Treatment of Herzberg-Teller and non-Condon effects in optical spectra with Hierarchical Equations of Motion

TL;DR

This paper develops a Hierarchical Equations of Motion approach to accurately model Herzberg-Teller and non-Condon effects in optical spectra, incorporating vibrational mode interactions and nonadiabatic couplings.

Contribution

It introduces a novel HEOM formulation that includes vibrational coordinate dependence in nonadiabatic couplings, enhancing spectral simulation accuracy.

Findings

HEOM accurately reproduces explicit vibrational mode calculations.

Effective Huang-Rhys factors can describe strong excitonic coupling effects.

The method improves understanding of vibronic spectral features.

Abstract

We derive a Hierarchical Equations of Motion (HEOM) description of nonadiabatic Herzberg-Teller type coupling effects and of non-Condon effects in a system of electronic transitions interacting with intra- and inter-molecular vibrational modes. We point out analogies between the auxiliary density operators (ADOs) of the hierarchy and the terms arising from explicit description of the vibrational modes in the Hamiltonian. In comparison with the standard formulation of HEOM, our equations contain additional connections between ADOs in the hierarchy scheme, which account for the dependence of the nonadiabatic coupling elements on the vibrational coordinates. We compare absorption spectra calculated with our HEOM methodology and with explicit treatment of vibrational DOF for a dimer system in the strong resonance coupling regime. Furthermore, we show that for sufficiently strong excitonic coupling, the corresponding effects in linear absorption spectra of vibronic dimers can be captured very well by the concept of effective Huang-Rhys factors.