Here, V NN is the nuclear-nuclear repulsion energy, p, q, r, and s denote molecular orbitals, h pq and g pqrs are one-and two-electron integrals, D pq are the elements of the one-electron reduced density matrices (1-RDMs) and E ot is a functional of the density (ρ) and the on-top pair-density (Π). The hybrid MC-PDFT energy 34 is expressed as: