  Multiconfiguration pair-density functional theory (MC-PFDT) has previously
been applied successfully to carry out ground-state and excited-state
calculations. However, because it includes no interaction between electronic
states, MC-PDFT calculations can give an unphysical double crossing of
potential energy surfaces (PESs) in a region near a conical intersection. We
have recently proposed state-interaction pair-density functional theory
(SI-PDFT) to treat nearly degenerate states; although this method is
successful, it is inconvenient because two SCF calculations and two sets of
orbitals are required and because it puts the ground state on an unequal
footing with the excited states. Here we propose two new methods, called
extended-multi-state-PDFT (XMS-PDFT) and variational-multi-state-PDFT
(VMS-PDFT), that generate the intermediate states in a balanced way with a
single set of orbitals. The former uses the intermediate states proposed by
Granovsky for extended multiconfiguration quasidegenerate perturbation theory
(XMC-QDPT); the latter obtains the intermediate states by maximizing the sum of
the MC-PDFT energies for the intermediate states. We also propose a Fourier
series expansion to make the variational optimizations of the VMS-PDFT method
convenient, and we implement this method (FMS-PDFT) both for conventional
configuration-interaction solvers and for density-matrix-renormalization-group
solvers. The new methods are tested for eight systems exhibiting avoided
crossings among two to six states. The FMS-PDFT method is successful for all
eight test cases studied in the paper, and XMS-PDFT is successful for all of
them except the mixed-valence case. Since both XMS-PDFT and VMS-PDFT are less
expensive than XMS-CASPT2, they will allow well-correlated calculations on much
larger systems for which perturbation theory is unaffordable.
