Absorption Intensity and Radiative Rates

Integration of absorption extinction coefficient (Eq. [127]) and emission rate (Eq. [128]) gives two alternative estimates for the adiabatic gas-phase transition dipole mu (in D) within the TSM frequency-dependent mu(v) (Eq. [132]) 

Equation [139] is not very practical because an accurate definition of the average wavenumber, Vav = Vav/c, demands knowledge of the emission spectrum for which Eq. [136] provides a direct route to the transition dipole. But Eq. [139] can be used in approximate calculations by assuming Vav = Vem- 

Equation [139] is exact for a two-state solute, but differs from the traditionally used connection between the transition dipole and the emission intensity by the factor Vo/Vav. The commonly used combination miiVo/Vav appears as a result of neglect of the frequency dependence of the transition dipole mi2(v) entering Eq. [129]. It can be associated with the condensed-phase transition dipole in the two-state approximation. Exact solution for a two-state solute makes the transition dipole between the adiabatic free energy surfaces inversely proportional to the energy gap between them. This dependence, however, is eliminated when the emission intensity is integrated with the factor 

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