Benchmarking mixed quantum-classical dynamics for collective electronic strong coupling

Abstract

Experiments indicate that collective coupling of molecular ensembles to confined optical modes can modify excited-state dynamics and photochemical reactivity. To describe such cavity-induced effects at atomic resolution, semi-classical molecular dynamics approaches have been developed that treat nuclear motion classically while describing the collective light-matter interaction within the Tavis-Cummings framework of quantum electrodynamics. Here, we benchmark mixed quantum-classical approaches, Ehrenfest dynamics and Fewest-Switches Surface Hopping (FSSH), for simulating nonadiabatic dynamics of electronically strongly coupled carbon monoxide molecules. Their predictions are compared against numerically exact quantum dynamics simulations performed with the multi-configuration time-dependent Hartree (MCTDH) method, which treats both electronic and nuclear degrees of freedom quantum mechanically. We find that the semi-classical approaches reproduce the qualitative features of the full quantum dynamics. Quantitative agreement is best achieved with FSSH when a decoherence correction is included. These results demonstrate that mixed quantum-classical methods provide a computationally efficient and quantitatively reliable alternative to fully quantum simulations for investigating nonadiabatic photochemistry under collective electronic strong coupling in systems beyond the reach of exact quantum treatments.

Figures (6)

• Figure 1: Adiabatic potential energy profiles of the bare CO molecule (a), and transition dipole moment between the ground, $V_0$ ($^1\Sigma$) and first excited, $V_1$ ($^1\Pi$), electronic states as a function of inter-nuclear distance, $R$ (b). Potential energy profile of one CO molecule in a cavity: The coupling strength is equal to zero (c) and 0.050 au (d). The profile without coupling shows the energy of the ground state shifted by the cavity mode energy (i.e., cavity mode excitation, $V_0+\omega_c$), as well as the ground and excited electronic states of the CO molecule without cavity mode excitation. Panel (d) shows the potential energy profiles of hybrid states that form when the coupling between the cavity and the molecule is 0.050 au. These profiles were obtained by diagonalizing the Tavis-Cummings Hamiltonian [cf. Eq. \ref{['eq:arrow_matrix']}].
• Figure 2: (a) The linear absorption spectrum of a bare CO molecule of the $^1\Pi$ electronic state is evaluated using both MCTDH (solid line) and MD with Gaussian (dashed dot) and Lorentzian (dashed line) convolution functions. (b) Expectation value of the inter-nuclear distance, $\langle{R}\rangle$, as a function of time after instantaneous excitation into the first excited electronic state of the CO molecule.
• Figure 3: The cavity-molecule interaction potential $V_\text{int,r}$, when a single CO molecule is coupled to the cavity mode after vertical excitation into the LP (solid lines) or UP (dashed lines) at different coupling strengths. The MD simulations are averaged over 200 initial conditions sampled from the Wigner distribution of the Morse potential. A value of $V_\text{int,r}$ = -1, or 1 denotes that the population remains trapped in the LP or UP state, respectively.
• Figure 4: The cavity-molecule interaction potential $V_\text{int,r}$, when the three CO molecules are interacting with the cavity mode after vertical excitation into the LP (solid lines) or UP (dashed lines) at different coupling strengths.
• Figure 5: The cavity-molecule interaction potential $V_\text{int,r}$, when the three CO molecules are interacting with the cavity mode after vertical excitation into the LP (solid lines) or UP (dashed lines) states at different coupling strengths. Static disorder ($\pm0.020~E_{\text{S}_1}$)is included such that the excitation energies of the CO molecules are all different.