Quantum corrections in vibrational and electronic condensed phase spectroscopy: line shapes and echoes

Various linear and nonlinear vibrational and electronic spectroscopy experiments in liquids are usually analyzed within the second-cumulant approximation, and therefore the fundamental quantity of interest is the equilibrium time-correlation function of the fluctuating transition frequency. In the usual approach the "bath" variables responsible for the fluctuating frequency are treated classically, leading to a classical time-correlation function. Alternatively, sometimes a quantum correction appropriate for relatively high temperatures is included, which adds an imaginary part to the classical time-correlation function. This approach, although appealing, does not satisfy detailed balance. One can consider a similar correction, but where detailed balance is satisfied, by using the harmonic quantum correction factor. In this article, we compare these approaches for a model system and two realistic examples. Our conclusion is that for linear spectroscopy the classical result is usually adequate, whereas for nonlinear spectroscopy it can be more important to include quantum corrections.