Developing the Multilayer Multiconfiguration Time-dependent Hartree Theory

科罗拉多丹佛大学的Haobin Wang获得了化学系化学理论、模型和计算方法项目的奖励，以开发一种称为多层多构型时间相关Hartree（ML-MCTDH）理论的计算机模拟方法，用于研究化学系统中的量子动力学。在这里，量子动力学处理的是受量子力学定律支配的化学系统的运动、能量和动量交换。量子动力学与量子计算和原子光学有关。 王教授正在开发ML-MCTDH作为一种先进的数值工具，用于将大型化学和物理问题中的巨大参数空间减少到可管理的水平，使用物理建模，数学重构和计算机软件工程的组合。ML-MCTDH是研究复杂系统超快运动的最成熟、最有效的压缩格式之一。在一些强系统中，ML-MCTDH是唯一已知的方法，可以提供定量预测和分析的可靠结果。这里研究的问题也可以提供一个基本的了解光化学过程和手性分子的设计。Haobin Wang的研究还对制药（和其他应用）中使用的科学，技术，软件工程和数学教育产生了更广泛的影响。王教授正在培训研究生和本科生，并为高中STEM教师和学生提供研究经验。本研究所开发的数值技术和软件在微分方程数值解、数值线性代数和并行计算等一系列应用问题中具有潜在的应用价值，本研究的目标是进一步发展强大的张量压缩格式、多层多组态含时Hartree格式（ML-MCTDH）理论，用于在更困难的物理机制中研究复杂的分子系统。沿着这条路线，Haobin Wang正在开发技术来解决紧迫的技术难题，使ML-MCTDH能够解决非常苛刻的问题：运动方程的适当正则化和在ML-MCTDH模拟中选择适当树结构的有效方法。他将ML-MCTDH从模拟波函数扩展到相应的密度矩阵或虚拟对偶希尔伯特空间中的等效波函数。这种可能性的关键是迭代或递归地实现ML-MCTDH，比以前更多的层，这将是不可能的，如果不解决本研究中解决的技术难题。此外，Haobin Wang正在推广ML-MCTDH来处理其他需要有效收缩高阶张量的问题。他采用ML-MCTDH方法来模拟层次运动方程（HEOM），旨在显着推动其极限。将应用变分原理通过将HEOM动力学映射到非厄米哈密顿算符上来导出工作方程，然后可以模拟开放系统的量子动力学。ML-MCTDH的开发和实际实施将使其适用于真正具有挑战性的问题。这些例子还可以提供对相关光化学过程的基本理解，这有助于控制特定反应以及设计手性分子的对映选择性相转移的新材料。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Haobin Wang of University of Colorado Denver is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry to develop a computer simulation method called multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory for studying quantum dynamics in chemical systems. Here, quantum dynamics deals with the motions, energy, and momentum exchanges of chemical systems that are governed by the laws of quantum mechanics. Quantum dynamics is relevant to quantum computing and atomic optics. Professor Wang is developing ML-MCTDH as an advanced numerical tool for reducing the huge parameter space in large chemistry and physics problems to a manageable level using a combination of physical modeling, mathematical reformulation, and computer software engineering. ML-MCTDH is among the most mature and efficient contraction schemes for studying ultrafast motions in complex systems. In some strongly systems, ML-MCTDH is the only known approach that can provide reliable results for quantitative predictions and analysis. The problems studied here can also offer a fundamental understanding of photochemical processes and the design of chiral molecules. Haobin Wang’s research also has a broader impact associated with science, technology, software engineering, and mathematics education used in pharmaceuticals (and other applications). Professor Wang is training graduate and undergraduate students and providing research experiences for high school STEM teachers and students. The numerical techniques and software developed in this project have potential application to a broad array of applied problems, such a numerical solution of differential equations, numerical linear algebra, and parallel computation.The goal of this research is to further develop the powerful tensor contraction scheme, the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory, for studying complex molecular systems in more difficult physical regimes. Along this line, Haobin Wang is developing techniques to solve pressing technical difficulties to make ML-MCTDH amendable to very demanding problems: appropriate regularization of the equations of motion and effective ways for choosing proper tree structures in ML-MCTDH simulations. He is extending ML-MCTDH from simulating wave functions to corresponding density matrices or equivalent wave functions in a fictitious dual Hilbert space. The key to this possibility is to iteratively or recursively implement ML-MCTDH with many more layers than before, which would not be possible without solving the technical difficulties addressed in this research. In addition, Haobin Wang is generalizing ML-MCTDH to handle other classes of problems that require effective contraction of high-rank tensors. He is employing the ML-MCTDH methodology to simulate hierarchy equations of motion (HEOM) that aim at significantly pushing its limit. Variational principle will be applied to derive the working equations by mapping the HEOM dynamics onto a non-Hermitian Hamiltonian operator, which can then simulate quantum dynamics for open systems. The development and practical implementation of ML-MCTDH will make it applicable to truly challenging problems. The examples can also offer a fundamental understanding of the relevant photochemical processes, which can help control specific reactions as well as design new materials for enantioselective phase transfer of chiral molecules.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.