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The second-order multireference driven similarity renormalization groupperturbation theory (DSRG-MRPT2) theory provides an efficient means ofcorrecting the dynamical correlation with the multiconfiguration referencefunction. The state-averaged DSRG-MRPT2 (SA-DSRG-MRPT2) method is the simplestmeans of treating the excited states with DSRG-MRPT2. In this method, theHamiltonian dressed with dynamical correlation is diagonalized in the CASCIstate subspace (SA-DSRG-MRPT2c) or the configuration subspace (SA-DSRG-MRPT2).This work develops the analytical gradient theory for spin-freeSA-DSRG-MRPT2(c) with the density-fitting (DF) approximation. We check theaccuracy of the analytical gradients against the numerical gradients. Wepresent applications for optimizing minimum energy conical intersections (MECI)of ethylene and retinal model chromophores (PSB3 and RPSB6). We investigate thedependence of the optimized geometries and energies on the flow parameter andreference relaxations. The smoothness of the SA-DSRG-MRPT2(c) potential energysurfaces near the reference (CASSCF) MECI is comparable to the XMCQDPT2 one.These results render the SA-DSRG-MRPT2(c) theory a promising approach forstudies of conical intersections.

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