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

通过假定系统-浴场的非线性耦合，重新考虑了谐振子的多维振动响应函数。除了标准的线性-线性(LL)体系-浴液相互作用外，我们还考虑了平方线性(SL)相互作用。L1相互作用引起振动能弛豫，而SL相互作用主要引起振动相弛豫。通过数值积分高斯-马尔可夫(GM)福克-普朗克(GM)福克-普朗克(Fokker-Planck)方程，研究了强耦合有色噪声浴场条件下相关系统的动力学，其中传统的微扰方法是不能应用的。在不同的激光和激光耦合强度组合下，计算了5h阶非共振喇曼光谱和三阶红外光谱或等效的二阶红外光谱和七阶非共振喇曼光谱的响应函数。然后研究了耗散双稳系统，给出了描述凝聚相反应动力学的最简单模型。用量子主方程方法计算多时间偶极关联函数，我们演示了耗散动力学如何用时间分辨三阶红外光谱来表征。因此，我们在红场弛豫张量中加入了LL和SL的体系-浴态相互作用。我们还研究了与GM谐振子池耦合的刚性转子的二维谱。用生成泛函方法得到了二维微波或远红外光谱能观偶极子的四倍关联函数的解析表达式。无阻尼谱是离散的，揭示了由于循环边界条件而量子化的角动量本征态之间的跃迁。

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.