Consistent Improvement on Both Exchange and Correlation within Hybrid Multiconfiguration Pair-density Functional Theory: tB4LYP

The great success of hybrid density functional approximations, e.g.~B3LYP and PBE0, is demonstrated by their substantial improvements over their parent methods, i.e.~the Hartree-Fock approximation and the generalized gradient approximation. They also surpass the second-order M\o{}ller-Plesset perturbation theory (MP2) having a much higher computational cost. Here, we generalize the linear scheme of hybrid multiconfiguration pair-density functional theory (HMC-PDFT) by introducing a cross-entropy approximation to achieve a balanced description of the static and dynamic correlation effects, providing a consistent improvement in describing both exchange and correlation energies. We demonstrated that the B3LYP-like translated on-top functional (tB4LYP) established within the new hybrid scheme is not only more accurate than the parent methods of the complete active space self consistent field (CASSCF) and the pure and hybrid MC-PDFT functional (tBLYP and tB3LYP), but also outdoes the complete active space second-order perturbation theory (CASPT2), which is one of the most popular multi-reference wave-function methods in quantum chemistry. Given that the computational cost of tB4LYP is much cheaper than that of CASPT2, we recommend tB4LYP for the study of complex molecular systems where dynamic and static correlation effects are of comparable importance.