Analytic gradients for state-averaged multiconfiguration pair-density functional theory

Abstract

Analytic gradients are important for efficient calculations of stationary points on potential energy surfaces, for interpreting spectroscopic observations, and for efficient direct dynamics simulations. For excited electronic states, as are involved in UV–Vis spectroscopy and photochemistry, analytic gradients are readily available and often affordable for calculations using a state-averaged complete active space self-consistent-field (SA-CASSCF) wave function. However, in most cases, a post-SA-CASSCF step is necessary for quantitative accuracy, and such calculations are often too expensive if carried out by perturbation theory or configuration interaction. In this work, we present the analytic gradients for multiconfiguration pair-density functional theory based on SA-CASSCF wave functions, which is a more affordable alternative. A test set of molecules has been studied with this method, and the stationary geometries and energetics are compared to values in the literature as obtained by other methods. Excited-state geometries computed with state-averaged pair-density functional theory have similar accuracy to those from complete active space perturbation theory at the second-order.

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

“…where vectors κ and P represent, respectively, the orbital and state rotation parameters 41,42 to compute the dipole moment. This is accomplished by using the method of Lagrange multipliers as was previously shown for the state-specific 41 and state-averaged 42,43 MC-PDFT analytical nuclear gradients.…”

“…The derivatives of the second and third terms in eq (8) are reminiscent of those used in the evaluation of the MC-PDFT nuclear-coordinate gradients, 42 except that the spatial derivatives of the one-electron integrals are replaced by the dipole integrals:…”

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

“…where vectors κ and P represent, respectively, the orbital and state rotation parameters 41,42 minimizing the state-specific CASSCF energy. Because MC-PDFT is a non-variational method, the  …”

Nonadiabatic Molecular Dynamics by Multiconfiguration Pair-Density Functional Theory

“…27 MC-PDFT computes the electron correlation by using a multireference wave function and a functional of the electron density and the on-top density, where the latter describes the probability of finding two electrons on top of each other at a given position in space. Analytical gradients (as required for efficient computation of forces on nuclei) have recently been developed for state-specific 28 and stateaveraged [29][30] MC-PDFT. This allows us to expand the application of MC-PDFT from calculating static properties via single-point calculations 31 to studying dynamical properties of strongly correlated systems.…”