On the quantum-mechanical virial theorem for molecular bending motions

Abstract

If bond distances are adjusted to their equilibrium values for each angle θ during a molecular bending motion. Nelander has shown that the quantum-mechanical virial theorem takes the form W(θ) = − T(θ), where W is the total electronic energy and T(θ) is the total electronic kinetic energy. For the Hartree-Fock and separated-electron-pair approximations follow ▪ These formulas provide an accurate resolution of the energy including nuclear-nuclear repulsion, into orbital or geminal components, and hence they validate the use of a one-electron or pair model in following W(θ) semiempirically. The quantities − t i (θ) are exhibited for the molecule H 2O, and it is shown that lone pair electrons dominate the change of W with θ when it is expressed in this way.