On the use of Gaussian shell type basis orbitals for single-center expansions. I. Evaluation of integrals

Formulas are derived for all Hamiltonian integrals required for molecular computations using a novel basis for single-center expansions. The basis orbitals depend exponentially upon α(r ? ρ)² where r and ρ are the distance from center to electron and to a variationally scaled spherical shell, respectively. Comparisons are made between these so-called Gaussian shell orbitals (GSO ) and the conventional GTO and STO bases for single-center calculations. A preliminary comparison on H using a single GSO , a non-integer STO , and a GTO gives the optimized energies: ?0.51089 a.u., ?0.50504 a.u., and ?0.50422 a.u., respectively.