR) are the Fermi-Dirac distribution
for the left and right electrode, respectively. The electrochemical potential for
72
5.2. Diamondoid within a gold nano gap
Figure 5.4: Final relaxed structure for: (top panel) a dithiol-tetramantane and
(bottom panel) a diNHC-tetramantane in between Au(111) layers.
the left electrode is given as µL = EF +Vb/2 and µR = EF −Vb/2 for the right
electrode. The Fermi energy EF is shifted to zero.
5.2.1 Structural Characteristics
We begin our analysis with the structural details of the various diamondoids in
the gold nano gap. Representative devices are depicted in Fig. 5.4 for dithiol-
and dicarbene-diamondoid devices. In all devices studied here, the diamon-
doids are bonded to both electrodes through the mediating molecules (thiol
group or carbene). In Fig. 5.4 bottom panel), the molecules are attached to
the surface only through the lower carbon atom of the carbene ring. Two of
the H atoms of the NHC molecule (on both electrodes) are very close (≈ 2.80
Å) to the gold surface and interact weakly with the surface. The bond length
of the molecule to the surfaces is in the range of (2.64 − 2.90) Å for the
dithiol-diamantane and (2.61 − 2.92) Å for the dithiol-tetramantane cases,
respectively and corresponds to the S-Au distance. In the diNHC-diamantane
and tetramantane cases, the C-Au distance for both electrodes is in the range of
(2.19 − 2.20) Å and (2.19 − 2.21) Å, respectively. The dithiol-diamondoids are
less flexible within the junction compared to the diNHC-diamondoids, hence
the difference in the bonding behavior to the metal surface. This is also quali-
tatively observed through the orientation of the molecules with respect to the
setups before structural relaxation.
In the dithiol cases, the preferred bonding site for S-Au is on the fcc center
bonded with three gold atoms. In the NHC cases, the on-top site is preferred
73
Chapter 5. Diamondoid-based molecular junction
for the C-Au bond. We have observed that the gold atom bonded to the
NHC moves closer (and out of the surface) to the lower carbon atom of the
carbene ring as reported in previous studies [97,127]. This is slightly visible in
(Fig. 5.4 bottom panel). The flexibility of the C-O-C bond between NHC and
diamondoid allows for additional conformational variability during relaxation.
Here, though only a certain conformation will be examined for simplicity. Note,
that a slight off-lattice movement of the Au atom bonded to the sulfur atom
also in the dithiol cases was evident (see Fig. 5.4 top panel). Regarding the
doped diamondoids, very small changes of about 2 − 4% in the bond lengths
at the vicinity of the dopants were observed with respect to the undoped
diamondoid cases. However, since B and N are typical dopants for carbon
materials and have electronic configurations very close to C, no significant
alterations in the structures have been observed. These small changes, though,
have a higher impact in the electronic and transport properties as will be shown
next. Note, that according to our simulations, the electronic band gaps for the
isolated dithiol diamantane, dithiol tetramantane, diNHC diamantane, and
diNHC tetramantane molecules are 5.29, 5.36, 3.19 and 3.24 eV, respectively.
5.2.2 Electronic properties
We next probe the electronic properties of the diamondoid gold-junction de-
vices through the electronic density of states (eDOS) as obtained from our
transport calculations. Although, DFT does not lead to accurate values for
electronic band gaps, a qualitative comparison of the respective properties of
the different nano gaps studied here is possible. All systems show a metallic
behavior arising from the contribution of the gold electrodes and can accom-
modate the flow of electronic current across these devices. In Fig. 5.5, the
partial density of states (PDOS) for representative functionalized tetraman-
tane molecules within the gold junction is shown. The results are shown for
the energy range [−3.0,−2.0] eV, as actually all the interesting characteristics
are found in this range. In the graphs, the contributions of the gold electrodes
and the different elements in the molecules are depicted. Clear peaks in the
PDOS are visible. Focus on the dithiol-tetramantane device in Fig. 5.5(a)
shows very sharp peaks in the total DOS, which are related to peaks in the
contributions from the diamondoid (C and H atoms). The baseline of the total
DOS is associated with the contribution of the gold electrodes as in all cases.
The thiol groups have also a small contribution in the total DOS in the cases
of the dithiol-diamondoids. For dithiol-tetramantane doped with nitrogen, the
role of the dopant is also underlined by characteristic peaks. Very close to the
Fermi level (at −0.4578 eV), the N dopant defines the total eDOS (inset of
Fig. 5.5(b)). In this energy range, the eDOS in the ideal case is rather flat
manifesting the additional electronic states nitrogen is adding to the system.
The next peak close to −2.2 eV coincides with electronic states coming from
the diamondoid and its carbon atoms.
The eDOS characteristics for the carbene functionalization differ qualitatively.
74
5.2. Diamondoid within a gold nano gap
All peaks in the PDOS are associated with the presence of the nitrogen and
oxygen atoms in the carbene molecule as evident from Fig. 5.5(c) for the ideal
diNHC-tetramantane device. Compared to the ideal dithiol-tetramantane elec-
trodes, more peaks in the total eDOS are seen in the respective carbene case.
The additional electronic states are related to the presence of the carbene
molecules, while the contribution of the diamondoid, mainly through its car-
bon atoms is quite smaller. Specifically, the N and O atoms in the carbene
molecules are responsible for the additional features in the eDOS. Charac-
teristic electronic states arising from the nitrogen atoms are the ones closer
to the Fermi level (set at 0 eV) than the other peaks. These coincide with
states from the carbon atoms but are more pronounced. Again, the metallic
behaviour in the eDOS arises from the gold electrodes. For the nitrogen doped
diNHC-tetramantane electrodes in Fig. 5.5(d), the peaks are lower compared
to the ideal case. The addition of the nitrogen dopant does not significantly
change the eDOS features, as this atom is only an excess N to the already
existing four N atoms of the carbene molecule. In this respect, the electronic
states corresponding to N are already characteristic of the eDOS in the ideal
case. Actually, the ideal and nitrogen doped diNHC-tetramantane cases have
the first peaks in their eDOS at lower energies (−1.70 and −1.23 eV, respec-
tively). These peaks are dominated by the contributions from the N and O
atoms of the carbene molecule and the C atoms of the tetramantane. The
doping with nitrogen shifts the first DOS peak about 0.5 eV towards the fermi
level. In this first peak for the N-doped diNHC-tetramantane, the O atoms
do not play a significant role. Their role is rather manifested in the second
peak. This second peak is shifted about −0.12 eV lower than in the undoped
diNHC-tetramantane case.
5.2.3 Electronic transport
Next, the electronic transport across the diamondoid junctions are analyzed.
The quantum transport calculations lead to the calculated zero-bias trans-
mission functions, T(E, V = 0) summarized in Fig. 5.6 for all cases studied
here. The electronic transport across the molecule is strongly influenced by
the choice of the functionalizing group through which the molecule is attached
to metal. We begin by investigating the effect of different functionalization
groups: the dithiol (Fig. 5.6 top panel) and diNHC cases (Fig. 5.6 bottom
panel) for undoped diamondoids on the transmission function. The first obser-
vation is that the transmission at the Fermi level for all dithiol diamondoids
is at least six orders of magnitude higher in comparison to their diNHC coun-
terpart. The zero bias conductance ( G = 2e2
h
T (EF )) for undoped di-thiol
diamondoids is summarized in Table 5.1 and are comparable to the values
reported for pi-conjugated organic compounds [131]. Consequently, with an
applied bias voltage, a dithiolated diamondoid is expected to lead to a higher
current flow in comparison to the diNHC counterpart. In all the undoped
cases, the first transmission peak (HOMO) is found to be further away from the
Fermi level. The HOMO levels are at -2.53 eV, -2.10 eV, -3.21 eV and -2.87 eV
75
Chapter 5. Diamondoid-based molecular junction
Au
C
H
S
Tot
N
O
-3 -2.8 -2.6 -2.4 -2.2 -2 -2.8 -2.6 -2.4 -2.2 -2
P
D
O
S
 (
ar
b
. 
u
n
it
s)
Energy (E - E
F
) (eV)
(a) (b)
(c) (d)
-0.9 -0.6 -0.3 0
Figure 5.5: Partial density of states (PDOS) are given for the following molec-
ular junctions: (a-b) dithiol- tetramantane and (c-d) dithiol N-doped tetra-
mantane. The contributions of the molecule, the electrodes, and the dopants
are shown together with the total DOS. The Fermi level is set at 0 eV.
for dithiol-diamantane, dithiol-tetramantane, diNHC-diamantane and diNHC-
tetramantane, respectively. The effect of dopants on the zero-bias transmission
function can also be seen in Fig. 5.6. The diNHC-based doped diamondoid
junctions have resonance peaks (Fig. 5.6 bottom panel) far below the Fermi
level (beyond the range of a practical bias voltage window) similar to the un-
doped case. This is not the case with the dithiol-based doped junctions. In all
dithiol cases, the transmission is higher for the N-doped diamondoids, which is
not the case in the diNHC cases. In order to understand this further, we turn
to the nitrogen doping on dithiol-based tetramantane junctions (Fig. 5.6 top
right panel). The first transmission peak below the Fermi level (HOMO) in this
case is found at around −0.45 eV. The calculations revealed that the resonance
peak (at −0.4578 eV) in the projected density of states (PDOS) corresponds
to a density of states contribution from nitrogen doping. The lowest unoc-
cupied molecular orbital (LUMO) is far from the Fermi level in all the cases.
We only observe prominent peaks of the LUMO beyond 2.5 eV for the dithiol
cases and beyond 2.0 eV for the diNHC cases respectively. In this respect, the
LUMO level is not of high importance to the conduction within a bias window
practically accessible in experiments. BN and B doping does not lead to any
improvement in the zero bias conductance of dithiol junctions as also easily ob-
served in Table 5.1. Interestingly, the B-doped diNHC-tetra junctions show the
highest zero bias conductance compared to all the diNHC-tetra cases. How-
ever, all zero bias conductance values for all diNHC-diamondoid electrodes are
at least five orders of magnitude lower than the respective dithiol-diamondoid
76
5.2. Diamondoid within a gold nano gap
undoped
B-doped
N-doped
BN-doped
10
-10
10
10
10
10
0
-2
-4
-6
-8
10
10
-3
10
10
10
1
0
-1
-2
10
T
ra
n
sm
is
si
o
n
Energy (E - E
F
) (eV)
-1.0 0.0 1.0 -1.0 0.0 1.0
Figure 5.6: The zero-bias transmission function is plotted on a semi-log scale
for all diamondoid-based devices studied in this work. In the top panel, data
for the dithiol diamantane (left) and dithiol tetramantane (right) based devices
are depicted. In the bottom panel, data for the diNHC diamantane (left) and
diNHC (right) tetramantane devices are shown. The colors in the legends
denote whether the diamondoids are doped or undoped.
cases. The respective values for the zero bias conductance at the Fermi level
for all nano gaps studied here are summarized in the bar charts of Fig. 5.7.
