When molecules are coupled to an optical cavity, new
light–matter
hybrid states, so-called polaritons, are formed due to quantum light–matter
interactions. With the experimental demonstrations of modifying chemical
reactivities by forming polaritons under strong light–matter
interactions, theorists have been encouraged to develop new methods
to simulate these systems and discover new strategies to tune and
control reactions. This review summarizes some of these exciting theoretical
advances in polariton chemistry, in methods ranging from the fundamental
framework to computational techniques and applications spanning from
photochemistry to vibrational strong coupling. Even though the theory
of quantum light–matter interactions goes back to the midtwentieth
century, the gaps in the knowledge of molecular quantum electrodynamics
(QED) have only recently been filled. We review recent advances made
in resolving gauge ambiguities, the correct form of different QED
Hamiltonians under different gauges, and their connections to various
quantum optics models. Then, we review recently developed ab initio
QED approaches which can accurately describe polariton states in a
realistic molecule–cavity hybrid system. We then discuss applications
using these method advancements. We review advancements in polariton
photochemistry where the cavity is made resonant to electronic transitions
to control molecular nonadiabatic excited state dynamics and enable
new photochemical reactivities. When the cavity resonance is tuned
to the molecular vibrations instead, ground-state chemical reaction
modifications have been demonstrated experimentally, though its mechanistic
principle remains unclear. We present some recent theoretical progress
in resolving this mystery. Finally, we review the recent advances
in understanding the collective coupling regime between light and
matter, where many molecules can collectively couple to a single cavity
mode or many cavity modes. We also lay out the current challenges
in theory to explain the observed experimental results. We hope that
this review will serve as a useful document for anyone who wants to
become familiar with the context of polariton chemistry and molecular
cavity QED and thus significantly benefit the entire community.