Accurate Hartree–Fock wave functions without exponent optimization. II. Basis functions with correct asymptotic exponents and powers

Abstract

Results of Hartree–Fock calculations for He, Be, and Ne using basis functions of the form rn−1 e–αrM(a,b;-cr), where M(a,b;-cr) is Kummer’s function, are reported. These functions allow the trial orbitals to attain the correct irrational asymptotic power and exponential decay at large r, without introducing spurious singularities. Parameters in the basis functions were chosen analytically by matching the asymptotic forms of the basis functions with terms in the asymptotic expansions of the exact orbitals. The results for He and Be surpass the accuracy of existing optimized basis sets of similar size without the need for any nonlinear optimizations, and a prediction that accurate estimation of orbital moments 〈rn〉 requires the inclusion of correct asymptotic powers when n is greater than the number of basis functions has been verified. However, our results for Ne imply that routinely including correct asymptotic powers in basis sets will only be feasible for very small systems.