Completing the Jacob’s ladder of multiconfiguration pair-density functional theory with a doubly hybrid functional

Here we introduce MC-xDH5, the first doubly hybrid functional within the multiconfiguration pair-density functional theory (MC-PDFT) framework, completing the top rung of the MC-PDFT Jacob’s ladder. Introducing perturbative correlation into MC-PDFT raises two challenges: double counting and reference selection. MC-xDH5 overcomes both through the cross-entropy of the natural orbital occupations, which subtracts an estimate of the correlation already contained in the reference and defines a saturation active space (SAS) for the perturbative step. With five optimized parameters, MC-xDH5 reaches mean absolute errors of 2.5 kcal·mol−1 on the training sets, 1.2 kcal·mol−1 on unseen GMTKN55 subsets, and 1.0 kcal·mol−1 across vertical excitation energies and singlet–triplet gaps for ten thermally activated delayed fluorescence molecules. MC-xDH5 thus brings chemical accuracy for multiconfigurational problems within reach at a computational cost comparable to its second-order perturbation theory.