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An analytical implementation of static dipole polarizabilities within the generalized Kohn–Sham semicanonical projected random phase approximation (GKS-spRPA) method for spin-restricted closed-shell and spin-unrestricted open-shell references is presented. General second-order analytical derivatives of the GKS-spRPA energy functional are derived using a Lagrangian approach. By resolution-of-the-identity and complex frequency integration methods, an asymptotic [Formula: see text] scaling of operation count and [Formula: see text] scaling of storage is realized, i.e., the computational requirements are comparable to those for GKS-spRPA ground state energies. GKS-spRPA polarizabilities are assessed for small molecules, conjugated long-chain hydrocarbons, metallocenes, and metal clusters, by comparison against Hartree–Fock (HF), semilocal density functional approximations (DFAs), second-order Møller–Plesset perturbation theory, range-separated hybrids, and experimental data. For conjugated polydiacetylene and polybutatriene oligomers, GKS-spRPA effectively addresses the “overpolarization” problem of semilocal DFAs and the somewhat erratic behavior of post-PBE RPA polarizabilities without empirical adjustments. The ensemble averaged GKS-spRPA polarizabilities of sodium clusters (Na n for n = 2, 3, …, 10) exhibit a mean absolute deviation comparable to PBE with significantly fewer outliers than HF. In conclusion, analytical second-order derivatives of GKS-spRPA energies provide a computationally viable and consistent approach to molecular polarizabilities, including systems prohibitive for other methods due to their size and/or electronic structure. 

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.