A Benchmark Study of Different Methods for Calculating One- And Two-Dimensional Optical Spectra

The accuracy and robustness of several approximate methods for computing linear and nonlinear optical spectra are considered. The analysis is performed in the context of a benchmark model that consists of a two-state chromophore with shifted harmonic potential surfaces that differ in frequency. The exact one- and two-dimensional spectra for this system are calculated and compared to spectra calculated via the following approximate methods: (1) The semiclassical forward-backward initial-value representation (FB-IVR) method, (2) the linearized semiclassical (LSC) method; (3) the standard second-order cumulant approximation which is based on the ground-state equilibrium frequency-frequency correlation function (2OC); (4) an alternative second-order cumulant approximation which is able to account for nonequilibrium dynamics on the excited-state potential surface (2OCa), All four approximate methods can be shown to reproduce the exact results when the frequencies of the ground and excited harmonic surfaces are identical. However, allowing for the ground and excited surfaces to differ in frequency leads to a more meaningful benchmark model for which none of the four approximate methods is exact. We present a comparison of one- and two-dimensional spectra calculated via the above-mentioned approximate methods to the corresponding exact spectra, as a function of the following parameters: (1) The ratio of excited state to ground-state frequencies; (2) Temperature; (3) The horizontal displacement of the excited-state potential relative to the ground-state potential; (4) The waiting time between the coherence periods in the case of two-dimensional spectra, The FB-IVR method is found to predict spectra which are practically indistinguishable from the exact ones over a wide region of parameter space. The LSC method is found to predict spectra which are in good agreement with the exact ones over the same region of parameter space. The 2OC and 2OCa are found to be highly inaccurate unless the frequencies of the ground and excited states are very similar. These observations give credence to the use of the LSC method for modeling spectra in complex systems, where exact or even FB-IVR-based calculations are prohibitively expensive.