Cross-entropy minimization for refinement of Gaussian basis sets

Abstract

Information theoretic techniques have been applied for the refinement of Gaussian basis sets. A refined distribution has been obtained by cross-entropy minimization starting from a near Hartree-Fock quality density distribution. For this purpose, the Kullback-Leibler cross-entropy, S[^ρ|^ρ₀]=∫^ρ(r)ln[^ρ(r)/^ρ₀(r)] dr, has been minimized subject to exact, theoretical or experimental, second moment constraints in position and momentum spaces. Here, ρ₀ is the starting density distribution and ρ is the corresponding refined one. The procedure has been applied to hydrogen, helium, lithium and beryllium atoms as test cases. Nearly all moments (-2 through 4), in coordinate as well as momentum spaces have improved over the original ones at an average worsening of the total energy by a mere 0.04%.