Constrained-pairing mean-field theory. III. Inclusion of density functional exchange and correlation effects via alternative densities.

The recently proposed constrained-pairing mean-field theory (CPMFT) is here extended to include exchange and correlation effects from density functional theory (DFT) via alternative densities. We transform from alpha and beta spin densities to alternatives based on the total and on-top pair densities. This transformation is needed because CPMFT produces correct spin-symmetry and space-symmetry adapted densities that traditional DFT functionals are not designed to work with. The inclusion of DFT exchange and correlation effects in CPMFT is well founded both on practical and methodological reasons. We present multiple benchmarks showing that in many cases our model accurately reproduces unrestricted hybrid functional energies (both regular and range separated) and does so on the correct space-symmetry and spin-symmetry surface. Our approach affords efficient inclusion of dynamical correlation effects absent in CPMFT.