FC2DES+HT: Including Herzberg-Teller effects in the simulation of 2D electronic spectra for harmonic Hamiltonians

Two-dimensional electronic spectroscopy (2DES) is a powerful experimental technique, as it directly probes the nonlinear (third-order) response function of the system, providing key insights into ultrafast energy transfer and relaxation processes. However, 2DES experiments are generally difficult to interpret, often relying on simulations in order to associate observed spectral features with specific underlying system dynamics. For this reason, the development of robust, computationally inexpensive theoretical methods for modeling these experiments remains an active area of research. We have recently derived such an approach for computing the exact finite-temperature nonlinear response function for harmonic Hamiltonians within the Condon approximation, assuming that the transition dipole moment is independent of nuclear coordinates. In this work, we extend our formalism to exactly account for non-Condon/Herzberg-Teller (HT) type contributions to the nonlinear response function, which are known to be crucial for accurately describing linear optical spectra in a wide range of molecular systems. We highlight the key insights that can be gained from our new method, named FC2DES+HT, by simulating the 2DES signals of two molecules with known non-Condon behavior, the phenolate anion and free-base porphyrin. The results demonstrate that Herzberg-Teller couplings substantially impact energy relaxation dynamics in these systems.