Nuclear Gradient Expressions for Molecular Cavity Quantum Electrodynamics Simulations using Mixed Quantum-Classical Methods

Abstract

We derive a rigorous nuclear gradient for a molecule-cavity hybrid system using the Quantum Electrodynamics Hamiltonian. We treat the electronic-photonic DOFs as the quantum subsystem, and the nuclei as the classical subsystem. Using the adiabatic basis for the electronic DOF and the Fock basis for the photonic DOF, and requiring the total energy conservation of this mixed quantum-classical system, we derived the rigorous nuclear gradient for the molecule-cavity hybrid system, which is naturally connected to the approximate gradient under the Jaynes-Cummings approximation. The nuclear gradient expression can be readily used in any mixed quantum-classical simulations and will allow one to perform the non-adiabatic on-the-fly simulation of polariton quantum dynamics. The theoretical developments in this work could significantly benefit the polariton quantum dynamics community with a rigorous nuclear gradient of the molecule-cavity hybrid system and have a broad impact on the future non-adiabatic simulations of polariton quantum dynamics.

Ab Initio Molecular Cavity Quantum Electrodynamics Simulations Using Machine Learning Models

“…Recently, various theoretical methods have been developed or extended to directly simulate the polariton dynamics. These include the full quantum dynamics simulations, [18][19][20][21] mixed-quantum-classical (MQC) dynamics, 12,13,[22][23][24][25] and non-adiabatic dynamics based on the mapping formalism. 6,26 Among them, the MQC dynamics methods describe the electronic-photonic DOFs quantum mechanically and treat the nuclear DOFs classically, hence well balance the computational cost and accuracy of the dynamics.…”

“…Thus, the MQC methods, including the Ehrenfest and trajectory surface hopping (TSH) methods, have been widely used in the nonadiabatic polariton dynamics recently. [11][12][13][14][15][16][17][23][24][25][26][27][28] In the propagation of the polariton dynamics with the MQC methods, besides the energies of the electron-photon hybrid states, we need to derive the nuclear gradients and the couplings between these states, where the derivatives of molecular dipoles (including permanent dipoles and transition dipoles) are the key ingredients. 25,26 For some model systems with well-defined diabatic electronic states, the dipoles of/between these diabatic states can be set to constants.…”

“…[11][12][13][14][15][16][17][23][24][25][26][27][28] In the propagation of the polariton dynamics with the MQC methods, besides the energies of the electron-photon hybrid states, we need to derive the nuclear gradients and the couplings between these states, where the derivatives of molecular dipoles (including permanent dipoles and transition dipoles) are the key ingredients. 25,26 For some model systems with well-defined diabatic electronic states, the dipoles of/between these diabatic states can be set to constants. 23,28 For model systems with adiabatic electronic states, the dipoles of/between these adiabatic states can be calculated through the discrete variable representation (DVR).…”

“…23,28 For model systems with adiabatic electronic states, the dipoles of/between these adiabatic states can be calculated through the discrete variable representation (DVR). 25,26 Evaluating the derivatives of molecular dipoles remains a theoretical bottleneck for simulating ab initio polariton quantum dynamics. These derivatives are neither readily available for most electronic structure methods nor computationally cheap to obtain.…”

“…To the best of our knowledge, there is no previous work on using correlated wavefunction level of theory to perform ab initio on-the-fly quantum dynamics simulations of polariton chemistry with the rigorous nuclear gradient. 25 In this work, we construct the dipoles (including permanent and transition dipoles) and their derivatives for realistic molecules using machine-learning techniques. [30][31][32][33][34] We apply the machine-learned dipoles and derivatives to ab initio on-the-fly polariton dynamics simulations of a realistic polyatomic molecular system, azomethane, coupled to an optical cavity.…”