Quantum Master Equations for Simulating Chemical Dynamics

密歇根大学的Eitan Geva教授得到了化学系化学理论、模型和计算方法(CTMC)项目的支持，以开发一种新的通用、经济高效的方法，该方法将能够对光合作用、光伏和纳米电子学等重要技术和生物过程背后的化学动力学进行计算机模拟。新的方法旨在缩小理论和实验之间的差距，侧重于可测量的数量，并将投入减少到所需的最低限度，以便了解这些可测量的数量如何随着时间的推移而变化。此外，Eitan Geva还将提出一种新颖的计算学习(C2L)教学法，该教学法基于同行领导的荣誉工作室，本科生在该工作室协作创建演示物理化学概念的公共领域互动计算机演示。由于女性入学率超过50%，c2L教学法是如何使教学规划具有包容性的典范。Eitan Geva和他的团队将开发和基准新类型的广义量子主方程，这些方程允许在感兴趣的电子观测及其维度方面比目前可用的更大的灵活性，从而产生更精简、更具成本效益和更有效的实施。每个广义量子主方程对应于为其导出的电子可见的精确运动方程。在这些方程中，投影输出自由度的影响以紧致记忆核和非齐次项的形式给出，这些项可以通过求解Volterra方程从无投影的输入中获得。通过映射到简谐模型和使用量子力学精确方法或使用基于线性半经典近似和映射哈密顿框架的准经典方法，发展了计算协议，用于计算化学凝聚相系统的全原子模型的无投影输入。此外，还发展了反映大量非微扰广义量子主方程的多个新的微扰量子主方程，以及通过用于计算无投影输入的相同方法来计算相应微扰记忆核的协议。开发的量子主方程将应用于新的基准模型、全原子模型和极化子化学模型，并在其上进行测试。我们还研究了利用初始态纠缠实现化学动力学量子控制的可能性。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Professor Eitan Geva of the University of Michigan is supported by an award from the Chemical Theory, Models and Computational Methods (CTMC) program in the Division of Chemistry to develop a new general purpose cost-effective and efficient methodology that will enable computer simulations of the chemical dynamics underlying technologically and biologically important processes, such as photosynthesis, photovoltaics and nanoelectronics. The new methodology aims at closing the gap between theory and experiment, by focusing on measurable quantities and reducing the inputs to the minimum required in order to understand how those measurable quantities change over time. In addition, Eitan Geva will also advance a novel Compute-to-Learn (C2L) pedagogy, which is based on a peer-led honors studio where undergraduate students work collaboratively to create public-domain interactive computer demos that demonstrate physical chemistry concepts. With above 50% female enrollment, the C2L pedagogy is a model for how to make teaching programming inclusive. Eitan Geva and his group will develop and benchmark new types of generalized quantum master equations that allow for much greater flexibility than is currently available with respect to the electronic observables of interest and their dimensionality, thereby giving rise to more streamlined, cost-effective and efficient implementations. Each generalized quantum master equation corresponds to the exact equation of motion for the electronic observable it is derived for. Within those equations, the effect of projected-out degrees of freedom is given in terms of compact memory kernels and inhomogeneous terms, which can be obtained from projection-free inputs by solving Volterra equations. Computational protocols are developed for calculating the projection-free inputs for all-atom models of chemical condensed-phase systems via either mapping onto harmonic models and using quantum-mechanically exact methods or using quasiclassical methods based on combining the linearized semiclassical approximation with the mapping Hamiltonian framework. In addition, multiple new perturbative quantum master equations that mirror the multitude of non-perturbative generalized quantum master equations are developed, as well as protocols for calculating the corresponding perturbative memory kernels via the same methods used for calculating the projection-free inputs. The quantum master equations developed will be applied to and tested on new benchmark models, all-atom models and polaritonic chemistry models. The potential of using initial state entanglement to achieve quantum control of chemical dynamics is also investigated.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.