Ab Initio Molecular Cavity Quantum Electrodynamics Simulations Using Machine Learning Models

Abstract

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.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

“…All possible permanent and transition dipoles (between all electronic states) as well as their derivatives are necessary ingredients to perform polariton dynamics simulations. However, these quantities are rarely available in most commonly used excited-state electronic structure methods and have required approximations toward obtaining these gradients. ,,, In this case, one may turn to machine learning techniques to circumvent this need . Recently, ref implemented such a scheme for the simulation of ab initio polariton dynamics.…”

“…However, these quantities are rarely available in most commonly used excited-state electronic structure methods and have required approximations toward obtaining these gradients. ,,, In this case, one may turn to machine learning techniques to circumvent this need . Recently, ref implemented such a scheme for the simulation of ab initio polariton dynamics. In this work, the authors employed the kernel ridge regression (KRR) method, which yields an accurate and analytically differentiable dipole.…”

Machine Learning Framework for Modeling Exciton Polaritons in Molecular Materials

“…A number of previous studies on utilizing ML to predict excited-state quantities have been published recently . These works include predicting adiabatic excited-state PES with NN or traditional ML methods, like kernel ridge regression (KRR) , or Gaussian process regression, transition dipole modeled with KRR, dipole moments and PES in diabatic representation, , nonadiabatic coupling vectors (NACRs), , and attempts on achieving transferability for excited-state modeling . Normally, a nonadiabatic simulation involves a manifold of excited states, with frequent crossings among them.…”

Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction Theory

“…There are at least two complementary approaches to this problem: so-called parametrized CQED methods and self-consistent CQED methods. The former parametrized approach involves solving two Schrödinger equations in series: a first for the molecular system alone using traditional tools of ab initio quantum chemistry, and the second for the coupled molecular-photonic system that is parametrized by the solutions to the molecular problem. ,, On the other hand, the self-consistent approach involves augmenting ab initio quantum chemistry methods to directly include coupling to photonic degrees of freedom. Such approaches have included quantum electrodynamics generalizations of density functional theory (QEDFT ,− and QED-DFT − ), real-time ,,− and linear-response ,, formulations of QED-TDDFT, configuration interaction (QED-CIS), cavity QED extension of second-order Møller-Plesset perturbation theory and the algebraic diagrammatic construction, , coupled cluster (QED-CC), ,− variational QED-2-RDM methods, and diffusion Monte Carlo .…”