The results are shown as a relative conductance using two different references:
(a) the case of the undoped diamondoid for each type of the device and (b) the
N-doped dithiol tetramantane nano gap, which is the ’best’ transmission case
showing the highest transmission closer to the Fermi level. Negative values
correspond to a lower transmission with respect to the reference device. In
case (a), the significance of doping with nitrogen is high for both the dithiol-
and diNHC-diamondoid electrodes considered here (left panel of Fig. 5.7).
Doping with boron shows a much larger conductance at the Fermi level only
Table 5.1: Conductance in units of 2e2/h at zero bias for the modified diamon-
doid junction at the Fermi level. The higher transmission for each junction is
given in boldface text.
type dithiol-diam dithiol-tetra diNHC-diam diNHC-tetra
undoped 6.94×10−3 1.77×10−3 4.34×10−9 8.00 ×10−10
B-doped 5.11×10−3 1.50×10−3 2.29 ×10−9 2.29×10−9
N-doped 1.67×10−2 2.49×10−3 5.55 ×10−9 3.81×10−10
BN-doped 6.65 ×10−3 1.36×10−3 1.10 ×10−8 3.02×10−10
77
Chapter 5. Diamondoid-based molecular junction
for diNHC-tetramantane, while doping with BN shows a much higher trans-
mission for the diNHC-diamantane device. In case (b), the behavior of all
devices is similar (right panel of Fig. 5.7). The decrease in the conductance
shows a very clear trend, moving from the undoped diamondoids to B-, N- and
BN-doping with respect to the dithiol N-doped diamantane. All diamondoid-
based electrodes at the Fermi level have a much lower conductance, with a
decrease up to 400% for the BN-doped diNHC-tetramantane case. The lowest
decrease in the conductance was found for all the ideal undoped diamondoids,
followed by the B-doped cases. The size of the diamondoid also seems to affect
Figure 5.7: Bar charts of the conductance at zero bias for the modified-
diamondoid nano gaps at the Fermi level compared to reference cases. In (a)
the undoped diamondoid device for each functionalized-diamondoid is taken as
the reference. The energy of all the ideal cases has been shifted to zero. In (b)
the N-doped dithiol diamantane case with a transmission value of 1.67 ×10−2
was taken as the reference. The energy for the dithiol N-doped tetramantane
electrodes has been shifted to zero.
the transmission. This is evident in the dithiol cases, in which the larger dia-
mondoid (tetramantane) shows sharper transmission peaks (below the Fermi
level) for the N- and BN-doped cases compared to the smaller diamantane,
as seen in the top panel of Fig. 5.6. Nevertheless, in the diNHC cases, the
transmission peaks are similarly sharp for both diamondoid sizes (lower panel
of the same figure). In the latter cases, the transmission peaks of the N- and
BN-doped diamantane are much broader, though almost at the same ener-
gies as in the respective tetramantane cases. The different features for the
diamondoid sizes indicate that the increment in the size of diamondoids has
an effect on the localization of the HOMO resonance peak close to the Fermi
level. Overall, though the thiol-diamondoid devices show a larger transmission
closer to the Fermi level, there are energy ranges in which the diNHC devices
can better accommodate the flow of current. This happens, for example, lower
than −1.5 eV in the diNHC B-doped tetramantane devices, as compared to the
78
5.2. Diamondoid within a gold nano gap
respective dithiol case. The zero bias conductance values presented in Table
5.1 imply that the conductance across the two dithiol-diamondoid junctions
is of the same order of magnitude, but slightly larger for the smaller diaman-
tane. Both the N-doped dithiol diamantane and N-doped dithiol tetraman-
tane cases show the zero bias conductance of 1.67×10−2G0 and 2.49×10−3G0,
which is comparatively higher with respect to the previously investigated sys-
tems [109]. The respective value for the N-doped tetramantane case, though,
is still higher than the values of the other tetramantane cases. This suggests
that diamondoids could be used as a molecular conductance junction in the
design of highly functional devices. In order to further understand the un-
doped vs doping among the dithiol-tetramantane junctions, we have plotted
the eigenchannel wavefunctions (EWF) [132]. For the undoped, N-doped and
BN-doped dithiol-tetramantane cases, these are plotted in Fig. 5.8, each at
two different energies. The EWF plotted correspond to the Fermi level at 0
eV and the first transmission peak below the Fermi level i.e. at −2.10, −0.45
and −0.68 eV for the undoped, N-, and BN-doped cases respectively. At the
Fermi level, due to finite transmission (of the order of 10−3 according to Fig.
5.6), the EWF are localized towards the left of the device and then decay off
in the transport direction. The peaks in the transmission across the doped
dithiol-tetramantane junctions in Fig. 5.6 (top panel) correspond to a strong
electronic coupling between the two electrodes as depicted in Fig. 5.8. For
both the doped dithiol-tetramantane junctions, the EWFs spread out across
the whole device region. In the undoped case, the molecular orbital corre-
sponding to strong electronic coupling is far below the Fermi level. Hence,
doping shifts transmission peaks closer to the Fermi level, which might con-
tribute to conductance in a practically accessible bias voltage region. A further
comparison of the dithiol N-doped tetramantane to the B-doped tetramantane
and the respective doped diNHC-tetramantane cases is given in Fig. 5.9.
The energy (−0.4578 eV) corresponding to the first transmission peak for the
dithiol N-doped tetramantane junction Fig. 5.6(b) is taken. At this energy, the
transmission curves of the other cases in Fig. 5.9 are very low. Hence, a strong
coupling of the electrodes in the dithiol N-doped tetramantane is evident as
the EWFs are spread out across the electrode surfaces and the functionalized
tetramantane. At this energy, the EWFs of the diNHC doped cases are asso-
ciated with the left electrode with a small contribution coming from the left
carbene molecule. No electronic current is flowing through these devices at
the specific energy. In the dithiol B-doped tetramantane electrodes, the EWFs
are more extended over the thiol group and half of the diamondoid, but no
coupling of the two electrodes is observed, thus no current flow can occur.
Finally, we observe a qualitative difference in the electronic coupling of the
dithiol and diNHC cases. For example, in the dithiol B-doped tetramantane
case, the wavefunctions are more spread-out, covering half of the diamondoid.
This is not the case in diNHC B-doped tetramantane, in which the EWFs
are spread-out only up to the first carbene molecule and its oxygen atom.
The same is observed in the respective diNHC N-doped case. These features,
79
Chapter 5. Diamondoid-based molecular junction
c)
0.00 eV -0.45 eV
0.00 eV -0.68 eV
0.00 eV -2.10 eVa) b)
c) d)
e) f)
Figure 5.8: Eigenchannel wavefunctions for the dithiol-tetramantane devices:
(a-b) undoped dithiol tetramantane, (c-d) N-doped dithiol tetramantane and
(e-f) BN-doped dithiol tetramantane each shown at the energy given in the
label. ’0.00’ eV corresponds to the Fermi level. The plots in the right panels
correspond to the first transmission peaks (HOMO) below the Fermi level for
each setup. For clarity, all wavefunctions are plotted for the same isovalues.
Positive values of the wavefunctions are in red and negative in blue.
80
5.3. Current-Voltage Characteristics
again manifest, the importance of the different structural characteristics of the
molecules on the transport details of the devices. Our results suggest, that a
careful choice of the molecule and the gating voltage in the experiments can
tune the current flow through such a diamondoid-based molecular device.
c)
(a) (b)
(c) (d)
Figure 5.9: Eigenchannel wavefunctions comparing the doped dithiol-
tetramantane and doped diNHC-tetramanane cases at the energy (−0.4578
eV) corresponding to the first peak in the transmission of the dithiol N-doped
tetramantane. The (a) dithiol N-doped tetramantane, (b) dithiol B-doped
tetramantane, (c) diNHC N-doped tetramantane, (d) diNHC B-doped tetra-
mantane are depicted. For clarity, all wavefunctions are plotted for the same
isovalues (0.01 eV). Positive values of the wavefunctions are red and negative
in blue.
5.3 Current-Voltage Characteristics
As a further analysis to understand the effect of doping, we report on the I-V
curve for undoped and N-doped dithiol-tetramantane junctions. We focus on
the bias-dependent transport properties of the junctions. We will also report on
the shift of the zero-bias ’reference’ transmission peak at −0.45 eV seen in (Fig.
5.6 top right panel) with respect to applied voltage bias. The current-voltage
(I-V) curves for two different cases a) dithiol tetramantane and b) N-doped
dithiol tetramantane are shown in Fig. 5.10. The asymmetric behavior of
the current at positive and negative bias in the range [−0.9,+0.9] V for both
the junctions, investigated in our work is evident from the I-V characteristic
81
Chapter 5. Diamondoid-based molecular junction
depicted in the upper panel of Fig. 5.10. The current in both the undoped
and doped cases seems to increase with the application of higher bias. There
is a clear distinction in the current for the undoped and doped cases. The
distinction being that the current in doped case is even more pronounced,
when we increase the bias in both positive and negative direction. For the
undoped case the current increases and reaches up to a maximum of ±0.087
µA for the applied bias voltages. However in the doped case, the current
was found to be −0.124 µA for −0.9 V and 0.128 µA for +0.9 V. In order
Bias (V)
C
u
rr
e
n
t 
(
µ
Α
)
 1.10
-0.10
 0.00
 0.10
 0.20
 1.08
 1.06
 1.04
 1.02
 1.00
 0.0
-0.20
-0.2-0.4-0.6-0.8  0.2  0.4  0.6  0.8
 0.0  0.2  0.4  0.6  0.8
 1.0 -1.0
 1.0
Bias (V)R
e
c
ti
fi
c
a
ti
o
n
 r
a
ti
o
 (
R
R
)
N-doped dithiol tetra
undoped dithiol tetra
Figure 5.10: I-V characteristics (top panel) and rectification ratio (bottom
panel) of undoped dithiol tetramantane (red) and N-doped dithiol tetraman-
tane (blue) based junctions at different bias voltages close to the Fermi level.
to compare the efficiency of doped devices, we have defined the rectification
ratio (RR) as : RR(V ) = |I(V )/I(−V )|. Our aim was to use RR as a means
to gain a qualitative understanding of the influence of doping and guide the
experiments towards a direction which would certainly affect the rectification.
Our work is not intended to fully evaluate in a quantitative way the rectification
effect. For this, a more extended study including additional molecules would
be needed. The rectification ratios for both the undoped and doped cases are
shown in the lower panel of Fig. 5.10. Dithiol N-doped tetramantane-based
junctions show a higher rectification ratio for the bias voltages applied in this
work as compared to the undoped case. We observe a sharp increase in the
rectification from 0.1 V up to 0.4 V. The highest efficiency of the junction
is found to be at 0.6 V, at which the rectification ratio is found to be 1.07.
There is a sudden drop at 0.7 V where the efficiency decreases up to 1.06.
