Exponential or scaled SCF orbitals in correlated wavefunctions for two-electron atoms

Abstract

Wavefunctions for the ground state of H−, He, Li+, and Be2+ are approximated by the product of orbitals with a correlation function. Use of optimally scaled SCF orbitals in place of fully optimized orbitals causes an additional energy error of at least 0.001 hartree. Exponential orbitals are superior to scaled SCF orbitals in open-shell cases or if the correlation function increases with (r1 − r2)2; otherwise SCF orbitals are superior. Application of correlation functions to open-shell wavefunctions causes the outer orbital to contract more than the inner orbital, which actually expands slightly except at low atomic numbers. If the correlation factor depends on (r1 − r2)2 as well as r12, the inner and outer exponential orbitals can become identical when Z is greater than 2. Several three-parameter wavefunctions have errors of 0.0010–0.0018 hartree. Good approximations to completely flexible correlation functions of r12 alone are 1 − A exp(− B r12) and (1 + A r12)C. In the latter function and [1+Ar12+B(r1−r2)2]C the optimum C can be predicted accurately by extrapolation.