Variational Active Space Selection with Multiconfiguration Pair-Density Functional Theory

The
selection of an adequate set of active orbitals for modeling
strongly correlated electronic states is difficult to automate because
it is highly dependent on the states and molecule of interest. Although
many approaches have shown some success, no single approach has worked
well in all cases. In light of this, we present the “discrete
variational selection” (DVS) approach to active space selection,
in which one generates multiple trial wave functions from a diverse
set of systematically constructed active spaces and then selects between
these wave functions variationally. We apply this DVS approach to
207 vertical excitations of small-to-medium-sized organic and inorganic
molecules (with 3 to 18 atoms) in the QUESTDB database by (i) constructing
various sets of active space orbitals through diagonalization of parametrized
operators and (ii) choosing the result with the lowest average energy
among the states of interest. This approach proves ineffective when
variationally selecting between wave functions using the density matrix
renormalization group (DMRG) or complete active space self-consistent
field (CASSCF) energy but is able to provide good results when variationally
selecting between wave functions using the energy of the translated
PBE (tPBE) functional from multiconfiguration pair-density functional
theory (MC-PDFT). Applying this DVS-tPBE approach to selection among
state-averaged DMRG wave functions, we obtain a mean unsigned error
of only 0.17 eV using hybrid MC-PDFT. This result matches that of
our previous benchmark without the need to filter out poor active
spaces and with no further orbital optimization following active space
selection of the SA-DMRG wave functions. Furthermore, we find that
DVS-tPBE is able to robustly and effectively select between the new
SA-DMRG wave functions and our previous SA-CASSCF results.