A similar drop is also observed for 0.9 V where the (RR) drops to 1.03. In
82
5.3. Current-Voltage Characteristics
the undoped case there is a drop in the (RR) at 0.5 V, but interestingly a
minor increase in the efficiency is seen at a higher bias, unlike the doped case.
A comparison of the transmission spectra under applied bias is depicted in
Fig. 5.11. We present the plots for 0 V, ± 0.6 V, and ± 0.9 V respectively.
For both the undoped and N-doped cases, we can observe an increase in the
conductance at the Fermi level for ± 0.9 V. We also observe notable peaks for
the positive energy range in the transmission spectrum. However, these are
not related to the LUMO levels, which are further away from the Fermi level
and not in the practically accessible range, as also previously discussed for the
zero-bias transmission spectra. At this point, there is no strong indication of
the origin of these small peaks and a further investigation is needed. In case
of the undoped case the molecular conductance was found to be 2.92×10−3G0
for +0.9 V and 2.94×10−3G0 for −0.9 V respectively. Similarly, for the doped
case the molecular conductance (Fermi level) was found to be 3.15×10−3G0
for +0.9 and 3.33×10−3G0 for −0.9 V, respectively.
10
-2
10
0
10
-2
10
0T
ra
n
sm
is
si
o
n
0 V
0.6 V
-0.6 V
0.9 V
-0.9 V
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4
Energy (E - E
F
) (eV)
Figure 5.11: Transmission spectra as a function of the applied bias for undoped
dithiol tetramantane (top panel) and N-doped dithiol tetramantane (bottom
panel).
As observed in the lower panel of Fig. 5.11, there is a characteristic shifting
of the zero-bias ’reference’ transmission peak with respect to the applied bias.
The shift in the positive and negative bias for the N-doped dithiol tetramantane
case results in rectification. After the comparison of shift for the reference
peaks among symmetric bias voltages (for example: -1, +1 V), we observe
that the shift for the positive bias up to 0.6 V is only slightly perturbed with
respect to the zero bias reference peak. Further increasing the positive voltage
bias moves the reference peak away from the zero bias case towards left. One
83
Chapter 5. Diamondoid-based molecular junction
can also observe that the bias dependent conductance at the Fermi level for
−0.9 is higher compared to its positive counterpart i.e +0.9. Combinations
of these factors could contribute to lowering of rectification ratios beyond an
applied bias of 0.6 V.
5.4 Discussion
Overall, in this chapter we have investigated certain conformations of the mod-
ified diamondoids within the gold nano gaps. Our aim was to provide a proof
of functioning principles for such molecular junctions. For a more extensive
analysis, a conformational scan of the molecules would be needed, which could
be the subject of a separate study. If a careful choice of the materials is made,
it can lead to highly functional devices with desired properties. Our work indi-
cates that the search for the molecule intended to fill a metallic junction should
be made with care, as small modifications in its structure significantly influ-
ence the properties of a diamondoid-based molecular device. Finally, we have
manifested the use of diamondoids in molecular devices and their rectification
effect.
84
Chapter 6
Conclusions and outlook
The main result of this work is the possibility to selectively tune the electronic,
transport, and optical properties of diamondoids by means of structural and
chemical modification. Doping and functionalization were used to modify these
small diamondoids. Using both DFT and TDDFT, we found out that the tun-
ing of the band gap of these modified diamondoid complexes was possible
through doping and/or functionalization. We observe that different dopants
and functional groups lead to interesting conduction and optical properties.
Double functionalization as compared to a single-functionalization was found
to further decrease the band gap moving it closer to the semiconducting re-
gion in the ground state and towards the visible region in the excited state.
Subsequently, synthesizing diamondoid complexes of a various size and mod-
ification has the potential to tune their conduction or optical properties. In
terms of industrial applications, the presence of doping and functional groups
provides additional functional properties. Functionalized diamondoids include
sites which not only tune their properties but also provide binding sites to
other structures. The fact that a double functionalization leads to a larger
increase in the conduction and optical properties provides the potential to
form novel diamondoid-based devices which include one functional group for
the attachment of diamondoid on the device and another atomic group which
provides the diamondoid with functionalities.
Modelling the adsorption of carbene-functionalized diamondoids on metal sur-
faces led to interesting results. Two different form of N-hetero-cyclic carbenes
were used as an alternative to thiol-based SAMs. Au(111) and Pt(111) were
found the most efficient metal surfaces for adsorbing carbene-mediated dia-
mondoid SAMs. Orbitals of d-symmetry were essential in order to have orbital
overlapping with carbon p-electrons and bond formation as in the case of the
Au(111) and Pt(111) surfaces. In Ag(111), the weaker bonding was justified
by the non-availability of the d-orbital of the metallic first layer of the surface
around the Fermi level. Calculation of the work functions of carbene-mediated
diamondoid SAMs on Au(111), Ag(111), and Pt(111) surfaces demonstrated
that the modulation of the work function with respect to the properties of clean
metal surfaces and a dynamic tuning can be easily achieved in NHC-ada/metal
85
Chapter 6. Conclusions and outlook
devices for organic electronic applications. The charge re-distribution and the
simulated STM images of the surfaces showed that on Pt(111) the whole car-
bene ring of the NHC-ada molecule is associated with the SAM/metal bonding,
increasing the adsorption energy of SAMs. By comparing the molecular ad-
sorption energies on reconstructed Au(111), Ag(111), and Pt(111) surfaces, we
conclude that these geometries are stable and of practical interest. However,
it is essential to examine the thermal stability of these structures and the in-
fluence of environmental conditions on their stability. Nevertheless, carbene
molecules have proven to be a better alternative to the thiol-based bonding
of diamondoids on metallic surfaces, opening up the path for more stable and
efficient SAMs/metal devices. Based on these findings and in view of elec-
tronic applications such as field emitting devices or sensors, optical properties
of carbene-mediated SAMs on metal surfaces need to be investigated.
Electronic transport across molecular junctions made up of functionalized and
doped diamondoids were also studied in this work. The comparison of the
results was discussed based on the functionalization, the type of dopants, and
the size of diamondoid. The dithiol linker group was found to be efficient
as compared to a carbene group attached to the Au(111) nano gap. The zero
bias transmission function of the undoped diamondoid systems reveals that the
HOMO peaks are away from the Fermi level, which is beyond any practical
voltage bias window (-1 to +1 V). We have selectively tuned the electronic and
transport properties of the diamondoid-based molecular junctions by doping
the molecules of boron and nitrogen. The doping with nitrogen leads to an
addition of a transmission peak very close to the Fermi level leading to higher
molecular conductance. Increasing the diamondoid size leads to a slight de-
crease in the zero bias conductance. Such a decrease was also observed when
using the carbene molecules as a linker of the diamondoid on the nano gap
surfaces. Bias dependent transport calculations revealed that doping leads to
a higher rectification ratio at very small applied bias voltages. This behavior
is the result of the energy shift of the HOMO peaks with respect to the zero
bias case. Overall, the rectifying effect in N-doped diamondoids is related to
the asymmetry in the structure when introducing the dopant. Since a similar
asymmetry is introduced by means of doping in the case of B and B-N co-
doping, we can assume that a similar rectifying behavior is observed also for
these latter cases. Nevertheless, a separate study needs to be carried out to
further quantify these effects.
The investigation carried out here has an impact on the design of novel molec-
ular devices for electronics and sensing applications. A careful choice of the
materials can lead to functional devices with desired properties. Our work
indicates that the search for the molecule intended to fill a metallic nano gap
should be made with care, as small modifications in its structure significantly
influence the properties of the molecular device. The use of a simple thiol
group for grafting the diamondoid on metal electrodes typically leads to high
electronic transmission. When a smaller transmission is desired the use of
86
molecules such as N-heterocyclic carbene is more suitable. Similarly, when a
larger conductance is needed further away from the Fermi level, than the NHC
molecule can be more efficient.
Overall, our results have shown that the choice of doping, functionalization,
as well as the choice of the molecule in the metal nano gap, could allow a very
specific tuning of the whole device by unveiling the electronic functionalities
of the single molecules. Specifically, the binding of the molecule on the gold
electrodes is crucial in controlling the flow of electrons from one electrode to
the other by introducing additional electronic states for promoting the elec-
tronic transport and increasing the conductance across the device. Additional
investigations should further quantify the effect of structural fluctuations of
the molecule in the device on the signal-to-noise ratio in the electronic mea-
surements. This issue was not tackled here but is expected to have a great
impact on the efficiency of the molecular device. These investigations need to
be supplemented by research at the circuit level in order to prove their optimal
functionality. It would also be very interesting to investigate the properties of
these modified diamondoids attached to a polymer backbone. Such a study
would be very promising in view of practical applications using polymer-based
electronics. Based on our findings and in view of electronic applications such as
field emitting devices or sensors, optical properties of carbene-mediated SAMs
on metal surfaces need to be investigated. In the end, it is chemically possible
to produce modified diamondoids of different sizes. What remains to be done
is to use these in novel applications along the above lines. This thesis clearly
showed the suitability of diamondoids for such applications.
87
Appendix A
Promoting assembly of carbon
onions
In this chapter, we perform atomistic simulations at two levels, classical and
quantum-mechanical in order to probe the binding possibilities of the smallest
multi-shelled concentric fullerenes, known as carbon onions. We focus on the
binding behavior of adjacent carbon onions and promote their binding through
the addition of vacancies, as well as through doping with boron and nitrogen
atoms. Molecular dynamics (MD) simulations are used to address the effect of
different conditions of temperature and pressure on the binding of the onions
and the thermal stability of the assembled structure. At a smaller scale, den-
sity functional theory (DFT) based calculations reveal the electronic structure
of the coalesced carbon onions, their charge density, and frontier orbitals. Our
main finding is that binding of adjacent carbon onions is promoted through
the addition of vacancies and/or dopants on the outer surface of the carbon
onions. The results are evaluated with respect to the relative distance between
the adjacent carbon onions, the number of vacancies, and the amount or type
of doping. We aim to optimize the conditions for assembling these nanoscale
building blocks and understand their corresponding electronic properties in
view of their potential in nano-assembling novel functional nanomaterials. In
section A.2, we present the methodology applied for the study of small car-
bon onions. Next, in section A.3 we discuss the binding possibilities, various
factors which guide coalescence and the corresponding electronic properties
and conclude in the final section A.4. This appendix is the part of our pub-
lished article "B. Adhikari et. al. Phys. Status Solidi A 211, No. 2, 277–287
(2014) Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with
permission. All rights reserved".
A.1 Introduction
The discovery of novel unconventional forms of carbon with fullerenes [133,134]
and carbon nanotubes [135] being the most representative examples led to a
potential broader use of carbon materials in various kinds of applications rang-
ing from electronic devices to drug delivery. Within this new era of carbon
88
A.1. Introduction
materials, carbon onions were synthesized [136]. These are concentric multi-
shelled fullerene clusters held together by van der Waals forces and are built
up of spherical graphene layers of up to a few nanometers in size [137–144].
