A Hybrid Meta On-Top Functional for Multiconfiguration Pair-Density Functional Theory

Multiconfiguration pair-density functional theory (MC-PDFT) was proposed a decade ago, but it is still in the early stage of density functional development. MC-PDFT uses functionals that are called on-top functionals; they depend on the density and the on-top pair density. Most MCPDFT calculations to date have been unoptimized translations of generalized gradient approximations (GGAs) of Kohn–Sham density functional theory (KS-DFT). A hybrid MCPDFT has also been developed, in which one includes a fraction of the CASSCF wave function energy in the total energy. Meta-GGA functionals, which use kinetic-energy densities in addition to GGA ingredients, have shown higher accuracy than GGAs in KS-DFT, yet the translation of meta-GGA has not been previously proposed for MC-PDFT. In this paper, we propose a way to include kinetic energy density in a hybrid on-top functional for MC-PDFT, and we optimize the parameters of the resulting functional by training with a new database containing a wide variety of systems with diverse characters. The resulting hybrid meta functional is called the MC23 functional. We find that MC23 has equally improved performance as compared to KS-DFT functionals for both strongly and weakly correlated systems. We recommend MC23 for future MC-PDFT calculations.