We present a mixed quantum-classical simulation of polariton
dynamics
for molecule–cavity hybrid systems. In particular, we treat
the coupled electronic–photonic degrees 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 nuclear gradient expression derived from the Pauli–Fierz
quantum electrodynamics Hamiltonian without making 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
electronic structure methods. To address this challenge, we use a
machine learning model with the Kernel ridge regression method to
construct the dipoles and further obtain 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 investigate 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 polariton dynamics results
also demonstrate the isomerization 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.