Carbon onions are considered to be the most stable among the carbon nanos-
tructures [145]. The smaller carbon onion is that with a C20 fullerene in the
core [146]. The onion-like graphite nanoparticles can occur in a wide range of
structures, from polyhedral to nearly spherical ones [147]. The striking impor-
tance of these carbon structures is that these can give a complete insight into
the mechanism by which carbon atoms rearrange themselves [148]. Carbon
onions can also be viewed as nano-building blocks with important applica-
tions in nanotechnology. The potential possibilities of tuning the electronic
and mechanical properties by stuffing the hollow graphitic onions with met-
als or also doping the carbon sheets themselves with atoms such as boron
seem endless [149,150]. The spherical structure of carbon onions can be better
described through the existence of pentagon-heptagon pairs [151–153], rather
than hexagons and heptagons [154,155]. Continuous loss of atoms due to sput-
tering induces a self-compression of the spherical carbon onions, which allows
diamond to nucleate in the core of the carbon onions [156]. Existing studies
have revealed the field emission characteristics [157], conductivity [158], optical
and tribological properties of carbon onions [159], their potential use as solid
lubricants, gas storage [160], supercapacitor electrode materials [161], while
they have good wear behavior, and buckle under hydrostatic pressure [162].
Carbon onions are often produced under extreme conditions and become strongly
interlinked or coalesced. This inter-linking is fundamental in understanding
new synthetic routes to selected carbon onion sizes and encapsulation com-
pounds. Coalescence is optimal for building novel materials from nano-building
blocks like carbon onions and render these particles candidates for molecular
electronics and composite materials applications [163]. Coalescence of spheri-
cal graphitic-like molecules was observed in nanotubes, where the encapsulated
fullerenes self-assembled in chains [164,165] forming a tubular structure [166].
The fullerene chains, which initially interact through van der Waals forces co-
alesce into interior tubes after high-temperature annealing [163] or when sub-
jected to high electron flux [167]. Theoretically, the topological rearrangements
that lead to coalescence of fullerene cages have been tracked [168]. Fusion of
fullerenes can also occur through molecular collision processes [169–171]. Car-
bon nanotubes have also been observed, both theoretically and analytically, to
coalesce. It was found that a zipper-like mechanism for coalescence can proceed
through the existence of vacancies on the nanotubes allowing the carbon atoms
to reorganize [172]. Along these lines, joining nanoscale units is of fundamental
and practical importance. Along these lines, we focus on the bonding possibil-
ities of carbon onions. In order to render carbon onions into building blocks in
nanotechnology, a controllable way to connect these units together is needed.
It is of high importance to qualitatively understand how the properties of car-
bon onions are altered because of their coalescence is of importance. In this
work, we try to understand and tune the binding possibilities of two adjacent
89
Appendix A. Promoting assembly of carbon onions
carbon onions by evaluating the effects of pressure, temperature, the number
of vacancies (experimentally induced through electron irradiation), separation
distance, as well as amount and type of doping.
A.2 Methodology
A multi-level approach for the investigation of the binding possibilities of small
carbon onions. Specifically, the focus is based on the effect of the external con-
ditions on their binding, as well as how this binding influences the electronic
properties of the isolated carbon onions. Within our approach, a density-
functional theory based simulations, as well as Molecular Dynamics are used.
The results obtained from each calculation are complementary and give a wider
overview on the binding possibilities of small carbon onions. At the smaller
scale, a density functional theory (DFT) based scheme is used as implemented
in the SIESTA code [59], in which the Kohn-Sham eigenstates are expanded
using a linear combination of atomic orbitals as the basis set. We use norm-
conserving Troullier-Martin pseudopotentials [83] and a split valence double
zeta polarized basis set. A mesh cutoff parameter (which corresponds to the
fineness of the real space grid) of 200Ry has been found to be optimal for the
calculations. We have been using the exchange-correlation functional VDW-
DF2 [173]. Due to the explicit inclusion of a strictly non-local correlation term,
this functional is found to describe dispersion interactions with improved accu-
racy in comparison to a semi-local generalized-gradient-approximation (GGA)
functional [174]. The geometry optimization was performed using the conju-
gate gradient algorithm and the structure was relaxed until forces on the atoms
were lower than 0.04 eV/Å. We refer to these calculations as static DFT in
the following. In addition to the static DFT calculations, we also performed
ab initio Molecular Dynamics (MD). (We refer to these as ab initio MD or
DFT-MD in the following sections.) For these simulations, a time step of 1.0
fs was used and the total simulation time varied between 2-5 ps. The temper-
ature was set at 2000 K and a Nose´ thermostat was used to ensure that this
temperature is reached. No pressure is applied in the DFT simulations.
At a next level, classical Molecular Dynamics simulations are performed as
implemented in the code LAMMPS [175], which performs well for materials
calculations. For the intra-molecular (among atoms on the same fullerene)
interaction, the bond-order Tersoff potential [176] is used. This potential has
been widely and efficiently used in simulations of various forms of carbon struc-
tures. The Tersoff potential includes also parameters for boron and nitrogen
atoms [177], which are used here as dopants. For the inter-molecular (among
atoms of the inner and outer fullerenes) interactions, a Lennard-Jones type of
potential is implemented. For this potential, parameters are taken which have
been previously published in the literature [178]. The simulation box is cubic,
with an edge length ranging between 3-10 nm. Periodic boundary conditions
are applied and the system is large enough so that finite size effects are not sig-
nificant. The time step of the simulations was set at 1.0 fs and the typical time
90
A.2. Methodology
for gathering statistics was 1 ns. Two types of simulations are being performed
in order to unveil the role of temperature and pressure in the binding process
of the two onions. Accordingly, our simulations are done separately under two
statistical ensembles, the (N,V,T) and the (N,P,T) ensemble. We fix always
the number of particles N in the (N,V,T) ensemble we fix the pressure at 0
bar and perform different simulations with temperatures ranging from 500 K
- 3500 K. Similarly, we set the temperature at 1000 K and 2000 K and per-
form different simulations with the pressure ranging from 0.01 bar to 10 bar.
In our simulations we have used Nose´-Hoover thermostat and barostat. We
refer to these calculations as empirical or classical MD in the following sections.
We have applied the computational schemes mentioned above to study the
binding possibilities of two small carbon onions, namely two adjacent C20@C96.
Each onion has an inner fullerene, the C20 which is concentric with an outer
larger fullerene, the C96. For the C96 we randomly chose one of its isomers,
namely, #96 with the C2 point group symmetry. The random choice was
based on the fact that all isomers could accommodate the inner C20. We have,
though, performed test simulations with another isomer, the C96(D3h) and
have seen that the results do not change qualitatively.
We have modelled these small structures instead of larger ones for computa-
tional efficiency. The diameter of the carbon onion (the outer C96) is 9.7 Å,
while the diameter of the inner (C20) fullerene is 3.7 Å. Accordingly, the dis-
tance between the inner and outer fullerenes is about 3.0 Å. Note, that here the
smallest carbon onion is modelled and this includes only 5- and 6-fold rings,
rather than 6- and 7-fold rings as in the case of larger carbon onions [151–153].
The two carbon onions are placed at close distances. This distance was var-
ied in order to promote the binding more easily and found that an initial 1.8
Å separation could lead to binding of the two carbon onions under specific
conditions. Using an initial larger separation would increase the computational
time and would also require a collision process, i.e. an initial velocity assigned
to each onion in order to move towards each other. We wanted to avoid this
and rather placed the carbon onions closer together. Nonetheless, here, we
are interested in how changes in the structure of the carbon onions (vacan-
cies, doping) or tuning the temperature or pressure applied, can promote their
binding.
Having this goal in mind, we focus on the following systems: (i) an ideal car-
bon onion, (ii) a carbon onion with vacancies, or (iii) dopants or (iv) carbon
onions with dopants and vacancies. The vacancies and dopants are introduced
in the outer (C96) fullerene. We vary the number of vacancies from 1 up to
5 on each of the adjacent outer (C96) carbon onion shells. The dopants that
were considered are nitrogen and boron. Nitrogen replaces a carbon atom on
the outer carbon onion shell, while boron dopes the outer fullerene of the ad-
jacent carbon onion. The two dopants are placed in such a way so that they
are exactly opposite each other and could potentially bond. In order to create
91
Appendix A. Promoting assembly of carbon onions
the vacancies in cases (ii) and (iv), carbon atoms on the sides of the outer
fullerenes which are closest to each other were randomly chosen and removed.
Creating vacancies resembles the irradiation of carbon onions with electrons.
The chosen set-up is simplified, but our aim is not to waste computational time
in searching for the conditions which could lead to coalescence. Rather we try
to bring our structures at optimum distances, with vacancies and dopants at
desired sites, so that the carbon onions may eventually bond under certain
pressure and temperature conditions. We should also mention here that we
have tried to use similar conditions for all the schemes we have used here,
and have tried to change one parameter at a time. However, all the meth-
ods describe the inter-atomic interactions in a different way. In addition, the
thermostat in the ab initio MD method is not exactly the same as the ones
in MD. We could unfortunately not avoid this as the Nose´-Hoover thermostat
is not implemented in the DFT code. Though we expect small deviations in
our results and not a significant qualitative difference arising from the different
thermostats, we cannot exclude it.
A.3 Results and discussions
In the following, focus is given on two adjacent C20@C96 . Two of these ideal
onions (without vacancies or donors) are taken and placed at different distances
ranging from 1.5 to 3.0 Å. As expected, these ideal, unmodified carbon onions
repel each other. It is energetically very unfavorable to break the five- and six-
fold rings on the carbon onion surface in order to form bonds to the adjacent
onion. Accordingly, in order to favor the binding of the two carbon onions,
we introduce different kinds of alterations on their structure. We begin with
the introduction of vacancies. on the outer carbon onion shells and at a next
step add dopants again on the outer shells of the carbon onions. The pressure
and temperature serve as free parameters to the problem. We fix one of the
two and vary the second. The temperature is varied from 500 to 3500 K while
the pressure from 0.01 to 10 bar. In all figures, different colors are used to
visualize the different fullerene cases of the carbon onions.
A.3.1 Introducing vacancies
Vacancies, which experimentally can be introduced by electron irradiation are
introduced on both the outer shells of the onions. The vacant sites are ran-
domly chosen but are always on opposite sides of the carbon onions in order
to promote the binding. In principle, irradiation can introduce vacancies on
the inner fullerenes as well, which is an additional study we have not focused
on here. We have found bonding of the two carbon onions in all the cases.
