Implications of the virial theorem for quantum-chemical calculations of vibrational frequencies and equilibrium distances

Abstract

Consider two theoretically calculated vibrational potential curves for a specific state of a diatomic molecule, both satisfying the quantum-mechanical virial theorem but the two giving slightly different predictions of equilibrium distance R e and harmonic force constant k e. Let the fractional changes in R e and k e between the two curves be ϱ and κ, and let t and v be t fractional changes in calculated kinetic and potential energies. Then it is shown that ϱ = t− v and κ = −3 t + 4 v. A certain mod class of molecules gives v= 1.20 t, so that κ= −9p. For Hartree-Fock H 2, v;= 1.17 t and κ= −10.0 ϱ.