  Polariton chemistry exploits the strong interaction between quantized
excitations in molecules and quantized photon states in optical cavities to
affect chemical reactivity. Molecular polaritons have been experimentally
realized by the coupling of electronic, vibrational, and rovibrational
transitions to photon modes, which has spurred tremendous theoretical effort to
model and explain how polariton formation can influence chemistry. This
tutorial review focuses on computational approaches for the electronic strong
coupling problem through the combination of familiar techniques from ab initio
electronic structure theory and cavity quantum electrodynamics, toward the goal
of supplying predictive theories for polariton chemistry. Our aim is to
emphasize the relevant theoretical details with enough clarity for newcomers to
the field to follow, and to present simple and practical code examples to
catalyze further development work.
