Multi-scale dynamics simulations of molecular polaritons: The effect of multiple cavity modes on polariton relaxation

Abstract

Coupling molecules to the confined light modes of an optical cavity is showing great promise for manipulating chemical reactions. However, to fully exploit this principle and use cavities as a new tool for controlling chemistry, a complete understanding of the effects of strong light–matter coupling on molecular dynamics and reactivity is required. While quantum chemistry can provide atomistic insight into the reactivity of uncoupled molecules, the possibilities to also explore strongly coupled systems are still rather limited due to the challenges associated with an accurate description of the cavity in such calculations. Despite recent progress in introducing strong coupling effects into quantum chemistry calculations, applications are mostly restricted to single or simplified molecules in ideal lossless cavities that support a single light mode only. However, even if commonly used planar mirror micro-cavities are characterized by a fundamental mode with a frequency determined by the distance between the mirrors, the cavity energy also depends on the wave vector of the incident light rays. To account for this dependency, called cavity dispersion, in atomistic simulations of molecules in optical cavities, we have extended our multi-scale molecular dynamics model for strongly coupled molecular ensembles to include multiple confined light modes. To validate the new model, we have performed simulations of up to 512 Rhodamine molecules in red-detuned Fabry–Pérot cavities. The results of our simulations suggest that after resonant excitation into the upper polariton at a fixed wave vector, or incidence angle, the coupled cavity-molecule system rapidly decays into dark states that lack dispersion. Slower relaxation from the dark state manifold into both the upper and lower bright polaritons causes observable photo-luminescence from the molecule–cavity system along the two polariton dispersion branches that ultimately evolves toward the bottom of the lower polariton branch, in line with experimental observations. We anticipate that the more realistic cavity description in our approach will help to better understand and predict how cavities can modify molecular properties.

Theoretical Challenges in Polaritonic Chemistry

“…27,94,142,143 The approach initially developed by Luk et al 94 already implements a QM/MM description of molecules in cavities, and has been extended to a multimode cavity characterized by a 1D dispersion. 29 Its current implementation already supports a large number of both wavefunction and density functional methods, interfaced with both surface hopping and Ehrenfest dynamics. 94 In the presence of many molecules and thus a large manifold of closely spaced PoPES, Ehrenfest dynamics provide more robust results compared to surface hopping approaches.…”

“…2,3 This new direction to modify and control the properties of molecular systems is nowadays known as polaritonic chemistry. [4][5][6] It has been shown to affect a wide range of processes, such as photochemical reactions both in single-molecule [7][8][9][10][11][12][13][14] and collective 2,3,[15][16][17][18][19][20] strong-coupling setups, as well as (possibly long-range) energy transfer, [21][22][23][24][25][26][27][28][29][30][31] and transitions between different spin multiplets, [32][33][34][35][36][37][38][39] among others. We emphasize that polaritonic chemistry is not a mere substitute of traditional chemistry techniques, as it can enable processes that are not possible in bare materials due to the long-range and collective nature of the polaritons.…”

“…The polaritonic modes are then delocalized over many molecules, giving rise to collective effects and effective long-range interactions between spatially separated molecules. 2,3,[16][17][18][19][21][22][23][24][25][26][27][28][29][30][31] While there is a wide range of designs that have been developed for optical light confinement, [69][70][71][72] experiments in polaritonic chemistry have almost exclusively used Fabry-Pérot cavities consisting of two planar mirrors. The mirrors are typically either made of metal or from distributed Bragg reflectors (DBRs, alternating layers of dielectric materials with different refractive indices).…”

Not dark yet: strong light-matter coupling can accelerate singlet fission dynamics

“…After a lot of progress in the field during the past decade, there is now a solid understanding on the fundamentals of electronic strong coupling with molecules, e.g., the modification of potential energy surfaces, 3,8-10 conical intersections [11][12][13][14][15] and electron and energy-transfer phenomena. [16][17][18][19][20][21][22] The finite lifetime of the cavity photons [23][24][25][26] and the presence of a dense dark state manifold [27][28][29][30][31][32][33][34][35] are key to understanding polaritonic chemistry phenomena. As already noted, dark states may wash out polaritonic effects in setups with collective, i.e., many-molecule, strong coupling, as there is a macroscopic number of them compared to only two polaritons per cavity mode.…”

Polariton relaxation under vibrational strong coupling: Comparing cavity molecular dynamics simulations against Fermi's golden rule rate

“…Two of the most nontrivial observations include (i) polariton mediated intermolecular vibrational energy transfer between two molecular species after the upper polariton (UP) pumping 27 and (ii) polariton enhanced molecular nonlinear absorption after the lower polariton (LP) pumping 7,26 . While there have been a few theory papers on polariton relaxation based on analytic models 39,42,46,47 and realistic modeling [48][49][50][51] , a systematic study of vibrational polariton relaxation when realistic molecules are considered is still unavailable, which will be the focus of this paper.…”