The results obtained from both ab initio DFT and empirical MD reveal a bond-
ing between the two onions, but the picture qualitatively differs as indicated
in Fig. A.1, where the results after 2 ps of DFT-MD and classical MD are
shown. In both cases, a preferential binding between the two carbon onions is
92
A.3. Results and discussions
Figure A.1: Snapshots of two C20@C96 placed initially at a separation of 1.8
Å. Three vacancies were introduced on each of the outer shells of the carbon
onions. The results are obtained through (a) ab initio MD, and (b)-(c) em-
pirical MD. In (b) only a temperature of 2000 K was applied, while in (c) a
pressure of 0.01 bar was additionally applied for the first 0.01 ns of the simula-
tion. All snapshots correspond to a time of 5 ps. In all cases, the temperature
was set at 2000 K. The silver bonds in (a) denote the interlinkings which are
formed between the carbon onions.
seen, which results in a more closed form of the ab initio MD case and a more
open compound in the classical MD case. The different structural details of
both results are given through a ring statistics analysis in Fig. A.2. Apart
from the 5- and 6-fold rings which compose the initial 2C20@C96, the DFT
description results in a structure with higher order rings only, while in the
coalesced structure formed within the classical MD description, also lower (3-
and 4-fold rings) exist. These smaller rank rings probably occur due to the
unphysical compression by increasing the pressure. Varying the temperature
in the empirical MD simulations revealed, that for higher temperatures the
inner fullerenes tend to open up, enclosed by the outer C96, which still form
a cage-like, but more open structure. The structures start to open up from
temperatures of about 1000 K. The two carbon onions do form bonds for all
temperatures. It was also observed that the application of pressure for the first
0.01 ns of the classical MD simulations results in a complete bonding than in
the case were the only temperature is applied. The result of such a simulation
with 0.1 bar applied for the first 0.01 ns and then removed is shown in Fig.
A.1(c) for comparison. The temperature was 2000 K. In order to underline the
role of pressure as obtained from the classical MD simulations, representative
conformations are shown in Fig. A.3. The panels of the figure show random
snapshots for the carbon onions with three vacancies each (six in total). The
snapshots in this figure correspond to a different amount of pressure, which
ranges from 0.01 bar up to 5 bar. In all the cases temperature was set at
93
Appendix A. Promoting assembly of carbon onions
Figure A.2: Ring statistics distributions for the DFT ab initioMD and classical
MD results depicted in Fig. A.1 after a simulation of 5 ps. The labels ’ab
initio MD’ and ’empirical MD’ correspond to panels (a) and (b) in Fig. A.1,
respectively. The term ’initial’ corresponds to the initial structure before the
application of either temperature or pressure.
2000 K. Binding of two carbon onions was evident in all cases, but occurred as
expected faster for a higher pressure. We present the bonded conformations at
a time 5 ps in order to promote comparison to the DFT results shown in Fig.
A.1(b). For the smallest pressure applied, 0.01 bar, it was observed that after
about 0.02 ns the two carbon onions have already merged. A similar behavior
occurred at about 0.01 ns when a pressure of 5 bar was applied. We conclude
that a pressure leads to a faster and more complete (more interlinkings between
the adjacent carbon onions) bonding, but should not be applied for a long time
(not over 5-10 ps) to avoid the collapse of the carbon onions. Coalescence of
the neighboring nano units was not exactly perfect, as in most of the cases the
outer C96 opens up increasing its diameter, as mentioned above. This opening
of the outer fullerene is most likely based on the interplay between the Tersoff
and Lennard-Jones potentials used here. The initial distance between the in-
ner and outer fullerenes is close to 3.0 Å. The minimum distance according to
the Lennard-Jones potential should be close to 3.4 Å(similar to the inter-layer
distance in graphite).
Accordingly, the Lennard-Jones potential tends to increase the inter-onion dis-
tance to this value. This is opposed to the Tersoff potential applied to the
atoms on the outer fullerene shell, which tends to keep the sp2 bond distances
close to the values for graphite. This interplay leads to a coalesced compound,
94
A.3. Results and discussions
Figure A.3: Snapshots of two C20@C96 placed initially at a separation of 1.8
Å on which a different amount of pressure is applied, as indicated from the
panels. The temperature is 2000 K and the snapshots correspond to 5 ps of
classical MD simulations.
which has a more open form and includes dangling bonds as well. Such a trend
was not observed in the DFT results. However, MD captures qualitatively the
bonding pathway. Coalescence was indeed observed (in a more complete-closed
form) in our DFT simulations. It should also be noted, that we have calculated
the mean values of the temperature and pressure in our calculations in order
to evaluate the differences between the data that we obtain from the classical
and ab initio MD simulations. Results are provided for the carbon onions with
three vacancies each. The mean temperature in the empirical MD simulations
was found to be 2046 K, while the same property in the ab initio MD simu-
lations was 2000 K. The averages were done over a time of 5 ps. The average
temperature over the total time of 1 ns in the classical MD calculations was
2095 K. For one of the simulations where a pressure of 0.5 bar was applied,
the average pressure was 1.15 bar and 0.32 bar over a time of 5 ps and 1 ns,
respectively.
A.3.2 Introducing dopants
We further investigate pathways to promote bonding of the carbon onions, by
adding dopant atoms on the outer fullerene cage of both carbon onions. Boron-
doped fullerene-like shells have been experimentally produced and exhibit a
polyhedral faceted circumference [179]. These may occur through irradiation-
induced solid-state phase transformation. Other doped carbon onions, such as
C48N12, have been the core of cross-linked carbon onions grown on a substrate
to yield thin solid films ideal for wear-protective applications [180]. Here, two
dopant atoms are used, one for each carbon onion and substitute with these
95
Appendix A. Promoting assembly of carbon onions
Figure A.4: (a) The initial and (b) final (after a 5 ps) structures of doped
carbon onions with an additional vacancy on each C96. The graph shows the
ring statistics analysis for these two structures. No pressure is applied and
the temperature is 2000 K. The different coloring corresponds to the different
fullerene cages and the dopant atoms. The silver bonds denote the interlinks
between different fullerene cages and the dopants. The results are obtained
through the classical MD simulations.
two carbon atoms. A reasonable choice is to choose elements, such as boron
and nitrogen, which are similar (in atomic size) to carbon. A similar scheme
for functionalization was used in the case of diamondoids [15], nano-building
blocks made up from diamond cages. This choice is also justified by another
study which studied the substitution of carbon atoms by nitrogen and boron in
fullerenes and nanotubes [181]. Similarly to that work, we substitute a carbon
atom on the outer shell of an onion with a boron and that of its adjacent carbon
onion with a nitrogen atom. Both dopant atoms are placed on opposite sides
of the carbon onions and are the nearest neighbors atoms of the neighboring
carbon onions. Vacancies are again introduced on both outer fullerenes. It
is expected that this substitution will enhance the binding of the two carbon
onions as it should result in a much stronger bond between the two doped car-
bon onions. Temperature and pressure are again varied separately. It is first
observed, that in the case of doped carbon onions an elevated temperature of
2000 K is sufficient to promote the binding of the adjacent structures. The
results are shown in Fig. A.4 for the doped carbon onions which also include
96
A.3. Results and discussions
Figure A.5: (a) The initial and (b) final (after a 5 ps) structures of doped
carbon onions with an additional vacancy on each C96. The graph shows the
ring statistics analysis for these two structures. No pressure is applied and
the temperature is 2000 K. The different coloring corresponds to the different
fullerene cages and the dopant atoms. The silver bonds denote the interlinks
between different fullerene cages and the dopants. The results are obtained
through the classical MD simulations.
two vacancies. The initial structure is also sketched together with the relevant
ring statistics analysis. Doped coalesced carbon onions form very few lower
order rings and higher order ones as in the undoped carbon onions discussed
in Fig. A.2.
The effect of pressure and temperature on differently doped carbon onions was
also investigated. The results are shown in Fig. A.6 for doped carbon onions
each with one or two additional vacancies, respectively. In all cases, binding
of the outer fullerene shells occurs, together with the interlinking of the two
inner fullerenes. The difference among the cases shown lies on the structure of
the inner C20s. These can be almost spherical, quite elongated, or open up and
become planar. This planarity occurs when parts of the outer fullerene also
tend to become planar. This occurs as the number of vacancies increases and
the very stable curved sp2 cages try to transform to a very stable graphite-like
structure. This is though to a large extent prevented due to the bonding of the
adjacent fullerenes. As a general remark regarding the doped carbon onions,
it was surprising to realize that the boron and nitrogen atoms do efficiently
promote the binding of adjacent carbon onions. The addition of dopants has
a larger effect on the coalescence of the adjacent nanostructures as solely the
addition of vacancies.
It was also very interesting to observe the following trend, which cannot be
97
Appendix A. Promoting assembly of carbon onions
Figure A.6: Snapshots of two doped C20@C96 placed initially at a separation
of 1.8 Å. The snapshots correspond to 0.1 ns simulation time. Different con-
formations occur when either temperature or pressure are applied to these
molecules, as denoted by the labels in the panels. The results are obtained
through the classical MD simulations
.
easily visualized in Fig. A.6: when only temperature is applied the boron
and nitrogen atoms remain bonded with some of the atoms, typically the ones
from the inner C20s. On the other hand, when pressure is applied, though these
dopants still promote binding between the adjacent carbon onions, once bind-
ing has occurred the dopants are then "expelled" from the coalesced molecule.
Boron and nitrogen at the either edges of carbon onions are strong donor and
acceptors and have a high tendency to bind first. The carbon atoms that come
along and form new bonds, tend to form these bonds with other carbon atoms
and not the dopants. The carbon atoms which bond to the dopants, similarly
prefer binding with other carbon atoms instead. A similar trend was previously
shown, as the carbon-carbon bond is preferred against the carbon-nitrogen or
carbon-boron bonds in carbon structures [182]. In our investigations, though,
the carbon-carbon bonding is preferred when pressure is also applied and not
temperature alone.
A.3.3 Electronic properties
At a next step, the electronic properties of a carbon onion are compared to
those of the fullerenes that make up the carbon onion. The results discussed
in this section are obtained through quantum mechanical simulations: static
and MD. The electronic properties are probed through the electronic density
of states and the frontier orbitals. The latter refer to the highest-occupied
98
A.3. Results and discussions
Figure A.7: Electronic density of states (eDOS) for the fullerenes that form
the carbon onion, C20 and C96, for C20@C96, as well as the two adjacent doped
C20@C96 having each an additional vacancy. Results for both the initial 2
C20@C96 and final 2 C20@C96 are given. The Fermi energy has been shifted
to zero. The results are obtained through the ab initio MD simulations and
correspond to a 5 ps simulation time.
molecular (HOMO) and lowest unoccupied molecular orbitals (LUMO), which
are involved in the bonding of two structures.
The electronic density of states (eDOS) of the ideal C20, C96, and C20@C96 are
sketched in Fig. A.7 together with the doped carbon onions with one vacancy
each. These are obtained from the static DFT calculations, where only energy
minimization was performed. In the same figure, we show results for two doped
carbon onions before and after the ab initioMD simulation. The results for the
initial configuration resemble the data for the ideal carbon onion. The eDOS
of the final coalesced carbon onions, though, is being considerably altered by
the exact presence of the interlinks between the two adjacent carbon onions.
