FORCE BALANCE AND FORCE RELAY IN MOLECULAR-INTERACTIONS - AN ANALYSISBASED ON NONLOCAL POLARIZABILITY DENSITIES

We have recently derived new results for dispersion, induction, and hy perpolarization forces, using nonlocal polarizability densities to cha racterize the changes in electronic charge density induced by molecula r interactions. In this work, we prove that the fundamental physical r equirement of force balance for two interacting molecules A and B is s atisfied within the nonlocal response theory, order by order. An expli cit proof is needed because of differences in the molecular properties that determine the forces on A and B. For example, at first order the force on A depends on the polarizability density of A, alpha(A)(r,r'; omega=0), while the first-order force on B depends on its polarizabili ty density; and for distinct species A and B, there is no relation bet ween alpha(A)(r,r';omega=0) and alpha(B)(r,r';omega=0). We show that f orce balance is derivable from a condition that we term ''force relay. '' Epstein has previously derived this condition for molecules in fixe d external fields, assuming that the electronic state adjusts adiabati cally to the perturbation: then the force of the external held on the nth order term in the electronic charge density equals the force on th e nuclei due to the (n+1)st order correction to the electronic charge density. Our work generalizes the condition to external fields that ar e modified by and correlated with the changes in the electronic charge distribution, as for two interacting molecules with negligible charge overlap. Force relay is guaranteed by relations that we have establis hed among permanent charge densities, linear response tensors, and non linear susceptibilities. All of the results stem from a hypervirial th eorem applied to the electronic momentum operator, and hence from tran slational invariance. The results are not limited to the framework of the polarizability density theory, but also hold for the standard pert urbation theory of interactions between nonoverlapping molecules, and for the Hellmann-Feynman theory of intermolecular forces.