The adiabatic connection fluctuation-dissipation theorem (ACFDT) formulation of density functional theory (DFT) seamlessly connects time-dependent DFT to the computation of the ground state correlation energy in many-electron system. The random phase approximation (RPA), the most popular variant of the ACFDT in use today, has proven to be suprior to semi-local density functionals for prediction of thermochemistry, weak interactions, and structural properties for moleculs and materials alike. RPA has even been shown to mimic static-correlation through its self-correlation error, which leads to more accurate barrier heights and kinetic predictions compared to semi-local methods and hints at RPA's ability to perform even for more "strongly correlated" systems. For the asymmetric Hubbard dimer model, we show that RPA is closer to the exact correlation energy than an exchange-only kernel correction, but inferior to the exact adiabatic kernel, as the system becomes strongly correlated. We also explore the structure and behavior of RPA renormalized perturbation theory for capturing the beyond-RPA correlation with the exact adiabatic approximation, and correlate these results with the behavior of the same perturbation expansion for real molecules and materials.

RPA renormalized perturbation theory applied to the asymmetric Hubbard dimer

ACS Fall 2021

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