Herzberg-Teller coupling in coherent multidimensional spectroscopy: analytical response functions for multilevel systems

TL;DR

This paper derives analytical response functions for Herzberg-Teller (non-Condon) vibronic coupling effects in multidimensional spectroscopy, enabling better interpretation of spectra in complex molecular and solid-state systems.

Contribution

It introduces a general analytical framework for non-Condon effects in multidimensional spectroscopy for multilevel systems, including a Python implementation.

Findings

Herzberg-Teller coupling adds oscillatory factors to response functions.

Spectral replicas are shifted by vibrational frequencies due to non-Condon effects.

The framework applies to systems with arbitrary electronic states and response orders.

Abstract

Coherent multidimensional spectroscopy enables detailed investigations of vibronic effects in molecular and solid-state systems. We present explicit analytical expressions for multidimensional nonlinear response functions in the presence of Herzberg-Teller (non-Condon) coupling, within the displaced harmonic oscillator model. The formulation applies to electronic systems with an arbitrary number N of electronic states and to response functions of arbitrary order M in the light-matter interaction. We show that Herzberg-Teller coupling introduces additional oscillatory factors in the time-domain response functions, leading, upon Fourier transformation, to replicas of the Franck-Condon multidimensional spectra shifted by integer multiples of the vibrational frequencies. The present results provide a general analytical framework for the interpretation of non-Condon effects in coherent multidimensional spectroscopies. A Python code that implements the present approach and simulates multidimensional spectra for N-level systems is available on GitHub.