Cusped gaussian wave function. I

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Abstract
The present paper describes the first part of an investigation into the possibility of finding a set of simple functions for the construction of molecular wave functions which satisfies two essential requirements: that the number of basis functions required to produce a given accuracy be comparable to the number of Slater functions required to give the same accuracy, and that the molecular multicentre integrals should be considerably easier to evaluate than those over Slater functions. It is shown that a basis made up of 1s gaussians supplemented by a single ‘cusp function’ of the form may be expected to satisfy the requirements for the s-orbitals in atoms other than hydrogen. Calculations of the ground-state orbital approximations of the helium and beryllium atoms show that an inner-shell 1s orbital can be satisfactorily described by the cusp function and two gaussians, whilst subsequent s-orbitals should require not more than two or three gaussians per orbital to produce better than ‘double-zeta’ accuracy.

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