The permanent electric dipole moments of cobalt monofluoride, CoF, and monohydride, CoH

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.

A data-driven approach to determine dipole moments of diatomic molecules

We present a data-driven approach for the prediction of the electric dipole moment of diatomic molecules, which is one of the most relevant molecular properties. In particular, we apply Gaussian process regression to a novel dataset to show that dipole moments of diatomic molecules can be learned, and hence predicted, with a relative error ⪅5%. The dataset contains the dipole moment of 162 diatomic molecules, the most exhaustive and unbiased dataset of dipole moments up to date. Our findings show that the dipole moment of diatomic molecules depends on atomic properties of the constituents atoms: electron affinity and ionization potential, as well as on (a feature related to) the first derivative of the electronic kinetic energy at the equilibrium distance.