where ⟨cos 2 θ⟩ is expressed in Eq. 76, λ b is molecular reorganization energy (c.f. Eq. 9), which accounts for the additional light-matter detuning when the cavity frequency is equal to the bare molecular excitation. For the model system considered here, which is in the slow bath limit (inhomogeneous limit), κ/2 = √ ln 2 • λ b kBT ℏ , and √ ln 2 is the half of Full-width half maximum (FWHM) conversion factor for a Gaussian lineshape. The real part of Eq. 80 gives the location of the polariton peaks, and the imaginary part gives the linewidth of the respective polaritons. For the resonance case, the Rabi splitting is expressed as