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arXiv · 2601.09346

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

Filippo Troiani
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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.

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Filippo Troiani. 2026-01-14. Herzberg-Teller coupling in coherent multidimensional spectroscopy: analytical response functions for multilevel systems. https://doi.org/10.1063/5.0322870

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