In order to evaluate qualitatively how the eDOS was altered through binding,
we have turned to the projected density of states (PDOS) for the outer and
inner fullerenes. The results are summarized in Fig. A.8. The total density of
states is also shown for comparison. The main contribution in the total density
of states comes from the outer C96 of the carbon onions. We also track the
atoms of the different fullerenes in the carbon onions, which are involved in
99
Appendix A. Promoting assembly of carbon onions
Figure A.8: Partial (projected) density of states (PDOS) for the carbon onions
with three vacancies each. The upper panel shows the PDOS of different
fullerenes consisting the carbon onions after the bonding has occured. The
lower panel shows the PDOS of all the bonded atoms corresponding to the
inter-carbon onion binding. The inset shows the PDOS of the bonded atoms,
which correspond to the intra-carbon onion binding (see text). The Fermi
energy has been shifted to zero. The results are obtained through 5 ps of ab
initio MD simulations.
the bonding of the two carbon onions and present the PDOS of these represen-
tative atoms in the same figure. This contribution is divided into two parts:
the PDOS of the atoms involved in the bonding of the two carbon onions and
the PDOS of the atoms of the different fullerenes in each carbon onion which
form bonds. The former correspond to the inter-carbon onion bonding and
the latter correspond to the intra-carbon onion bonding and are shown in the
lower panel of the figure and its inset, respectively. Regarding the contribution
of the atoms that are involved in the carbon onion coalescence, we could not
observe any specific signatures. Only a peak coming from the bonded atoms
of the molecule is observed.
In order to understand in more detail the bonding behavior of the doped
carbon onions their frontier orbitals, which are essential for understanding the
coalescence are shown in Fig. A.9. These are compared to the orbitals for
C20, C96, and C20@C96 in the same figure. Inspection of this figure reveals the
100
A.3. Results and discussions
change in the HOMO, LUMO orbitals when two carbon onions are brought
together. This change is more pronounced when these carbon onions include
defects. It is interesting to observe that when defects such as vacancies are
introduced on the carbon onion surfaces the frontier orbitals of the neighboring
carbon onions overlap. This is an indication, that the binding of the carbon
onions can easily be triggered, as long as certain conditions are reached, as
for example an elevated temperature. In essence, this can be described by the
frontier molecular orbital theory [183], which states that the occupied orbitals
of one molecule and the unoccupied orbitals of another molecule interact with
each other causing attraction. In this case, the two molecules - here the carbon
onions - clearly interact with each other. Similar results for the doped carbon
onions with one vacancy each are presented and compared to the distributions
of the frontier orbitals before and after the ab initio MD simulations, that is
the initial and final configuration after 5 ps. The frontier orbitals are sketched
in Fig. A.10 in a 3-D representation. These orbitals are also represented as
2-D contours on a plane passing through the midpoint along the direction
where the coalescence occurs. There is again a higher "activity" close to the
doped/defect regions clearly evident in both these representations. The frontier
orbitals become more confined in the final coalesced case, and the electrons are
more localized close to the interlinks. In fact, the LUMO states are associated
with the inner C20, while the HOMO is extended on the C96 and close to the
center of the coalesced compound. This HOMO state is strongly involved in
the bonding between the outer C96s.
Figure A.9: The frontier orbitals (HOMO, LUMO) for the molecules labelled
in the panels. The results are obtained through the static DFT simulations
.
101
Appendix A. Promoting assembly of carbon onions
Figure A.10: The 3-D iso-surfaces of the frontier orbitals (HOMO, LUMO)
for the doped carbon onions with one additional vacancy on each structure.
The results are shown for the initially generated (upper panel) and the final
MD structure (lower panel), respectively. The results are obtained through
the ab initio MD simulations and correspond to a simulation time of 2 ps and
a temperature of 2000 K.
A.4 Summary and conclusions
In summary, in this work we have studied the binding possibilities of small con-
centric carbon onions. Binding is promoted by introducing vacancies and/or
dopants on the outer surfaces of the carbon onions and in some cases also by
applying pressure and/or increasing temperature. Binding could potentially
also be promoted by other ways, such as Stone-Wales defects on the carbon
onions, but this was not the subject of this work. Focus was given to the quan-
tification of the factors that guide the coalescence of two carbon onions. The
structural and electronic properties of the coalesced carbon onions were ana-
lyzed. Although binding was promoted under different structural (vacancies,
dopants) and external (temperature, pressure) conditions as mentioned above,
the bonding characteristics of the two carbon onions do differ. An additional
detailed insight on these characteristics was gained by analyzing the electronic
properties, such as the total and partial electronic density of states and the
frontier orbitals. Through these, the distribution of the frontier states was
revealed. These orbitals are involved in the coalescence and are distributed
102
A.4. Summary and conclusions
Figure A.11: The 2-D contours are shown along the bonding direction of the
two C20@C96s and exactly at the midpoint. The results are obtained through
the ab initio MD simulations and correspond to a simulation time of 2 ps and
a temperature of 2000 K.
closely to the interface between the two carbon onions.
Overall, it was found that the presence of dopants more effectively leads to
coalescence of the carbon onions compared to the introduction of vacancies
alone. An elevated temperature is sufficient to promote the coalescence and
the application of pressure leads to a faster and a complete bonding of the car-
bon onions. Most importantly, wen only temperature is applied, the resulting
coalesced compound is more stable and does not include any unphysical bond-
ing as sometimes introduced due to the presence of pressure. The effect of the
van der Waals forces in the binding was also evaluated and can potentially also
lead to the formation of a small nanotube. Finally, small carbon onions were
included in our studies for computational efficiency. Our aim was to indicate
a coalescence pathway and present a proof of principles regarding the binding
of two small nano-units, like the carbon onions. This study can be further ex-
panded to include higher order carbon onions with additional defects/vacancies
or dopant atoms, which are expected to enhance the functionalization of these
as well as similar nano-carbons.
103

List of Tables
3.1 Structural properties of ideal and functionalized adamantane.
Bond lengths are given in Å and angles in degrees. . . . . . . . . 40
3.2 Structural properties of ideal and functionalized diamantane.
Bond lengths are given in Å and angles in degrees. . . . . . . . . 44
4.1 Structural properties and adsorption energies (Eads) for the carbene-
mediated diamondoid SAMs on metal surfaces . . . . . . . . . . 56
4.2 Bader charge analysis comparing the charges on the SAM and
the metal surfaces before and after adsorption . . . . . . . . . . 64
5.1 Conductance in units of 2e2/h at zero bias for the modified
diamondoid junction at the Fermi level . . . . . . . . . . . . . . 77
105

List of Figures
1.1 Different sizes and shapes of diamondoids are shown . . . . . . . 3
1.2 Fused diamond cages along the tetragonal axes of the bulk dia-
mond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Illustration of a self-assembled monolayer of diamondoid . . . . 4
2.1 General sketch of a pseudopotential . . . . . . . . . . . . . . . . 13
2.2 The SCF algorithm implemented in DFT. . . . . . . . . . . . . 14
2.3 The schematic arrangement of a molecular junction . . . . . . . 17
3.1 Ideal, doped, single- and double-functionalized diamondoids are
sketched . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Variation of bond length and bond angle of doped adamantane 27
3.3 Variation of the substitution energies for doped and functional-
ized adamantane . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Electronic density of states (eDOS) for doped and functionalized
adamantane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5 The frontier orbitals for the ideal, doped, and functionalized
adamantane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.6 2-D contour plots for ideal, doped, and functionalized adamantane 31
3.7 Electronic band gap for doped, single, and double-functionalized
adamantane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.8 The electronic density of states (eDOS) for the ideal and double-
functionalized tetramantane isomers . . . . . . . . . . . . . . . . 33
3.9 The electronic band gaps for the ideal and double-functionalized
tetramantane structures . . . . . . . . . . . . . . . . . . . . . . 34
3.10 Frontier orbitals for the four double functionalized tetramantane
isomers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.11 The variation of band gap for double-functionalized for higher
diamondoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.12 2-D contour plots for double-functionalized higher diamondoids 36
3.13 Electronic density of states for the double-functionalized higher
diamondoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.14 Optimized geometries of ground state and excited state of doped
and functionalized adamantane . . . . . . . . . . . . . . . . . . 39
3.15 Excited state geometries, HOMO, and LUMO of ideal and func-
tionalized adamantane . . . . . . . . . . . . . . . . . . . . . . . 41
3.16 Absorption spectra for ideal, single, and double-functionalized
adamantane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
107
LIST OF FIGURES
3.17 Optimized geometries of the ground state and excited state of
doped and functionalized diamantane . . . . . . . . . . . . . . . 43
3.18 Excited state geometries, HOMO, and LUMO of ideal and func-
tionalized diamantane . . . . . . . . . . . . . . . . . . . . . . . 46
3.19 Absorption spectra for ideal, single and double functionalized
diamantane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.20 The variation of the optical band gap for functionalized adaman-
tane and diamantane . . . . . . . . . . . . . . . . . . . . . . . . 48
3.21 Frontier orbitals at the ground state and excited state for both
adamantane and diamantane . . . . . . . . . . . . . . . . . . . . 49
4.1 General structural formula of imidazolylidene-structures . . . . . 52
4.2 The NHC1-functionalized adamantane (left) and the NHC2-
functionalized adamantane (right). . . . . . . . . . . . . . . . . 53
4.3 Adsorption of diamondoids on metal surfaces . . . . . . . . . . . 54
4.4 Charge density of HOMO and LUMO . . . . . . . . . . . . . . . 58
4.5 Projected density of states (PDOS) for both carbene-functionalized
adamantane molecules before adsorption . . . . . . . . . . . . . 59
4.6 Projected density of states (PDOS) for both carbene-functionalized
adamantane molecules after adsorption . . . . . . . . . . . . . . 60
4.7 Total density of states (TDOS) of the NHC1 and NHC2 molecules 61
4.8 Contributions of the s-, p-, and d-orbitals to the PDOS of the
metal surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.9 Plane averaged electrostatic profiles of the two different con-
figurations of carbene-functionalized adamantane SAMs on all
three surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.10 Simulated STM images of the systems after adsorption on metal
surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.11 Re-distribution of the charge density after adsorption on metal
surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1 A general setup for the transport calculations . . . . . . . . . . 69
5.2 The relaxed atomic structures of the dithiol-molecules which
will be inserted in the gold nano gap . . . . . . . . . . . . . . . 70
5.3 The relaxed atomic structures of the dicarbene-molecules which
will be inserted in the gold nano gap. . . . . . . . . . . . . . . 71
5.4 Final relaxed structures of dithiol-tetramantane and diNHC-
tetramantane in between gold layers . . . . . . . . . . . . . . . . 73
5.5 Partial density of states (PDOS) for the dithiol- and N-doped
tetramantane molecular junctions . . . . . . . . . . . . . . . . . 76
5.6 The zero-bias transmission function is plotted on a semi-log
scale for all diamondoid-based devices . . . . . . . . . . . . . . . 77
5.7 Bar charts of the conductance at zero bias for the modified-
diamondoid nano gaps at the Fermi level . . . . . . . . . . . . . 78
5.8 Eigenchannel wavefunctions for the dithiol-tetramantane devices 80
5.9 Eigenchannel wavefunctions comparing the doped dithiol-tetramantane
and doped diNHC-tetramanane cases . . . . . . . . . . . . . . . 81
108
LIST OF FIGURES
5.10 I-V characteristics and rectification ratio of undoped dithiol
tetramantane and N-doped dithiol tetramantane based junctions 82
5.11 Transmission spectra as a function of the applied bias for un-
doped dithiol tetramantane (top panel) and N-doped dithiol
tetramantane (bottom panel). . . . . . . . . . . . . . . . . . . 83
A.1 Snapshots of two C20@C96 placed initially at a separation of 1.8
Å. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
A.2 Ring statistics distributions for the DFT ab initio MD and clas-
sical MD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
A.3 Snapshots of two C20@C96 placed initially at a separation of 1.8
Å with applied pressure . . . . . . . . . . . . . . . . . . . . . . 95
A.4 Initial and final structures of doped carbon onions with vacancy 96
A.5 Ring statistics of initial and final structures after 5 ps . . . . . . 97
A.6 Snapshots of two doped C20@C96 placed initially at a separation
of 1.8 Å . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
A.7 Electronic density of states (eDOS) for the fullerenes that form
the carbon onion . . . . . . . . . . . . . . . . . . . . . . . . . . 99
A.8 Partial (projected) density of states (PDOS) for the carbon
onions with three vacancies each . . . . . . . . . . . . . . . . . . 100
A.9 The frontier orbitals (HOMO, LUMO) for ideal carbon onions
and carbon onions with vacancies . . . . . . . . . . . . . . . . . 101
A.10 The frontier orbitals (HOMO, LUMO) for the doped carbon
onions with one additional vacancy on each structure . . . . . . 102
A.11 The 2-D contours are shown along the bonding direction of the
two C20@C96s and exactly at the midpoint . . . . . . . . . . . . 103
109

Bibliography
[1] A. T. Balaban and P. V. R. Schleyer, Tetrahedron 34, 3599 (1978).
