Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods.

We compare two procedures to gain efficiency by approximating two-electron integrals in molecular electronic structure calculations. The first one is based on a Cholesky decomposition (CD) of two-electron integrals, the second one on the use of preoptimized auxiliary or fitting basis sets employed in a "resolution of the identity" (RI) technique. We present and test auxiliary bases for approximating the Coulomb term, which further improves accuracy over previously proposed fitting bases. It is shown that RI methods lead to insignificant errors only, which are partly comparable to or even better than that of CD treatments; but RI procedures are superior in speed. CD methods have certain advantages, however, particularly for extended basis sets.