Toward Long-Range Correlation Energies from Charge Fluctuations: Incorporating Exact Exchange into ACKS2$ω$

Abstract

Long-range electronic correlation can be represented in terms of coupled fluctuations of atomic charges and higher multipoles, motivating a density-response description beyond local dipolar polarization, particularly in low-dimensional, conducting, and small-gap systems where collective electronic fluctuations become important. We extend the frequency-dependent polarizable force field ACKS2$ω$ to electronic-structure references containing exact exchange by deriving both the static and additional frequency-dependent exchange contributions, with particular attention to HFsrPBE, which combines long-range Hartree--Fock exchange with short-range PBE exchange and correlation. Numerical validation of ACKS2$ω$ using dipole polarizabilities and $C_6$ dispersion coefficients for the 27 molecules of the TS27 set, with HF, PBE, B3LYP, and HFsrPBE as the underlying electronic-structure references, shows that including the exchange contributions and enriching the response basis improve agreement with the corresponding orbital-space linear-response calculations, although finite-response-basis errors remain molecule dependent. Long-range correlation energies evaluated through the adiabatic-connection fluctuation-dissipation theorem using the ACKS2$ω$ parameters reproduce the corresponding HFsrPBE orbital-space results for small test molecules when the response basis is made complete within the chosen orbital basis, while a local multipole decomposition resolves the finite-basis energies into monopole--monopole, mixed, dipole--dipole, and remaining higher-multipole contributions, providing a route to evaluating long-range correlation energies in terms of charge fluctuations within atom-condensed models.