Internuclear Separation Derivatives of the Energy of a Diatomic Molecule

Abstract

General formulas for the higher-order derivatives of the energy with respect to the internuclear separation of a diatomic molecule are derived from the Hellmann-Feynman theorem and the integral Hellmann-Feynman theorem. The phenomenon of the cancellation of terms involving the charge density and its derivatives, which has been observed for the second-order derivative by Salem, is shown to prevail for third-and higher-order derivatives. On this basis an approximate working formula is suggested. A new condition under which an approximate wavefunction satisfies the Hellmann-Feynman theorem rigorously is given. With such an approximate wavefunction, the formulas for the general derivatives of the energy derived are also shown to be valid.