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  1. 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 a 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.

     
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  2. We combine ab initio molecular electronic Hamiltonians with a cavity quantum electrodynamics model for dissipative photonic modes and apply mean-field theories to the ground- and excited-states of resulting polaritonic systems. In particular, we develop a non-Hermitian configuration interaction singles theory for mean-field ground- and excited-states of the molecular system strongly interacting with a photonic mode and apply these methods to elucidating the phenomenology of paradigmatic polaritonic systems. We leverage the Psi4Numpy framework to yield open-source and accessible reference implementations of these methods. 
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