) which is included in the hybridization. We refer to hybrid calculations by using the language of hybrid functionals, for example we refer to using Eq. 16 with λ equal to 0.25 and the tPBE functional in the MC-PDFT term as an HMC-PDFT calculation with the hybrid functional tPBE0. Because it has been found that hybrid functionals, such as tPBE0, are more accurate than non-hybrid ones for certain systems, we also construct a hybrid linearized PDFT (HL-PDFT) Hamiltonian.