where ε is the molar absorption coefficient, Ψ i and Ψ j are wave functions of the molecular vibrational modes at the ground and excited states, respectively, μ is the dipole moment operator, µ 0 is the dipole moment of the equilibrium position, Q k is the small displacement, dτ is the elementary volume, ν is frequency of light, N A is Avogadro constant, h is Plank constant, c is speed of light, ε 0 is the permittivity of vacuum. The last term in Eqn. 3 is transition moment M, which is the dipole moment change of a molecular vibrational mode described as: