Ab initio methods for polariton chemistry

Polariton chemistry exploits the strong interaction between quantized excitations in molecules and quantized photon states in optical cavities to affect chemical reactivity. Polariton chemistry has so far been experimentally realized by the coupling of both vi- brational and electronic transitions to photon modes, which has spurred tremendous theo- retical effort to model and explain these effects. This tutorial review focuses on a particular thrust in theoretical chemistry and chemical physics aimed at merging techniques from ab-initio electronic structure theory with cavity quantum electrodynamics with the goal of providing predictive theories for polariton chemistry. Our goal 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.