[2] H. Schwertfeger, A. Fokin, and P. Schreiner, Angewandte Chemie Inter-
national Edition 47, 1022 (2008).
[3] Y. Lifshitz et al., Science 297, 1531 (2002).
[4] J. E. Dahl, S. G. Liu, and R. M. K. Carlson, Science 299, 96 (2003).
[5] M. Yao et al., Carbon 49, 1159 (2011).
[6] J. Zhang et al., ACS Nano 6, 8674 (2012).
[7] S. B. Legoas, R. P. B. dos Santos, K. S. Troche, V. R. Coluci, and D. S.
Galva˜o, Nanotechnology 22, 315708 (2011).
[8] J. B. Crumpton and W. L. Santos, Chem. Commun. 48, 2018 (2012).
[9] G. Sivaraman and M. Fyta, Nanoscale 6, 4225 (2014).
[10] W. L. Yang et al., Science 316, 1460 (2007).
[11] S. Roth et al., Chemical Physics Letters 495, 102 (2010).
[12] J. E. Dahl et al., Angewandte Chemie International Edition 49, 9881
(2010).
[13] Y. Wang et al., Nat Mater 7, 38 (2008).
[14] G. Zhang, Physics Today 66 (2013).
[15] G. C. McIntosh, M. Yoon, S. Berber, and D. Toma´nek, Phys. Rev. B
70, 045401 (2004).
[16] Y. Xue and G. A. Mansoori, International Journal of Molecular Sciences
11, 288 (2010).
[17] J. Reiser, E. McGregor, J. Jones, R. Enick, and G. Holder, Fluid Phase
Equilibria 117, 160 (1996).
[18] L. Landt et al., The Journal of Chemical Physics 132 (2010).
[19] L. Landt et al., The Journal of Chemical Physics 132 (2010).
111
BIBLIOGRAPHY
[20] N. D. Drummond, A. J. Williamson, R. J. Needs, and G. Galli, Phys.
Rev. Lett. 95, 096801 (2005).
[21] U. Drechsler, B. Erdogan, and V. M. Rotello, Chemistry - A European
Journal 10, 5570 (2004).
[22] B. D. Gates et al., Chemical Reviews 105, 1171 (2005).
[23] R. G. Nuzzo and D. L. Allara, Journal of the American Chemical Society
105, 4481 (1983).
[24] J. C. Love, L. A. Estroff, J. K. Kriebel, R. G. Nuzzo, and G. M. White-
sides, Chemical Reviews 105, 1103 (2005).
[25] C. D. Bain et al., Journal of the American Chemical Society 111, 321
(1989).
[26] A. D. Jewell, H. L. Tierney, and E. C. H. Sykes, Phys. Rev. B 82, 205401
(2010).
[27] D. V. Leff, L. Brandt, and J. R. Heath, Langmuir 12, 4723 (1996).
[28] D. I. Gittins and F. Caruso, Angewandte Chemie International Edition
40, 3001 (2001).
[29] C. Vericat, M. E. Vela, G. Benitez, P. Carro, and R. C. Salvarezza,
Chem. Soc. Rev. 39, 1805 (2010).
[30] J. J. Gooding and S. Ciampi, Chem. Soc. Rev. 40, 2704 (2011).
[31] J. Noh, H. S. Kato, M. Kawai, , and M. Hara, The Journal of Physical
Chemistry B 110, 2793 (2006).
[32] L. Srisombat, A. C. Jamison, and T. R. Lee, Colloids and Surfaces A:
Physicochemical and Engineering Aspects 390, 1 (2011).
[33] C. Vericat, G. A. Benitez, D. E. Grumelli, M. E. Vela, and R. C. Sal-
varezza, Journal of Physics: Condensed Matter 20, 184004 (2008).
[34] D. R. Hartree, Mathematical Proceedings of the Cambridge Philosophi-
cal Society 24, 89 (1928).
[35] P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).
[36] J. Callaway, Phys. Rev. 97, 933 (1955).
[37] D. R. Hamann, M. Schlüter, and C. Chiang, Phys. Rev. Lett. 43, 1494
(1979).
[38] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
[39] M. Born and R. Oppenheimer, Annalen der Physik 389, 457 (1927).
112
BIBLIOGRAPHY
[40] W. Kohn and L. J. Sham, Physical Review 140, A1133 (1965).
[41] J. P. Perdew, Phys. Rev. Lett. 55, 1665 (1985).
[42] S. K. Ghosh and R. G. Parr, Phys. Rev. A 34, 785 (1986).
[43] A. D. Becke, The Journal of Chemical Physics 98 (1993).
[44] O. Gunnarsson, M. Jonson, and B. Lundqvist, Physics Letters A 59,
177 (1976).
[45] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865
(1996).
[46] V. Fock, Zeitschrift für Physik 61, 126 (1930).
[47] A. Dreuw, J. L. Weisman, and M. Head-Gordon, The Journal of Chem-
ical Physics 119, 2943 (2003).
[48] J. N. Harvey, Physical Chemistry C 102, 203 (2006).
[49] L. O. Wagner, E. M. Stoudenmire, K. Burke, and S. R. White, Phys.
Chem. Chem. Phys. 14, 8581 (2012).
[50] E. M. Stoudenmire, L. O. Wagner, S. R. White, and K. Burke, Phys.
Rev. Lett. 109, 056402 (2012).
[51] E. Fermi, Rend. Accad. Naz. Lincei 6, 32 (1927).
[52] N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 (1991).
[53] D. Vanderbilt, Phys. Rev. B 41, 7892 (1990).
[54] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
[55] P. Giannozzi et al., Journal of Physics: Condensed Matter 21, 395502
(19pp) (2009).
[56] X. Gonze et al., Computer Physics Communications 180, 2582 (2009).
[57] F. Bloch, Zeitschrift für Physik 52, 555 (1929).
[58] N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart
and Winston, New York, 1976).
[59] J. M. Soler et al., J.Phys.-Condens. Mat. 14, 2745 (2002).
[60] G. H. Wannier, Phys. Rev. 52, 191 (1937).
[61] C. Toher and S. Sanvito, Physical Review Letters 99, 056801 (2007).
[62] M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Phys. Rev. B 31,
6207 (1985).
113
BIBLIOGRAPHY
[63] E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).
[64] M. Brandbyge, J. Mozos, P. Ordejón, J. Taylor, and K. Stokbro, Phys.
Rev. B 65, 165401 (2002).
[65] M. W. Schmidt et al., Journal of computational chemistry 14, 1347
(1993).
[66] H.-J. Werner and P. J. Knowles, The Journal of chemical physics 89,
5803 (1988).
[67] K. Andersson, P.-Å. Malmqvist, and B. O. Roos, The Journal of chemical
physics 96, 1218 (1992).
[68] G. E. Scuseria, Chemical physics letters 176, 27 (1991).
[69] N. D. Drummond, A. J. Williamson, R. J. Needs, and G. Galli, Phys.
Rev. Lett. 95, 096801 (2005).
[70] L. Landt et al., Phys. Rev. Lett. 103, 047402 (2009).
[71] M. Vörös, T. Demjén, T. Szilvási, and A. Gali, Phys. Rev. Lett. 108,
267401 (2012).
[72] A. A. Fokin and P. R. Schreiner, Molecular Physics 107, 823 (2009).
[73] A. A. Spasov, T. V. Khamidova, L. I. Bugaeva, and I. S. Morozov, Phar-
maceutical Chemistry Journal 34, 1 (2000).
[74] H. Huang, E. Pierstorff, E. Osawa, and D. Ho, Nano Letters 7, 3305
(2007).
[75] J. R. Schnell and J. J. Chou, Nature 451, 591 (2008).
[76] W. J. Geldenhuys, S. F. Malan, J. R. Bloomquist, A. P. Marchand, and
C. J. Van der Schyf, Medicinal Research Reviews 25, 21 (2005).
[77] Y. Xue and G. A. Mansoori, International Journal of Nanoscience 07,
63 (2008).
[78] A. S. Barnard, S. P. Russo, and I. K. Snook, The Journal of Physical
Chemistry B 109, 11991 (2005).
[79] A. V. G. Chizmeshya et al., Chemistry of Materials 18, 6266 (2006).
[80] H. Uetsuka, D. Shin, N. Tokuda, K. Saeki, and C. E. Nebel, Langmuir
23, 3466 (2007).
[81] J. C. Randel et al., Nature Communications 5 (2014).
[82] J. P. Perdew et al., Phys. Rev. B 46, 6671 (1992).
[83] N. Troullier and J. L. Martins, Physical Review B 43, 8861 (1991).
114
BIBLIOGRAPHY
[84] T. Yanai, D. P. Tew, and N. C. Handy, Chemical Physics Letters 393,
51 (2004).
