  Complete active space self-consistent field (CASSCF) computations can be
realized at polynomial cost via the variational optimization of the
active-space two-electron reduced-density matrix (2-RDM). Like conventional
approaches to CASSCF, variational 2-RDM (v2RDM)-driven CASSCF captures
nondynamical electron correlation in the active space, but it lacks a
description of the remaining dynamical correlation effects. Such effects can be
modeled through a combination of v2RDM-CASSCF and on-top pair-density
functional theory (PDFT). The resulting v2RDM-CASSCF-PDFT approach provides a
computationally inexpensive framework for describing both static and dynamical
correlation effects in multiconfigurational and strongly correlated systems.
On-top pair-density functionals can be derived from familiar Kohn-Sham
exchange-correlation (XC) density functionals through the translation of the
v2RDM-CASSCF reference densities [Li Manni et al., J. Chem. Theory Comput. 10,
3669-3680 (2014)]. Translated and fully-translated on-top PDFT versions of
several common XC functionals are applied to the potential energy curves of N2,
H2O, and CN-, as well as to the singlet/triplet energy splittings in the linear
polyacene series. Using v2RDM-CASSCF-PDFT and the translated PBE functional,
the singlet/triplet energy splitting of an infinitely-long acene molecule is
estimated to be 4.87 kcal/mol.
