Electronic Bases of Molecular Vibrations. II. Generalized Energy Theorems and the Force Constants of Polyatomic Molecules

Abstract

Molecular electronic energy derivatives with respect to nuclear displacement coordinates are investigated in detail. By suitably scaling all electronic and nuclear position coordinates, hypervirial operators are introduced which (1) permit generalization of the virial theorem for polyatomic molecules so as to include non‐Coulombic and external field contributions and (2) generate expressions relating the force constants of polyatomic molecules to integrals over the electronic‐charge distribution. It is shown that the molecular force constants can be defined as a type of derivative of the Hellmann—Feynman force, provided several conditions are satisfied by molecular electronic wavefunctions. These conditions are always met for exact solutions of the electronic Hamiltonian, and may serve as rules for the construction of reliable approximate wavefunctions in addition to the usual energy criterion. Suggestions are made for applications of these procedures to other molecular properties.