Can the truncated cumulant expansion capture effects of anharmonicity in nonlinear electronic spectra?

Nonlinear electronic spectroscopy is a powerful tool to determine coupling of electronic states, the effects of solvent interactions on dephasing, and the nature of energy transfer from excited states. Modeling nonlinear electronic spectroscopy has become an area of wide investigation due to the increasing accessibility and power of computational software. Despite these abilities, harmonic approximations to the potential energy surfaces are still generally employed, often resulting in the omission of higher energy vibronic structure. Nonlinear response functions composed of the 2^nd and 3^rd order truncations of the cumulant expansion have shown great ability to simulate realistic complex systems and their environmental interactions, while also potentially capturing some anharmonic effects by computing energy gaps from a realistic molecular dynamics trajectory. However, little is understood about precisely what degree of anharmonicity cumulant truncations can accurately model. I will present results using a model Morse oscillator system to analyze in detail how anharmonicity is treated in cumulant expansion techniques for modeling linear and nonlinear electronic spectra (2DES), examining both the computed dynamic Stokes shift and the transient absorption spectrum.