[85] J. Junquera, O. Paz, D. Sánchez-Portal, and E. Artacho, Phys. Rev. B
64, 235111 (2001).
[86] M. J. Peach et al., Physical Chemistry Chemical Physics 8, 558 (2006).
[87] M. L. Zimmerman, M. G. Littman, M. M. Kash, and D. Kleppner, Phys-
ical Review A 20, 2251 (1979).
[88] S. Hirata and M. Head-Gordon, Chemical Physics Letters 314, 291
(1999).
[89] R. Richter et al., Physical Chemistry Chemical Physics 16, 3070 (2014).
[90] T. Rander et al., The Journal of chemical physics 138, 024310 (2013).
[91] M. Vörös and A. Gali, Phys. Rev. B 80, 161411 (2009).
[92] A. J. Arduengo, R. L. Harlow, and M. Kline, Journal of the American
Chemical Society 113, 361 (1991).
[93] O. Schuster, L. Yang, H. G. Raubenheimer, and M. Albrecht, Chemical
Reviews 109, 3445 (2009).
[94] J. C. Y. Lin et al., Chemical Reviews 109, 3561 (2009).
[95] M. Niehues et al., Organometallics 21, 2905 (2002).
[96] J. P. Wagner and P. R. Schreiner, Journal of Chemical Theory and
Computation 12, 231 (2016).
[97] C. M. Crudden et al., Nat Chem 6, 409 (2014).
[98] R. G. Nuzzo, B. R. Zegarski, and L. H. Dubois, Journal of the American
Chemical Society 109, 733 (1987).
[99] D. Ota´lvaro, T. Veening, and G. Brocks, The Journal of Physical Chem-
istry C 116, 7826 (2012).
[100] P. J. Feibelman et al., The Journal of Physical Chemistry B 105, 4018
(2001).
[101] B. Adhikari and M. Fyta, Nanotechnology 26, 035701 (2015).
[102] G. Henkelman, A. Arnaldsson, and H. Jo´nsson, Computational Materials
Science 36, 354 (2006).
[103] D. Xiang, X. Wang, C. Jia, T. Lee, and X. Guo, Chemical Reviews 116,
4318 (2016).
115
BIBLIOGRAPHY
[104] M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Science
278, 252 (1997).
[105] A. Nitzan and M. A. Ratner, Science 300, 1384 (2003).
[106] Y. Matsuura, Computational and Theoretical Chemistry 1074, 131
(2015).
[107] A. Aviram and M. A. Ratner, Chemical Physics Letters 29, 277 (1974).
[108] T. A. Su, M. Neupane, M. L. Steigerwald, L. Venkataraman, and
C. Nuckolls, Nature Reviews Materials 1, 16002 (2016), Review Ar-
ticle.
[109] D. M. Guldi, H. Nishihara, and L. Venkataraman, Chem. Soc. Rev. 44,
842 (2015).
[110] S. V. Aradhya and L. Venkataraman, Nat Nano 8, 399 (2013), Review.
[111] J. R. Heath, Annual Review of Materials Research 39, 1 (2009).
[112] J. K. Gimzewski and C. Joachim, Science 283, 1683 (1999).
[113] M. R. Stan, P. D. Franzon, S. C. Goldstein, J. C. Lach, and M. M.
Ziegler, Proceedings of the IEEE 91, 1940 (2003).
[114] Q. Yan et al., Nano Letters 7, 1469 (2007).
[115] T. B. Martins, R. H. Miwa, A. J. R. da Silva, and A. Fazzio, Phys. Rev.
Lett. 98, 196803 (2007).
[116] S.-S. Yu and W.-T. Zheng, Nanoscale 2, 1069 (2010).
[117] W. Yao, K. Yao, G. Gao, H. Fu, and S. Zhu, Solid State Communications
153, 46 (2013).
[118] J. Prasongkit, A. Grigoriev, B. Pathak, R. Ahuja, and R. H. Scheicher,
The Journal of Physical Chemistry C 117, 15421 (2013).
[119] S. Chakrabarty, A. H. M. A. Wasey, R. Thapa, and G. P. Das, AIP
Advances 5 (2015).
[120] D. H. Zhang, K. L. Yao, and G. Y. Gao, Journal of Applied Physics 110
(2011).
[121] A. Pramanik, S. Sarkar, and P. Sarkar, The Journal of Physical Chem-
istry C 116, 18064 (2012).
[122] A. Batra et al., Nano Letters 13, 6233 (2013).
[123] X. Q. Deng et al., Applied Physics Letters 100 (2012).
116
BIBLIOGRAPHY
[124] J. Zeng, K.-Q. Chen, J. He, Z.-Q. Fan, and X.-J. Zhang, Journal of
Applied Physics 109 (2011).
[125] J. Zheng et al., The Journal of Physical Chemistry C 115, 8547 (2011).
[126] H. Wang and Y. Leng, The Journal of Physical Chemistry C 119, 15216
(2015).
[127] B. Adhikari, S. Meng, and M. Fyta, Nanoscale 8, 8966 (2016).
[128] G. Sivaraman, R. G. Amorim, R. H. Scheicher, and M. Fyta, Nanoscale
8, 10105 (2016).
[129] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
[130] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
[131] W. Ding et al., Journal of Chemical Theory and Computation 11, 5888
(2015).
[132] M. Paulsson and M. Brandbyge, Phys. Rev. B 76, 115117 (2007).
[133] H. W. Kroto et al., Nature 318, 162 (1985).
[134] W. Kratschmer, L. D. Lamb, K. Fostiropoulos, and D. Huffman, Nature
347, 27 (1990).
[135] S. Iijima et al., Nature 354, 56 (1991).
[136] D. Ugarte, Nature 359, 707 (1992).
[137] S. Iijima, Journal of Crystal Growth 50, 675 (1980).
[138] H. Terrones, M. Terrones, and W. Hsu, Chemical Society Reviews 24,
341 (1995).
[139] R. S. Ruoff, D. C. Lorents, B. Chan, R. Malhotra, and S. Subramoney,
Science 259, 346 (1993).
[140] V. L. Kuznetsov, A. L. Chuvilin, Y. V. Butenko, I. Y. Mal’kov, and
V. M. Titov, Chemical Physics Letters 222, 343 (1994).
[141] E. Thune, T. Cabioc´h, M. Jaouen, and F. Bodart, Physical Review B
68, 115434 (2003).
[142] T. Cabioc’h, J. Riviere, and J. Delafond, Journal of Materials Science
30, 4787 (1995).
[143] M. Chhowalla et al., Physical Review Letters 90, 155504 (2003).
[144] R. Powles, N. Marks, and D. Lau, Physical Review B 79, 075430 (2009).
[145] D. Toma´nek, W. Zhong, and E. Krastev, Physical Review-Series B 48,
15461 (1993).
117
BIBLIOGRAPHY
[146] S. Erkoc, Nano Letters 2, 215 (2002).
[147] S. Tomita, T. Sakurai, H. Ohta, M. Fujii, and S. Hayashi, The Journal
of Chemical Physics 114, 7477 (2001).
[148] H. Kroto, Nature 359, 670 (1992).
[149] F. Banhart, Reports on Progress in Physics 62, 1181 (1999).
[150] B.-S. Xu, New Carbon Materials 23, 289 (2008).
[151] C. Brabec, A. Maiti, and J. Bernholc, Chemical Physics Letters 219,
473 (1994).
[152] H. Terrones and M. Terrones, Journal of Physics and Chemistry of Solids
58, 1789 (1997).
[153] K. R. Bates and G. E. Scuseria, Theoretical Chemistry Accounts 99, 29
(1998).
[154] H. Kroto, Science 242, 1139 (1988).
[155] A. Maiti, C. Brabec, and J. Bernholc, Physical review letters 70, 3023
(1993).
[156] F. Banhart and P. Ajayan, Nature 382, 433 (1996).
[157] O. Mamezaki, H. Adachi, S. Tomita, M. Fujii, and S. Hayashi, Japanese
Journal of Applied Physics 39, 6680 (2000).
[158] V. Kuznetsov, Y. V. Butenko, A. Chuvilin, A. Romanenko, and
A. Okotrub, Chemical Physics Letters 336, 397 (2001).
[159] T. Cabioc’h et al., Journal of Applied Physics 91, 1560 (2002).
[160] N. Sano et al., Journal of Applied Physics 92, 2783 (2002).
[161] J. K. McDonough et al., Carbon 50, 3298 (2012).
[162] M. G. Fyta and P. C. Kelires, Fullerenes, Nanotubes, and Carbon Nanos-
tructures 13, 13 (2005).
[163] B. W. Smith and D. E. Luzzi, Chemical Physics Letters 321, 169 (2000).
[164] C. Yeretzian, K. Hansen, F. Diederichi, and R. L. Whetten, Nature 359,
44 (1992).
[165] B. W. Smith, M. Monthioux, and D. E. Luzzi, Nature 396, 323 (1998).
[166] S. Bandow, M. Takizawa, K. Hirahara, M. Yudasaka, and S. Iijima,
Chemical Physics Letters 337, 48 (2001).
[167] J. Sloan et al., Chemical Physics Letters 316, 191 (2000).
118
BIBLIOGRAPHY
[168] Y. Zhao, R. E. Smalley, and B. I. Yakobson, Physical Review B 66,
195409 (2002).
[169] E. Campbell, V. Schyja, R. Ehlich, and I. Hertel, Physical Review Letters
70, 263 (1993).
[170] Y. Xia, Y. Xing, C. Tan, and L. Mei, Physical Review B 53, 13871
(1996).
[171] J. Jakowski, S. Irle, and K. Morokuma, Physical Review B 82, 125443
(2010).
[172] M. Terrones, H. Terrones, F. Banhart, J.-C. Charlier, and P. Ajayan,
Science 288, 1226 (2000).
[173] K. Lee, É. D. Murray, L. Kong, B. I. Lundqvist, and D. C. Langreth,
Physical Review B 82, 081101 (2010).
[174] J. Klimeš and A. Michaelides, The Journal of Chemical Physics 137,
120901 (2012).
[175] S. Plimpton, Journal of Computational Physics 117, 1 (1995).
[176] J. Tersoff, Physical Review B 37, 6991 (1988).
[177] C. Sevik, A. Kinaci, J. B. Haskins, and T. Çağın, Physical Review B
84, 085409 (2011).
[178] L. Girifalco, M. Hodak, and R. S. Lee, Physical Review B 62, 13104
(2000).
[179] D. Golberg, Y. Bando, K. Kurashima, and T. Sasaki, Applied Physics
Letters 72 (1998).
[180] L. Hultman et al., Phys. Rev. Lett. 87, 225503 (2001).
[181] D. Golberg, Y. Bando, W. Han, K. Kurashima, and T. Sato, Chemical
Physics Letters 308, 337 (1999).
[182] M. F. Genisel et al., Journal of Applied Physics 110 (2011).
[183] K. Fukui, T. Yonezawa, and H. Shingu, The Journal of Chemical Physics
20 (1952).
119