Hypervirial Theorems Applied to Molecular Quantum Mechanics

Abstract

Previous discussions of hypervirial theorems in wave mechanics have been extended in three ways. (1) A particular class of operators called compound hypervirial operators is introduced, and the particular point transformations which they may be said to generate are studied. (2) An example of these new operators is an electron‐correlation hypervirial, which modifies a wave function when two electrons are near together but exerts little influence when they are a long way apart. (3) A study is made of possible wave functions for a diatomic molecule which satisfy the Hellmann‐Feynman theorem and provide a means of deducing the shape of the potential energy curve, or its slope at a particular internuclear distance.