Analytic gradients for multiconfiguration pair-density functional theory with density fitting: Development and application to geometry optimization in the ground and excited states

Abstract

Density fitting reduces the computational cost of both energy and gradient calculations by avoiding the computation and manipulation of four-index electron repulsion integrals. With this algorithm, one can efficiently optimize the geometries of large systems with an accurate multireference treatment. Here, we present the derivation of multiconfiguration pair-density functional theory for energies and analytic gradients with density fitting. Six systems are studied, and the results are compared to those obtained with no approximation to the electron repulsion integrals and to the results obtained by complete active space second-order perturbation theory. With the new approach, there is an increase in the speed of computation with a negligible loss in accuracy. Smaller grid sizes have also been used to reduce the computational cost of multiconfiguration pair-density functional theory with little effect on the optimized geometries and gradient values.

Nonadiabatic Molecular Dynamics by Multiconfiguration Pair-Density Functional Theory

“…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 and state-averaged , MC-PDFT. This allows us to expand the application of MC-PDFT from calculating static properties via single-point calculations to studying dynamical properties of strongly correlated systems.…”

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

“…We presented analytic gradients for MC-PDFT in a series of three papers concerned successively with MC-PDFT based on CASSCF orbitals, 146 MC-PDFT based on SA-CASSCF orbitals, 147 and MC-PDFT with the calculation of two-electron integrals speeded up by density fitting using Cholesky decomposition. 148 …”

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.…”

“…Because MC-PDFT is a nonvariational method, the ∂ κ /∂ F x and ∂ P /∂ F x partial derivatives are generally not equal to zero, and thus, the response of the wave function is required to compute the dipole moment. This is accomplished using the method of Lagrange multipliers as was previously shown for the state-specific and state-averaged , MC-PDFT analytical nuclear gradients. If the CASSCF wave function is chosen as the reference wave function in MC-PDFT, the Lagrangian takes the form where z orb is a Lagrange multiplier for orbital rotation and z CI is a Lagrange multiplier for state rotation.…”