On the Theory of Shifts and Broadening of Electronic Spectra of Polar Solutes in Polar Media

When a polar-solute molecule undergoes an electronic transition and forms a state of different polarity, the Franck—Condon principle shows that the new system is first formed in a nonequilibrium thermodynamic state. An expression for the spectral shift and broadening by a series of solvents of differing polarity is derived in the present paper in terms of thermodynamic properties of certain equilibrium distribution systems. For this purpose use is made of a recent particle description of nonequilibrium and equilibrium polar media, which emphasizes functional dependence and avoids, thereby, the usual more specific assumptions. A relation between the broadening and the shift is then deduced under certain conditions. Expressions are also derived for the effect of pressure and temperature on the shift, in terms of the polar contribution to the volume and entropy of solvation, respectively, and for the influence of applied electrical fields. An expression is obtained for the solvent-reversal shift of Brooker in terms of the polarizability difference of the initial and final states of the solute. Introduction of more specific assumptions is then made for purposes of comparison with earlier works, which constitute special cases of the present one, and for estimation of dipole moments and polarizabilities of excited states from spectral and electrical shifts.