Modified Gaussian functions and their use in quantum chemistry. I. Integrals

A modified Gaussian function g(u, v, w, a, R ) = const s(a, R ) is considered where l = u + v + w, s (a, R ) is a 1s-type Gaussian function centered at R , a is the coefficient in the exponent of the 1 s Gaussian function and X, Y, Z are components of R . General formulae are derived for overlap integrals, kinetic energy integrals, nuclear attraction integrals, and electron repulsion integrals, valid for any l. The formulae are much simpler than those derived by Huzinaga for Cartesian Gaussian functions.