High-Order Response Functions with Duschinsky Coupling and Finite Temperature: Application to Two-Dimensional Resonance Raman Spectroscopy

Abstract

In this work, we derive closed-form expressions for multi-time correlation functions underlying higher-order nonlinear spectroscopic response functions within the harmonic approximation. Our method includes displacements, frequency changes, and Duschinsky rotation between the vibrational modes of different electronic states while retaining polynomial scaling with the number of degrees of freedom. Finite temperature is accounted for without summation over vibrational eigenstates. To show the capabilities of our method, we apply it to calculate fifth-order two-dimensional resonance Raman (2DRR) spectra of two-mode model systems and naphthalene. Comparison with the displaced harmonic oscillator model shows that Duschinsky rotation modifies the positions and relative intensities of diagonal and cross peaks. Overall, our results demonstrate that 2DRR spectroscopy is particularly sensitive to changes in normal coordinates between electronic states and can provide distinct signatures of Duschinsky coupling in molecular systems.