in which h pq and g pqrs are the one-and two-electron integrals, and D n pq the one-body density matrix of |n⟩. All non-classical correlation in MC-PDFT is treated through the "on-top" functional E ot , which is a functional of the density (ρ n ) and on-top density (Π n ) of the CAS wave function. In practice, the on-top functional is a "translated" Kohn-Sham density functional, with tPBE, the translated PBE functional, being the standard choice. The DVS approach (explained in section 2.3) variationally selects active spaces by means of their tPBE energies.