Theoretical Interpretation of Force Constants

The quantum-mechanical definition of the force constant k of a diatomic molecule is given. The three main approaches to the calculation of force constants—the perturbation approach, the virial theorem approach, and the strict Hellmann—Feynman approach—are discussed. Several new expressions for k are derived. In particular the Hellmann—Feynman theorem leads to a general expression for k in terms of the charge density ρ and of the change δρ/δR with internuclear distance R. It is also possible to relate the force constant to the quadrupole coupling constant (eqQ) of either nucleus by the formula k=ZAqA+43πρ(A)− ∫ (∂ρ/∂XA) (cosθA/rA2) dτ.The experimentally observed relation k≅qH for diatomic hydrides is then interpreted in terms of the properties of the charge density of these molecules.