Analytical Gradient Theory for Spin-Free State-Averaged Second-Order Driven Similarity Renormalization Group Perturbation Theory (SA-DSRG-MRPT2) and Its Applications for Conical Intersection Optimizations

TL;DR

This paper develops an analytical gradient theory for spin-free SA-DSRG-MRPT2, enabling efficient optimization of conical intersections in complex molecules, and demonstrates its accuracy and applicability through computational studies.

Contribution

The work introduces the first analytical gradient formulation for spin-free SA-DSRG-MRPT2 with density fitting, enhancing its utility for conical intersection optimization.

Findings

Analytical gradients agree well with numerical gradients.

SA-DSRG-MRPT2(c) provides smooth potential energy surfaces near MECIs.

The method is effective for optimizing conical intersections in complex chromophores.

Abstract

The second-order multireference driven similarity renormalization group perturbation theory (DSRG-MRPT2) theory provides an efficient means of correcting the dynamical correlation with the multiconfiguration reference function. The state-averaged DSRG-MRPT2 (SA-DSRG-MRPT2) method is the simplest means of treating the excited states with DSRG-MRPT2. In this method, the Hamiltonian dressed with dynamical correlation is diagonalized in the CASCI state subspace (SA-DSRG-MRPT2c) or the configuration subspace (SA-DSRG-MRPT2). This work develops the analytical gradient theory for spin-free SA-DSRG-MRPT2(c) with the density-fitting (DF) approximation. We check the accuracy of the analytical gradients against the numerical gradients. We present applications for optimizing minimum energy conical intersections (MECI) of ethylene and retinal model chromophores (PSB3 and RPSB6). We investigate the dependence of the optimized geometries and energies on the flow parameter and reference relaxations. The smoothness of the SA-DSRG-MRPT2(c) potential energy surfaces near the reference (CASSCF) MECI is comparable to the XMCQDPT2 one. These results render the SA-DSRG-MRPT2(c) theory a promising approach for studies of conical intersections.