Dispersion size-consistency

Abstract

A multivariate adiabatic connection (MAC) framework for describing dispersion interactions in a system consisting of N non-overlapping monomers is presented. By constraining the density to the physical ground-state density of the supersystem, the MAC enables a rigorous separation of induction and dispersion effects. The exact dispersion energy is obtained from the zero-temperature fluctuation–dissipation theorem and partitioned into increments corresponding to the interaction energy gained when an additional monomer is added to a K-monomer system. The total dispersion energy of an N-monomer system is independent of any partitioning into subsystems. This statement of dispersion size consistency is shown to be an exact constraint. The resulting additive separability of the dispersion energy results from multiplicative separability of the generalized screening factor defined as the inverse generalized dielectric function. Many-body perturbation theory (MBPT) is found to violate dispersion size-consistency because perturbative approximations to the generalized screening factor are nonseparable; on the other hand, random phase approximation-type methods produce separable generalized screening factors and therefore preserve dispersion size-consistency. This result further explains the previously observed increase in relative errors of MBPT for dispersion interactions as the system size increases. Implications for electronic structure theory and applications to supramolecular materials and condensed matter are discussed.