Application of the Hellmann—Feynman and Virial Theorems to the Theoretical Calculation of Molecular Potential Constants

Abstract

The Hellmann—Feynman‐theorem expression for the z component of the force on a single nucleus is differentiated successively to obtain expressions which are related to the harmonic and anharmonic potential constants in a molecule. The method used to simplify the differentiations is also used to derive two expressions for the field‐gradient part of the nuclear‐quadrupole coupling constant; the two expressions involve only convergent integrals. The virial‐theorem expression for diatomic molecules is differentiated to obtain equations for the cubic and quartic potential constants and for the Dunham constants a₁ and a₂. Application of the equations to quantum‐chemical calculation of the potential constants is discussed.