Analytic energy gradient of excited electronic state within TDDFT/MMpol framework: Benchmark tests and parallel implementation

The time-dependent density functional theory (TDDFT) has become the most popular method to calculate the electronic excitation energies, describe the excited-state properties, and perform the excited-state geometric optimization of medium and large-size molecules due to the implementation of analytic excited-state energy gradient and Hessian in many electronic structure software packages. To describe the molecules in condensed phase, one usually adopts the computationally efficient hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) models. Here, we extend our previous work on the energy gradient of TDDFT/MM excited state to account for the mutual polarization effects between QM and MM regions, which is believed to hold a crucial position in the potential energy surface of molecular systems when the photoexcitation-induced charge rearrangement in the QM region is drastic. The implementation of a simple polarizable TDDFT/MM (TDDFT/MMpol) model in Q-Chem/CHARMM interface with both the linear response and the state-specific features has been realized. Several benchmark tests and preliminary applications are exhibited to confirm our implementation and assess the effects of different treatment of environmental polarization on the excited-state properties, and the efficiency of parallel implementation is demonstrated as well