Dipole Moment Calculations Using Multiconfiguration Pair-Density Functional Theory and Hybrid Multiconfiguration Pair-Density Functional Theory

The
dipole moment is the molecular property that most directly
indicates molecular polarity. The accuracy of computed dipole moments
depends strongly on the quality of the calculated electron density,
and the breakdown of single-reference methods for strongly correlated
systems can lead to poor predictions of the dipole moments in those
cases. Here, we derive the analytical expression for obtaining the
electric dipole moment by multiconfiguration pair-density functional
theory (MC-PDFT), and we assess the accuracy of MC-PDFT for predicting
dipole moments at equilibrium and nonequilibrium geometries. We show
that MC-PDFT dipole moment curves have reasonable behavior even for
stretched geometries, and they significantly improve upon the CASSCF
results by capturing more electron correlation. The analysis of a
dataset consisting of 18 first-row transition-metal diatomics and
6 main-group polyatomic molecules with a multireference character
suggests that MC-PDFT and its hybrid extension (HMC-PDFT) perform
comparably to CASPT2 and MRCISD+Q methods and have a mean unsigned
deviation of 0.2–0.3 D with respect to the best available dipole
moment reference values. We explored the dependence of the predicted
dipole moments upon the choice of the on-top density functional and
active space, and we recommend the tPBE and hybrid tPBE0 on-top choices
for the functionals combined with the moderate correlated-participating-orbitals
scheme for selecting the active space. With these choices, the mean
unsigned deviations (in debyes) of the calculated equilibrium dipole
moments from the best estimates are 0.77 for CASSCF, 0.29 for MC-PDFT,
0.24 for HMC-PDFT, 0.28 for CASPT2, and 0.25 for MRCISD+Q. These results
are encouraging because the computational cost of MC-PDFT or HMC-PDFT
is largely reduced compared to the CASPT2 and MRCISD+Q methods.