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

通过假设非线性系统池耦合，重新考虑谐振子的多维振动响应函数。除了标准的线性-线性（LL）系统池相互作用之外，我们还考虑了平方线性（SL）相互作用。LL相互作用引起振动能量松弛，而SL相互作用主要引起振动相松弛。通过对高斯-马尔可夫（GM） Fokker-Planck方程在有色噪声池强耦合条件下的数值积分，研究了相关系统的动力学特性，其中传统的微扰方法无法应用。计算了5h阶非谐振拉曼光谱和3阶红外光谱，即2阶红外光谱和7阶非谐振拉曼光谱在LL和SL耦合强度的不同组合下的响应函数。然后我们研究了一个耗散双稳态系统，给出了描述凝聚相反应动力学的最简单模型。利用量子主方程方法计算多时间偶极相关函数，我们演示了如何用时间分辨三阶红外光谱表征耗散动力学。因此，我们将LL和SL系统浴相互作用纳入到Redfield弛豫张量中。我们还研究了耦合到GM谐振子槽的刚性旋转器的二维谱。用生成泛函方法得到了二维微波或远红外光谱观测到的偶极子的四次相关函数的解析表达式。在没有阻尼的情况下，谱是离散的，并且显示了由于循环边界条件而量子化的角动量的本征态之间的转换。

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.