Vibrational response functions for multidimensional electronic spectroscopy in the adiabatic regime: a coherent-state approach

TL;DR

This paper develops a coherent state framework for calculating vibrational response functions in multidimensional electronic spectroscopy, enabling analysis of nuclear-electronic interactions and vibrational relaxation effects.

Contribution

It introduces a novel coherent state approach to derive analytical response functions for vibronic dynamics in the linearly displaced oscillator model, including thermal and relaxation effects.

Findings

Analytical expressions for third-order response functions derived

Generalization to arbitrary M-th order response functions achieved

Inclusion of vibrational relaxation effects via non-Hermitian Hamiltonian

Abstract

Multi-dimensional spectroscopy represents a particularly insightful tool for investigating the interplay of nuclear and electronic dynamics, which plays an important role in a number of photophysical processes and photochemical reactions. Here we present a coherent state representation of the vibronic dynamics and of the resulting response functions for the widely used linearly displaced oscillator model. Analytical expressions are initially derived for the case of third-order response functions in an N-level system, with ground state initialization of the oscillator (zero-temperature limit). The results are then generalized to the case of M-th order response functions, with arbitrary M. The formal derivation is translated into a simple recipe, whereby the explicit analytical expressions of the response functions can be derived directly from the Feynman diagrams. We further generalize to the whole set of initial coherent states, which form an overcomplete basis. This allows one in principle to derive the dependence of the response functions on arbitrary initial states of the vibrational modes and is here applied to the case of thermal states. Finally, a non-Hermitian Hamiltonian approach is used to include in the above expressions the effect of vibrational relaxation.