Multiconfigurational short-range on-top pair-density functional theory

We present the theory and implementation of a fully variational wave function-density functional theory (DFT) hybrid model, which is applicable to many cases of strong correlation. We denote this model as the multiconfigurational self-consistent on-top pair-density functional theory (MC-srPDFT) model. We have previously shown how the multiconfigurational short-range DFT (MC-srDFT) hybrid model can describe many multiconfigurational cases of any spin symmetry and also state-specific calculations on excited states [Hedegård et al., J. Chem. Phys. 148(21), 214103 (2018)]. However, the srDFT part of the MC-srDFT has some deficiencies that it shares with Kohn-Sham DFT; in particular, (1) self-interaction errors (albeit reduced because of the range separation), (2) that different MS states incorrectly become non-degenerate, and (3) that singlet and non-singlet states dissociating to the same open-shell fragments incorrectly lead to different electronic energies at dissociation. The model that we present in this paper corrects these deficiencies by introducing the on-top pair density as an auxiliary variable replacing the spin density. Unlike other models in the literature, our model is fully variational and employs a long-range version of the on-top pair density. The implementation is a second-order optimization algorithm ensuring robust convergence to both ground and excited states. We show how MC-srPDFT solves the mentioned challenges by sample calculations on the ground state singlet curve of H2, N2, and Cr2 and the lowest triplet curves for N2 and Cr2. Furthermore, the rotational barrier for ethene is investigated for the S0 and T1 states. The calculations show correct degeneracy between the singlet and triplet curves at dissociation and the results are invariant to the choice of the MS value for the triplet curves.