AO integral evaluation using Cartesian exponential type orbitals (CETOs)

CETO functions and their properties are defined and described, to provide a means of obtaining general expressions for many-center many-electron integral formulae. Compact integral expressions are written by means of nested summation symbols, a new concept developed in this paper. Integrals over CETO functions are computed by means of a set of several auxiliary integral forms. No transformations other than frame rotations are needed to compute the usual integral terms. The formulae obtained are immediately programmable in any high level language and the parallelizable terms are obtained with a simple rule. Results can be considered an encouraging alternative way to solve the STO integral problem. Keywords: many-center AO integrals, molecular basis sets, ETO, STO, CETO.