State-averaged CASSCF with polarizable continuum model for studying photoreactions in solvents: Energies, analytical nuclear gradients, and non-adiabatic couplings

This paper presents state-averaged complete active space self-consistent field in polarizable continuum model (PCM) for studies of photoreactions in solvents. The wavefunctions of the solute and the PCM surface charges of the solvent are optimized simultaneously such that the state-averaged free energy is variationally minimized. The method supports both fixed weights and dynamic weights where the weights are automatically adjusted based on the energy gaps. The corresponding analytical nuclear gradients and non-adiabatic couplings are also derived. Furthermore, we show how the new method can be entirely formulated in terms of seven basic operations, which allows the implementation to benefit from existing high-performance libraries on graphical processing units. Results demonstrating the accuracy and performance of the implementation are presented and discussed. We also apply the new method to the study of minimal conical intersection search and photoreaction energy pathways in solvents. Effects from the polarity of the solvents and different formulas of dynamic weights are compared and discussed