Multiconfiguration pair-density functional theory (MC-PDFT) is a multireference method that can be used to calculate excited states. However, MC-PDFT potential energy surfaces have the wrong topology at conical intersections because the last step of MC-PDFT is not a diagonalization of a model-space Hamiltonian matrix, as done in, for example, multistate second-order perturbation theory (MS-CASPT2). We have previously proposed methods that solve this problem by diagonalizing a model-space effective Hamiltonian matrix, where the diagonal elements are MC-PDFT energies for intermediate states, and the off-diagonal elements are evaluated by wave function theory. One previous method is called variational multistate PDFT (VMS-PDFT), whose intermediate states maximize the trace of the effective Hamiltonian, namely, the sum of the MC-PDFT energies of the model-space states; the VMS-PDFT is very robust but is more computationally expensive than another method, extended multistate PDFT (XMS-PDFT), in which the transformation to intermediate states is accomplished without needing any density functional evaluations. However, although VMS-PDFT was accurate in all cases tested, XMS-PDFT was accurate in only some of them. In the present paper, we propose a new method, called compressed-state multistate PDFT (CMS-PDFT), that is as efficient as XMS-PDFT and as accurate as VMS-PDFT. The new method maximizes the trace of the classical Coulomb energy of the intermediate states such that the electron densities of the intermediate states are compressed. We show that CMS-PDFT performs robustly even where XMS-PDFT fails.
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The authors thank Matthew Hermes for valuable help on this project. The authors thank Laura Gagliardi for vital and continuing collaboration on MC-PDFT and for helpful discussion of this work. This work was supported in part by the Air Force Office of Scientific Research by grant FA9550-16-1-0134.