Study of molecular clusters with explicitly correlated wave function methods

Abstract

In the classical ideal gas there are no interparticular forces. The Dutch scientist Johannes Diderik van der Waals derived a correction leading to the van der Waals equation. The interparticular forces in the van der Waals equation can not be explained by covalent bonds (characterized by the sharing of electron pairs) of the particles (atoms and molecules) in the gas. Those forces can only be explained via weak interactions and can be attractive or repulsive. The weak interactions between atoms and molecules have later been named after Johannes Diderik van der Waals. Weak interactions are not restricted to intermolecular interactions but can also occur intramolecular. In both cases the weak interactions can be responsible for the shape of molecules, supersystems and clusters. A famous example for this is the protein folding in RiboNucleic Acid (RNA) and DeoxyriboNucleic Acid (DNA). The effect of medical compounds often is founded on weak interactions with something in the human body. Unfortunately, the calculation of weak interactions is a challenging task. Very accurate ab initio quantum mechanical methods and a good description of the molecular orbitals are needed. Both requirements lead to high computational demands (calculation time and storage usage for main memory and hard disc). In ab initio quantum chemistry one normally only calculates the (total) energy E of a system. This is done with an accuracy of approximately 99% (when compared to the exact result) if the Hartree-Fock method (HF) is used. For many cases this accuracy is not sufficient to achieve the chemical accuracy of 1 kcal/mol. In contrast to thermochemistry where (reaction) enthalpies are typically calculated from standard enthalpies of formation (which are of the same order of magnitude as the reaction enthalpies and a certain accuracy of the formation enthalpies leads to a result of similar quality of the relative energies) in ab initio quantum chemistry calculations, the calculated total energies are larger by orders of magnitude than the energy of the desired property. For weak interactions the ratio of calculated values and the desired property is even larger and dynamic electron correlation, which is not covered at all by HF, plays a larger role or is sometimes responsible for the complete interaction energy. In particular the dispersion energy is a pure electron correlation effect. Methods that give a correction to HF to include dynamic electron correlation in the calculated energy need larger basis sets for the description of the molecular orbitals than HF itself. In the example of the interaction energy of the benzene dimer, the total electronic energy of the dimer is approximately 300000 kcal/mol, whereas the interaction energy is approximately 3 kcal/mol. This ratio of 105 illustrates why an accuracy of more than 99% and hence methods that cover dynamic electron correlation are necessary. The Coupled Cluster method with single and double excitations and triple excitations at perturbation theory level (CCSD(T)) (see Section 3.10) is considered to be highly accurate for most weak interactions. The convergence of the total energy with the basis set size can be greatly improved by the introduction of explicit correlation. Unfortunately CCSD(T) is rather expensive and systems with more than 30 atoms are very hard to calculate. Many systems of interest with weak interactions are larger, and therefore CCSD(T) is not feasible for their calculation. The MP2 method is much cheaper[c] than the CCSD(T) method, but unfortunately not as accurate. Earlier attempts to improve MP2 like SCS-MP2 have been successful to some extent but were never totally satisfying. Other attempts such as MP2.5 are more expensive and therefore also restricted to smaller systems. The goal of this work was to test the effects of explicit correlation in the CCSD(T) method and to develop a new method for the calculation of weak interactions that is able to improve on MP2 and SCS-MP2 towards CCSD(T). A new method - Dispersion-Weighted-MP2[d] (DW-MP2) has been developed in this work. It combines MP2 and SCS-MP2 and will be shown to achieve the accuracy needed for chemical accuracy.

Eine Methode, die die Genauigkeit von CCSD(T) mit dem eher niedrigen Rechenaufwand von MP2 verbindet wurde deshalb entwickelt. In dieser Methode werden MP2 und SCSMP2 zu Dipersion-Weighted-MP2 (DW-MP2) kombiniert. Es wird die Leistungsfähigkeit der neu entwickelten Methode gezeigt. Es wird gezeigt, daß die hohe intrinsische Genauigkeit von CCSD(T) mit der Verwendung von DW-MP2 bei einer Abweichung von ca. 0,5 kcal/mol für fast alle Systeme reproduziert werden kann, abgesehen von Alkan-Clustern. Außerdem wird die Leistungsfähigkeit von DW-MP2-F12 für die Verwendung bei numerischen Gradienten untersucht. Die (gezeigten) Resultate werden mit Standardmethoden verglichen. Hiermit zeigt diese Arbeit, daß mit der Kombination von Beidem — DW-MP2 und expliziter Korrelation (DW-MP2-F12) — die genaue Beschreibung der schwachen Wechselwirkungen mit (sehr) annehmbarem Rechenaufwand möglich ist. Die DW-MP2-F12 Methode verursacht keinerlei zusätzliche Kosten im Vergleich zu MP2-F12 und reduziert damit die Rechenkosten drastisch verglichen mit der CCSD(T∗)-F12 Methode. Die DWMP2-F12Methode kann voll automatisch verwendet werden (Black-Box) und macht damit genaue quantenmechanische ab initio Rechnungen für schwach wechselwirkende Systeme mit 100 Atomen oder mehr möglich.