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 br

Second-order multireference-driven similarity renormal-ization group perturbation theory (DSRG-MRPT2) provides anefficient means of correcting the dynamical correlation with themulticonfiguration reference function. The state-averaged DSRG-MRPT2 (SA-DSRG-MRPT2) method is the simplest means of treatingthe excited states with DSRG-MRPT2. In this method, the Hamiltoniandressed with dynamical correlation is diagonalized in the CASCI statesubspace (SA-DSRG-MRPT2c) or the configuration subspace (SA-DSRG-MRPT2). This work develops analytical gradient theory for spin-free SA-DSRG-MRPT2(c) with the density-fitting approximation. Wecheck the accuracy of the analytical gradients against the numericalgradients. We present applications for optimizing minimum energy conical intersections (MECI) of ethylene and retinal modelchromophores (PSB3 and RPSB6). We investigate the dependence of the optimized geometries and energies on theflow parametersand reference relaxations. The smoothness of the SA-DSRG-MRPT2(c) potential energy surfaces near the reference (completeactive space self-consistentfield) MECI is comparable to the XMCQDPT2 one. These results render SA-DSRG-MRPT2(c) theory apromising approach for studies of conical intersections.