FC2DES: Modeling 2D electronic spectroscopy for harmonic Hamiltonians

Two-dimensional electronic spectroscopy (2DES) can provide detailed insight into the energy transfer and relaxation dynamics of chromophores by directly measuring the nonlinear response function of the system. However, experiments are often difficult to interpret, and the development of computationally affordable approaches to simulate experimental signals is desirable. For linear spectroscopy, optical spectra of small to medium-sized molecules can be efficiently calculated in the Franck-Condon approach. Approximating the nuclear degrees of freedom as harmonic around the ground- and excited-state minima, closed-form expressions for the exact finite-temperature linear response function can be derived using path-integral approaches, fully accounting for Duschinsky mode-mixing effects. In the present work, we demonstrate that a path-integral approach can be utilized to yield analogous closed-form expression for the finite-temperature nonlinear (third-order) response function of harmonic nuclear Hamiltonians. The resulting approach, named FC2DES, is implemented on graphics processing units (GPUs), allowing efficient computations of 2DES signals for medium-sized molecules containing hundreds of normal modes. Benchmark comparisons against the widely used cumulant method for computing 2DES signals are performed on small model systems, as well as the nile red molecule. We highlight the advantages of the FC2DES approach, especially in systems with moderate Duschinsky mode mixing and for long delay times in the nonlinear response function, where low-order cumulant approximations are shown to fail.