In this paper, we use this Shin-Metiu three-level system to demonstrate two different regimes of ground state modification. To demonstrate the ground state potential modification when coupling a molecule to the cavity, we use the Shin-Metiu 39 single-electron proton-transfer model truncated to three matter levels for the matter Hamiltonian. This model consists of fixed donor and acceptor ions with a proton being transferred between them, yielding one nuclear coordinate. The matter truncation is done in the MH basis, creating a model three-level system with donor (D), acceptor (A), and covalent (C) diabatic states, such that {|µ i } ∈ {|D , |A , |C }.