Light-Matter interaction is essential in chemistry, physics, and material science. Modifying potential energy surfaces due to light-matter interactions leads to new chemical reaction pathways. A deep understanding of the fundamental details of light-matter interactions usually requires simulations of non-adiabatic transitions among a dense manifold of excited states. We recently developed several formalisms to address the light-matter interaction-induced non-adiabatic phenomena. First, I will discuss our recent developments in theory and numerical methods for simulating plasmon-mediated chemical reactions and the physical insights obtained. Then, we will present our recent developments of theoretical methods for calculating polariton states and simulating polariton dynamics, including QED coupled-cluster theory and ab-initio multiple cloning methods.
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