Quantum-Classical Path Integral Methodology

伊利诺伊大学的Nancy Makri获得了化学系化学理论，模型和计算方法计划的奖项，以开发新的，严格的计算方法来研究电子和质子转移过程。经典的轨道模拟方法可以有效地描述大型化学或生物系统中的许多动力学过程。 然而，化学和生物反应经常涉及电子或质子的转移。 这些轻粒子通常需要用量子力学来研究。 电子和许多质子转移反应表现出明显的量子效应和经典的轨迹是不足以模拟这样的过程。 然而，量子力学运动方程的数值解在计算上要求极高。 对于任何规模的系统，最有利可图的方法是量子和经典轨迹模拟工具的结合。 联合收割机结合经典和量子力学而不引入可能导致不准确结果的严格近似并不总是容易的。 这是因为经典力学在空间中是局部化的，即，在每一个时间点上，每个原子都有一个确定的位置和动量。 量子力学通常用离域的波来表示。 Makri通过一种新的量子经典路径积分（QCPI）方法解决了这种明显的不兼容性，该方法使用量子粒子的局部描述，消除了近似的需要，并允许以前所未有的精度进行模拟。 Makri和她的研究小组教授她开发的名为“音乐、光和原子”的实践讲座课程。 它针对高中生，通过类比音乐来展示量子力学的基本思想。QCPI表述通过沿每个量子-经典路径的沿着动力学相位以完全原子细节处理量子自由度和经典自由度之间的相互作用。然而，量子路径的数量随传播时间呈指数增长，并且每个量子路径指定不同的经典轨迹。 通过利用相位关系对退相干有明显的贡献，马克里证明了QCPI表达式可以用适度的计算工作来计算。 拟议的工作引入了基于量子干涉，零点能和自发声子发射的新思想，可用于进一步加速QCPI计算的数量级，从而产生一种适用于复杂化学过程的高度准确的方法，其工作量可与典型分子动力学模拟中采用的方法相媲美。

Nancy Makri of the University of Illinois is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry to develop new, rigorous computational methods to study electron and proton transfer processes. Many dynamical processes in large chemical or biological systems can be described successfully and very efficiently through classical trajectory simulations. However, chemical and biological reactions frequently involve the transfer of electrons or protons. These light particles often need to be studied using quantum mechanics. Electron and many proton transfer reactions exhibit pronounced quantum effects and classical trajectories are not adequate for modeling such processes. Numerical solution of the quantum mechanical equations of motion, however is extremely computationally demanding. The most profitable approach for systems of any size is the combination of quantum and classical trajectory simulation tools. It is not always easy to combine classical and quantum mechanics without introducing severe approximations which may result in inaccurate results. This is because classical mechanics is localized in space, i.e., at each point in time, each atom has a definite position and momentum. Quantum mechanics is usually represented in terms of waves, which are delocalized. Makri addresses this apparent incompatibility via a novel quantum-classical path integral (QCPI) approach, which uses a local description of the quantum particles, eliminating the need for approximations and allowing simulations with unprecedented accuracy. Makri and her research group teach a hands-on lecture course entitled "Music, light and the atom" which she developed. It is aimed at high school students, presenting the basic ideas of quantum mechanics through analogies to music. The QCPI formulation treats the interaction between quantum and classical degrees of freedom in full atomistic detail through a dynamical phase along each quantum-classical path. However, the number of quantum paths grows exponentially with propagation time, and each quantum path specifies a different classical trajectory. By exploiting phase relations that make distinct contributions to decoherence, Makri has shown that the QCPI expression can be evaluated with only modest computational effort. The proposed work introduces new ideas based on quantum interference, zero-point energy and spontaneous phonon emission that can be used to further accelerate QCPI calculations by orders of magnitude, leading to a highly accurate methodology applicable to complex chemical processes with effort comparable to that employed in typical molecular dynamics simulations.