Linear and nonlinear Herzberg-Teller vibronic coupling effects. I: Electronic photon echo spectroscopy

The dependence of the transition dipole moment on nuclear coordinates gives rise to non-Condon interaction, signaling that the adiabatic Herzberg-Teller vibronic coupling should be considered. This coupling manifests itself in linear spectroscopy through the breakdown of the mirror image symmetry between the absorption and emission spectra. The stronger the non-Condon interaction, the more pronounced is the absorption-emission asymmetry. A nuclear exponential function is used as a simple model to represent the electronic transition dipole moment, the purpose of which is to avoid the use of eigenstate-approach, convergence issues, and finally be able to extend its applicability to nonlinear spectroscopy inexpensively while accounting for linear and nonlinear non-Condon effects (Herzberg-Teller vibronic coupling). The non-Condon effects on linear and nonlinear spectroscopic signals (e.g. 2-pulse photon echo) are examined. Closed-form expressions of the non-Condon electronic transition dipole moment time correlation functions, accounting for Herzberg-Teller vibronic coupling effects, are derived. It is shown that nonlinear optical signals in time domain such as 2-pulse photon echo signal, conspicuously reflects the degree of the non-Condon interaction (mostly constructive interference in this work) despite the inhomogeneous broadening disguising the homogeneous structural aspects of the molecular system of interest. As such, this study should be useful in relation to extracting structural and dynamical information of condensed molecular systems. Model calculations of absorption and emission spectra and 2-pulse photon echo signals of Herzberg-Teller vibronically coupled systems are presented. The method presented here seems to more efficient computationally, fast and stable compared to the methods which involve perturbation theory and eigenstate expansion.