Numerical analysis of Gaussian approximations in quantum chemistry

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