Study of H2 and He 2+2 using three- and four-parameter non-integral-n 1s basis functions

Abstract

Introduction of non-integral power of r of the elliptical coordinate ξ into the definition of the 1s atomic orbital gives better approximate wavefunctions for the ground state of H₂ and He²⁺₂ than other functions of comparable complexity. This trend is examined in the framework of a limited configuration interaction calculation using numerical integration for molecular one-and two-electron integrals. A new four-parameter basis function; χ=(1+pRξⁿ) exp(–αξ±βη)R is presented as a generalization of the Guillemin–Zener function. The single-term expansion energies optimized in the latter case are only 0.000 24 and 0.000 55 a.u. above the “SCF limit” for H₂(at R= 1.4 a.u.) and He²⁺₂(at R = 1.3 a.u.) respectively.