A comparison of the Liptay theory of electroabsorption spectroscopy with the sum-over-state model and its modification for the degenerate case

This study has theoretically clarified the relationship between two descriptions of electroabsorption (EA) spectrum: the Liptay equation and the sum-over-state (SOS) model. The former describes the EA spectrum by the linear combination of derivatives of the linear absorption and the latter describes it by a third-order nonlinear optical susceptibility. The EA spectrum described by the SOS model is equivalent to that by the Liptay equation except the coefficient of the zeroth-order derivative, when the optically forbidden (dark) state is not degenerate with the optically allowed (bright) state. Also when the dark state is degenerate with the bright state, the EA spectrum can be described by a formal Liptay equation with some modifications of the coefficients, as well as by the SOS model. Such a modified Liptay equation can bring us new information on the transition dipole moment concerned with the dark state, as demonstrated in an experiment for β−carotene homologs. Differences between the two descriptions are discussed, and our results are compared with the previous two-state model.