Recent theoretical works have focused on investigating a single molecule coupled to a cavity mode and try to obtain some insights into the VSC-modified reactivities. For simplicity, we assume that the direction of the dipole is always aligned with cavity field polarization direction, such that μ•ê = μ. The universal light-matter Hamiltonian for this ground state reaction problem is given by ĤPF (Eq. 70) and using the projection operator that only includes the electronic ground state as P = |ψ g (R)⟩⟨ψ g (R)|, the projected light-matter Hamiltonian becomes