Electronic Structure: Hartree-Fock and Correlation Methods

Christof Hättig
Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany

Multiscale Simulation Methods in Molecular Sciences, J. Grotendort, N. Attig, S. Blügel, D. Marx (Eds.), Institute for Advanced Simulation, Forschungszentrum Jülich, NIC Series, Vol 42, ISBN 978-3-9810843-8-2, pp. 77-120 (2009).

Hartree-Fock theory is the conceptually most basic eletronic structure method and also the starting point for almost all wavefunction based correlation methods. Technically, the Hartree-Fock self-consistent field method is often also the starting point for the development of molecular Kohn-Sham density functional theory codes. We will briefly review the main concepts of Hartree-Fock theory and modern implementations of the Rothaan-Hall self-consistent field equations with emphasis on the techniques used to make these approaches applicable to large systems. The second part of the chapter will focus on wavefunction based correlation methods for large molecules, in particular second order M{\o}ller-Plesset perturbation theory (MP2) and, for calculations on excited states, the approximate coupled-cluster singles-and-doubles method CC2, both treating the electron-electron interaction correct through second order. It is shown how the computational costs (CPU time and storage requirements) can be reduced for these methods by orders of magnitudes using the resolution-of-the-identity approximation for electron repulsion integrals. The demands for the auxiliary basis sets are discussed and it shown how these approaches can parallelized for distributed memory architectures. Finally a few prototypical applications are reviewed.

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