Developing the multilayer multiconfiguration time-dependent Hartree theory

新墨西哥州州立大学的Haobin Wang获得了化学系化学理论，模型和计算方法以及计算和数据支持科学与工程（CDS& E）计划的奖项，以开发和应用计算方法来研究几种技术上重要的材料和器件中的电子转移过程，如染料敏化太阳能电池，分子结器件，和新的电子/磁性材料。因为电子是非常小的物体，它们服从量子力学定律。 为了得到这些系统的足够精确的描述，量子力学方法必须同时应用于电子和原子核。 Wang教授和他的同事们开发了一种精确而有效的量子力学方法，该方法被称为多层多构型时间相关哈特里（ML-MCTDH）理论。从这项研究中获得的基本认识有助于新材料的合理设计，如太阳能转换和分子电子学。 在这个项目中开发的数值技术和软件对科学和工程中的广泛问题具有潜在的应用，例如，数值方法、信号压缩和并行计算。 本科生和研究生都为这项研究做出了贡献。将ML-MCTDH推广到处理全同粒子的第二量子化表象，使理论形式上完整。当前研究的目的是：（i）调查尽可能多的重要物理模型，可以通过当前的ML-MCTDH实现准确地处理;和（ii）在ML-MCTDH框架内开发新的算法来处理更一般的模型。具体来说，首席研究员和他的同事将当前的理论应用于物理和化学中的各种重要和具有挑战性的问题，例如，使用Anderson-News模型的异质电子转移，其中电子和核自旋被同等对待的自旋弛豫，以及使用安德森杂质模型的近藤效应。除了这些简单的应用，ML-MCTDH理论的当前实现正在扩展到更一般形式的势能函数。 进一步的目标是改进相关的ML-MCTDH算法，例如，采用多层改进松弛法生成低温下的初始密度矩阵，对一系列算子进行分组和简化求值，并修改ML-MCTDH运动方程，去除数值奇异性的正则化。在这项研究中开发的软件将免费提供给研究界。

Haobin Wang, of New Mexico State University is supported by an award from the Chemical Theory, Models and Computational method in the Chemistry Division and the Computational and Data-Enabled Science and Engineering (CDS&E) program to develop and apply computational approaches to study electron transfer processes in several technologically-important materials and devices such as dye sensitized solar cells, molecular junction devices, and new electronic/magnetic materials. Because electrons are very small objects, they obey the laws of quantum mechanics. To get a sufficiently accurate description of many of these systems, quantum mechanical methods must be applied to both the electrons and the atomic nuclei. Professor Wang and his colleagues have developed an accurate and efficient quantum mechanical approach that is designed for this purpose called the multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) theory. The fundamental understanding resulting from this research contributes to the rational design of new materials such as for solar energy conversion and molecular electronics. The numerical techniques and software developed in this project have potential applications to a broad range of problems in science and engineering, e.g., numerical methods, signal compression, and parallel computation. Both undergraduate and graduate students contribute to this research. With the extension of ML-MCTDH to the second quantization representation for treating identical particles, the theory is formally complete. The purpose of the current research is: (i) to investigate as many important physical models as possible that can be treated accurately via the current ML-MCTDH implementation; and (ii) to develop new algorithms within the ML-MCTDH framework to treat more general models. Specifically, the principal investigator and his coworkers apply the current theory to a variety of important and challenging problems in physics and chemistry, e.g., heterogeneous electron transfer using the Anderson-News model, spin relaxation where the electronic and nuclear spins are treated on equal footing, and the Kondo effect using the Anderson impurity model. Beyond those straightforward applications the current implementation of the ML-MCTDH theory is being extended to more general forms of potential energy functions. Further goals are to improve the relevant ML-MCTDH algorithms, e.g., using multilayer improved relaxation to generate the initial density matrix at low temperatures, grouping and streamlined evaluation of a series of operators, and modifying ML-MCTDH equations of motion that remove the regularization of the numerical singularities. The software developed in this research will be made freely available to the research community.