Investigating Molecular Exciton Polaritons Using Ab Initio Cavity Quantum Electrodynamics

Abstract

Coupling molecules to the quantized radiation field inside an optical cavity creates a set of new photon–matter hybrid states called polariton states. We combine electronic structure theory with quantum electrodynamics (QED) to investigate molecular polaritons using ab initio simulations. This framework joins unperturbed electronic adiabatic states with the Fock state basis to compute the eigenstates of the QED Hamiltonian. The key feature of this “parametrized QED” approach is that it provides the exact molecule–cavity interactions, limited by only approximations made in the electronic structure. Using time-dependent density functional theory, we demonstrated comparable accuracy with QED coupled cluster benchmark results for predicting potential energy surfaces in the ground and excited states and showed selected applications to light-harvesting and light-emitting materials. We anticipate that this framework will provide a set of general and powerful tools that enable direct ab initio simulation of exciton polaritons in molecule–cavity hybrid systems.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

“…The two small organic molecules (Figure a,c) showcase the most scattered of the dipole matrices, the LiF (Figure b) shows a block-like structure (due to the reduced dimensionality), and the large organic species (Figure d) shows an intermediate regime where the high-energy states are weakly coupled and have some structure while the low-energy states showcase a strong degree of coupling in a block-like fashion. In this molecule, there is evidence of charge-transfer states (e.g., states 2 and 3) with large permanent dipoles due to the large spatial reorganization of charge upon electronic excitation …”

“…Recently, Zhang, Nelson, and Tretiak implemented analytic nuclear gradients on the dipole and simulated the photoexcited dynamics of the stilbene molecule . In this work, the authors modified the NEXMD software package ,,− to include the pQED Hamiltonian (see Section ) at the Jaynes-Cummings level with all proper gradients required for this Hamiltonian (i.e., without DSE and making the rotating wave approximation). Additionally, the gradients on the potential energy surfaces, nonadiabatic couplings, and dipole gradients were achieved analytically at the TD-AM1 level of theory in the collective electronic oscillator (CEO) framework. ,, Most importantly, the nuclear gradient on the bare transition dipole between the ground and excited electronic states was computed as μ 0α = Tr[ μ̂ X̂ 0α ] in the atomic orbital { o , v } basis and can be understood as, ∂ μ 0 α ∂ R j = ∑ o v ∂ μ o v ∂ boldR j X v o 0 α + μ o v ∂ X v o 0 α ∂ R j where X vo 0α is the transition density matrix similar to that found in eq between the ground and α th excited electronic state in the CIS-approximation ,,, (see additional discussion in Sec.…”

Cavity Born–Oppenheimer Hartree–Fock Ansatz: Light–Matter Properties of Strongly Coupled Molecular Ensembles

“…This molecular dipole–dipole interaction term E dse (2 J ) in combination with E dse ( nuc ) is commonly used as a first-order approximation , of the DSE energy. Note that the full E dse can also be approximated with the help of permanent dipole moments and transition dipole moments in a resolution of identity approach by summing over excited-electronic states. ,, …”

“…Note that the full E dse can also be approximated with the help of permanent dipole moments and transition dipole moments in a resolution of identity approach by summing over excited-electronic states. 22,27,61 By solving eq 5 with an SCF approach, E CBO is minimized for a given configuration of classic nuclei and a fixed photon displacement coordinate (parametric photon field). The ground state for the combined electronic−photonic subsystem is obtained by minimizing E CBO with respect to the photon displacement coordinate, which leads to the following expression:…”

Theory for Cavity-Modified Ground-State Reactivities via Electron–Photon Interactions

“…Our theory predicts that for a proton-coupled electron transfer model system (Shin–Metiu model), the ground-state barrier height can be modified through light–matter interactions when the cavity frequency is in the electronic excitation range. This novel change in the ground-state chemical reactivity is achieved through strong electronic coupling as opposed to the more common use of vibrational strong coupling for modifying the ground state. ,,− Our simple theory explains several recent computational investigations that discovered the same effect for proton-transfer systems ,, and has the potential to add valuable insights into many more ground-state polariton studies. ,− ,− We further demonstrate that under the deep strong coupling limit of the light and matter, the polaritonic ground and first excited eigenstates become the Mulliken–Hush (MH) diabatic states, which are the eigenstates of the dipole operator. This work provides a simple but powerful theoretical framework to understand how strong coupling between molecule and cavity can modify ground-state reactivities.…”