Adiabatic Connection Correlation Functionals in Metallic Solids from Hartree–Fock Gaussian Basis Set Ground State

Adiabatic Connection Integrand Interpolation (ACII) methods, which mix the Görling-Levy second-order perturbation theory (GL2) correlation with density functionals from the strong interaction regime, have been successfully applied to molecular systems, strongly correlated systems, as well as the uniform electron gas (UEG). Here, we consider real metallic solids, including transition metals, where the GL2 term diverges. We tested different ACII approaches, with increased accuracy in reproducing the UEG correlation, and with different strong interaction functionals within the Point-charge-plus-Continuum (PC) model. Calculations are based on the Hartree-Fock (HF) ground state, which has been obtained with a Gaussian Type Orbital basis set, properly reoptimized toward the HF global minimum, with a derivative-free approach introduced here. We compare different metallic properties such as lattice constants, cohesive energies, and bulk total correlation energies with accurate reference results and state-of-the-art Density Functional Theory (DFT) approaches. We found that only the ACII approach with high accuracy for the UEG, namely, the Density Parameter Interpolation (DPI), and with the strong interaction functional reproducing the exact PC model for the Wigner crystal yields a correct second-order gradient-expansion correlation coefficient. This allows reproducing lattice constants and bulk correlation energies with an accuracy comparable to the best state-of-the-art approaches. When DPI is combined with GL2 correlation of atoms, accurate cohesive energies are obtained without error cancellation, which is common in DFT methods.