Development of computer programs for two dimensional Raman and Infrared vibrational spectroscopy

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Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian (GM) Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the 5h-order nonresonant Raman and the 3rd-order infrared or equivalently the 2nd-order infrared and the 7th-order nonresonant Raman spectra are calculated under the various combinations of the LL and the SL coupling strengths. We then study a dissipative bistable system presents the simplest model to describe condensed phase reaction dynamics. Using a quantum master equation approach to calculate multitime dipole correlation functions we demonstrate how the dissipative dynamics can be characterized by time-resolved 3rd-order infrared spectroscopy. Thereby we incorporate LL and SL system-bath interaction into the Redfield relaxation tensor. We also investigate a 2D spectra of a rigid rotator coupled to a GM harmonic oscillator bath. The analytical expression of a four-time correlation function of a dipole that is the observable of 2D microwave or far-infrared spectroscopy is obtained from a generating functional approach. The spectra in the absence of damping are discrete and reveal transitions between eigenstates of the angular momentum quantized due to the cyclic boundary condition.