NONSINGULAR HANKEL FUNCTIONS AS A NEW BASIS FOR ELECTRONIC-STRUCTURE CALCULATIONS

As a basis for electronic structure calculations, Gaussians are inconv enient because they show unsuitable behavior at larger distances, whil e Hankel functions are singular at the origin. This paper discusses a new set of special functions which combine many of the advantageous fe atures of both families. At large distances from the origin, these ''s moothed Hankel functions'' resemble the standard Hankel functions and therefore show behavior similar to that of an electronic wave function . Near the origin, the functions are smooth and analytical. Analytical expressions are derived for two-center integrals for the overlap, the kinetic energy, and the electrostatic energy between two such functio ns. We also show how to expand such a function around some point in sp ace and discuss how to evaluate the potential matrix elements efficien tly by numerical integration. This supplies the elements needed for a practical application in an electronic structure calculation. (C) 1998 American Institute of Physics.