Browsing by Author "Knizia, Gerald"

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Explicitly correlated quantum chemistry methods for high-spin open-shell molecules
(2010) Knizia, Gerald; Werner, Hans-Joachim (Prof. Dr.)
The calculation of the electronic structure of molecules solely from first principles is a subject of intensive research programs worldwide. The goal of these efforts is to develop efficient computational methods for determining molecular properties. Such methods are based on quantum mechanical many-body methods, which allow for a correct description of the complex correlated motion of electrons. However, despite the immense advances in the computational capabilities during the last decades, highly accurate calculations are still limited to molecules containing no more than ten to twenty atoms. In this context, one of the most severe problems is that the intrinsic accuracy of the employed many-body methods is generally hard to reach in practical calculations. This is a side effect of the expansion of molecular wave functions in terms of a finite basis of one-particle functions ("molecular orbitals"): A large number of basis functions per atom is required for accurately describing the microstructure of the wave function which is caused by the divergent Coulomb interaction. Calculations become very expensive very quickly. Explicitly correlated methods offer a promising approach to circumvent this problem of basis set convergence. Basically, such methods are variants of the common many-body methods of quantum mechanics (e.g., perturbation theory or Coupled Cluster methods) in which the common wave function ansatz is extended by additional terms which contain the inter-electronic distance explicitly. Methods of this form with a potential for routine applications were first proposed by Kutzelnigg and Klopper in 1991. During the last years the explicitly correlated methods were developed to such a degree that they now can clearly surpass the accuracy-to-cost ratio of their conventional counterparts. Such explicitly correlated methods were developed as a part of this dissertation. Concretely, open-shell variants of Møller-Plesset perturbation theory and of Coupled Cluster Singles & Doubles were produced. Apart from that, also theoretical aspects are discussed, like the interpretation of F12 wave functions or special issues arising when handling open-shell species. Also technical aspects are considered, like the robust solution of the occurring equation systems and the avoidance of numerical problems. Furthermore, methods are developed to correct for Hartree-Fock basis set deviations in the context of explicitly correlated calculations, and simple approximations are investigated which accelerate the basis set convergence of perturbative triple excitations in Coupled Cluster calculations. Extensive benchmark calculations are essential for facilitating the practical application of new calculation methods. This applies particularly if the new methods are supposed to have a "black box" character, like it is the case here. As a consequence, a great part of this work is concerned with performing and evaluating calculations, in order to establish the accuracy of the developed methods and in order to derive optimal default calculation parameters. In this regard, different families of atomic orbital basis sets are investigated for their compatibility with F12 calculations, and the effect of the free length scale parameter of the theory is quantified. In pursuance of a wide range of application scenarios, the new methods are tested on a great variety of different calculation tasks. A special emphasis is placed on difficult problems, like the calculation of atomization energies, of electron affinities and ionization potentials, and of potential energy curves of diatomic molecules and of atomic dipole polarizabilities. The quantum chemical methods developed here can reduce the computational cost of highly accurate calculations by more than two order of magnitude since, due to their fast basis set convergence, less basis functions are required to achieve a desired accuracy. Therefore this work significantly extends the range of molecules for which such highly accurate calculations are possible.