Analytical Gradient Theory for Resolvent-Fitted Second-Order Extended Multiconfiguration Perturbation Theory (XMCQDPT2).

We present the formulation and implementation of an analytical gradient algorithm for extended multiconfiguration quasidegenerate perturbation theory (XMCQDPT2) with the resolvent-fitting approximation by Granovsky. This algorithm is powerful when optimizing molecular configurations with a moderate-sized active space and many electronic states. First, we present the powerfulness and accuracy of resolvent-fitting approximations compared to canonical XMCQDPT2 theory. Then, we demonstrate the utility of the current algorithm in frequency analyses, optimizing the minimum energy conical intersection geometries of the retinal chromophore model RPSB6 and evaluating nuclear gradients when there are many electronic states. Furthermore, we parallelize the algorithm using the OpenMP/MPI hybrid approach. Additionally, we report the computational cost and parallel efficiency of the program.