Ab Initio Molecular Cavity Quantum Electrodynamics Simulations Using Machine Learning Models

We present a mixed quantum-classical simulation of po- lariton dynamics for molecule-cavity hybrid systems. In particular, we treat the coupled electronic-photonic de- grees of freedom (DOFs) as the quantum subsystem and the nuclear DOFs as the classical subsystem and use the trajectory surface hopping approach to simulate non- adiabatic dynamics among the polariton states due to the coupled motion of nuclei. We use the accurate nu- clear gradient expression derived from the Pauli-Fierz Quantum Electrodynamics Hamiltonian without mak- ing further approximations. The energies, gradients, and derivative couplings of the molecular systems are obtained from the on-the-fly simulations at the level of complete active space self-consistent field (CASSCF), which are used to compute the polariton energies and nuclear gradients. The derivatives of dipoles are also necessary ingredients in the polariton nuclear gradient expression but are often not readily available in elec- tronic structure methods. To address this challenge, we use a machine learning model with the Kernel ridge re- gression method to construct the dipoles and further ob- tain their derivatives, at the same level as the CASSCF theory. The cavity loss process is modeled with the Lindblad jump superoperator on the reduced density of the electronic-photonic quantum subsystem. We inves- tigate the azomethane molecule and its photoinduced isomerization dynamics inside the cavity. Our results show the accuracy of the machine-learned dipoles and their usage in simulating polariton dynamics. Our po- lariton dynamics results also demonstrate the isomer- ization reaction of azomethane can be effectively tuned by coupling to an optical cavity and by changing the light-matter coupling strength and the cavity loss rate.