Force balance and force relay in molecular interactions: An analysis based on nonlocal polarizability densities

Liu, P.-H.; Hunt, K. L. C.
February 1994
Journal of Chemical Physics;2/15/1994, Vol. 100 Issue 4, p2800
Academic Journal
We have recently derived new results for dispersion, induction, and hyperpolarization forces, using nonlocal polarizability densities to characterize the changes in electronic charge density induced by molecular interactions. In this work, we prove that the fundamental physical requirement of force balance for two interacting molecules A and B is satisfied within the nonlocal response theory, order by order. An explicit 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, αA(r,r’;ω=0), while the first-order force on B depends on its polarizability density; and for distinct species A and B, there is no relation between αA(r,r’;ω=0) and αB(r,r’;ω=0). We show that force balance is derivable from a condition that we term ‘‘force relay.’’ Epstein has previously derived this condition for molecules in fixed external fields, assuming that the electronic state adjusts adiabatically to the perturbation: then the force of the external field on the nth order term in the electronic charge density equals the force on the nuclei due to the (n+1)st order correction to the electronic charge density. Our work generalizes the condition to external fields that are 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 established among permanent charge densities, linear response tensors, and nonlinear susceptibilities. All of the results stem from a hypervirial theorem applied to the electronic momentum operator, and hence from translational invariance. The results are not limited to the framework of the polarizability density theory, but also hold for the standard perturbation theory of interactions between nonoverlapping...


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