时间分辨荧光Stokes位移是研究化学动力学的有力工具，而线性响应理论则是描述荧光Stokes位移的重要手段，特别在以色氨酸为光学探针的蛋白质水动力学的研究中它们有着不可或缺的地位与作用。其中，对于蛋白质溶液体系的线性响应理论的有效性探究一直是研究者们关注的重点。

本文以线性响应理论为基石，将分子动力学基本原理与欧拉运动学相结合，对色氨酸水溶液体系进行分子动力学模拟，探究了体系非平衡态荧光Stokes位移的弛豫与水分子运动关联。进一步从分子运动层面解释了荧光Stokes位移的弛豫来源，诠释了水分子的运动对线性响应理论有效性的影响。本文主要研究内容如下：

（1）本文通过对色氨酸水溶液体系进行分子动力学模拟，探究了色氨酸体系荧光Stokes位移的弛豫过程，并将其分解为水分子运动平动分量与转动分量的贡献。进而从分子运动层面解释荧光Stokes位移弛豫的物理内涵。

（2）本文将系统的自然涨落与非平衡态荧光Stokes位移的弛豫相关联，计算了系统平衡态自然涨落的溶剂化响应函数，并将其分解为平动分量与转动分量的贡献。探究了分子运动对于线性响应理论有效性的影响。

（3）能量的概率分布与高阶时间关联函数的关系，一直是探究线性响应理论有效性关注的重点。本文计算了水分子能量的概率分布并将其分解为平动分量与转动分量，探究了水分子能量及其分量的能量概率分布对高阶时间关联函数动力学过程的影响。

（4）时间关联函数的计算方式是探究蛋白质水动力学过程的关注重点之一，本文计算了体系的速度时间关联函数，并从速度时间关联函数推导至时间关联函数。在此过程中，解析水分子平动与转动的耦合关系，最终从分子运动层面验证了速度时间关联函数到时间关联函数的可行性。

Ultrafast fluorescence technology has been used to explore the dynamics of molecules, atoms and other microscopic systems, especially in the study of hydrodynamics using tryptophan as optical probe has an indispensable position and role. The Indole fluorophore of tryptophan in the system was excited by ultrafast fluorescence technology, and the corresponding Stokes shift was radiated. The linear response theory holds that the non-equilibrium relaxation of the system in the excited process is intrinsically related to the natural fluctuation of the excited state, and has the same dynamic process. Therefore, linear response theory is often used to interpret the correlation between Stokes shift and the natural fluctuation of the equilibrium state of the system. In particular, the validity of linear response theory has always been the focus of researchers.

Based on the linear response theory, this thesis combines the basic principles of molecular dynamics with Euler kinematics to simulate the tryptophan aqueous solution system by molecular dynamics, and explores the relationship between the relaxation of the non-equilibrium fluorescence Stokes displacement of the system and the movement of water molecules. Further explained the relaxation source of fluorescence Stokes shift from the perspective of molecular motion, and explained the influence of water molecule motion on the effectiveness of linear response theory. The main research content of this article is as follows:

(1) This thesis explores the relaxation process of fluorescence Stokes shift in tryptophan aqueous solution system through molecular dynamics simulation, and decomposes it into the contributions of the translational and rotational components of water molecule motion. Further explain the physical connotation of fluorescence Stokes shift relaxation from the perspective of molecular motion.

(2) This thesis associates the natural fluctuations of the system with the relaxation of non equilibrium fluorescence Stokes shifts, calculates the solvation response function of the system's equilibrium natural fluctuations, and decomposes it into the contributions of the translational and rotational components. Explored the impact of molecular motion on the effectiveness of linear response theory.

(3) The relationship between the probability distribution of energy and the higher-order time correlation function has always been a key focus in exploring the effectiveness of linear response theory. This thesis calculates the probability distribution of water molecule energy and decomposes it into translational and rotational components, exploring the influence of the energy probability distribution of water molecule energy and its components on the dynamic process of higher-order time correlation functions.

(4) The calculation method of the time correlation function is one of the focuses in exploring protein hydrodynamics processes. This thesis calculates the velocity time correlation function of the system and derives it from the velocity time correlation function to the time correlation function. During this process, the coupling relationship between the translational and rotational motion of water molecules was analyzed, and the feasibility of converting the velocity time correlation function to the time correlation function was ultimately verified from the molecular motion level.