On the damped multipole expansion of the induction energy in H⁺₂

Abstract

Following early work by Kutzelnigg on the correlation cusp, we have attempted to improve convergence of the damped multipole expansion of the second-order induction energy for H⁺ ₊ by including a separately determined cusp correction of the form φ = f(r _B)ψ₀ into the first-order function in order to avoid divergency at the proton position when r _B = 0. Three different cusp wavefunctions, all derived from the Taylor expansion of f(r _B) into positive powers of r _B have been examined, and the best compromise between simplicity and accuracy is found for the function φ = -r _Bψ₀. Few residual multipoles, variationally approximated in terms of one-centre linear pseudostates, are then found necessary to reproduce accurately the induction energy at the distance of the chemical bond.