Numerical analysis of Gaussian approximations in quantum chemistry

Author(s) : Markus Bachmayr , Huajie Chen , Reinhold Schneider

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 27-2012

MSC 2000

65N25 Eigenvalue problems

65N15 Error bounds

Abstract :
Bases of atomic-like functions provide a natural, physically motivated description of electronic states, and Gaussian-type orbitals are the most widely used basis functions in molecular simulations. This paper aims at developing a systematic analysis of numerical approximations based on linear combinations of some Gaussian-type orbitals. We give a priori error estimates for Hermite-type Gaussian bases and for even-tempered Gaussian bases. Some numerical results are presented to support the theory.