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CDS&E: Two-electron Reduced Density Matrices in Quantum Chemistry and Physics

CDS

基本信息

批准号：
1565638
负责人：
David Mazziotti
金额：
$ 45万
依托单位：
University of Chicago
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-07-15 至 2022-03-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1565638&HistoricalAwards=false
关键词：
CDS&amp Two electron Reduced Density

项目摘要

David Mazziotti of the University of Chicago funded by an award from the Chemical Theory, Models and Computational Methods program for developing new approaches to quantum chemistry. Discovering novel molecules and materials that are optimal for capturing energy from the sun or fighting disease in the human body requires detailed knowledge of the distributions of their electrons. Electrons, however, are very small particles; in fact, they are 1000 times less massive than a single hydrogen atom. Consequently, electrons obey the laws of quantum mechanics. Like Schrödinger's famous cat, who is paradoxically both half alive and half dead simultaneously, electrons can be found in two or more physical states at the same time. When electrons in a molecule occupy many more states than the number of electrons, the electrons in the molecule are described by scientists as being strongly correlated (or entangled). Strongly correlated electrons are present in some of the most fascinating molecules and materials from the transition-metal catalysts in nitrogen fixation to the copper-oxide planes in high-temperature superconductors. Despite the importance of strongly correlated electrons, however, the computational cost of describing them by the laws of quantum mechanics traditionally increases exponentially with the number of electrons, dramatically limiting the number of strongly correlated systems describable by theoretical chemistry and physics. In this project, Mazziotti and his research group are further developing a novel approach to strongly correlated molecules in which the energies and properties are computed as functions of only two electrons in the "sea" of charge from the remaining electrons. These so-called two-electron reduced density matrix (2-RDM) methods are able to treat strongly correlated molecules efficiently and accurately with a computational cost that does not grow exponentially when the system becomes large. Recently, the 2-RDM method has been applied to several interesting and very different types of chemical systems, for example to model the efficient release of energy in firefly bioluminescence. Mazziotti and his research group are currently working to extend the 2-RDM methods to larger molecular systems as well as time-dependent phenomena with important implications for describing molecules in studies ranging from materials to medicine. Mazziotti also produces a journal for high school students named E = mc2 which publishes research by students. The journal provides a forum for encouraging high school students to pursue careers in the mathematical sciences. The many-electron wave function contains much more information than necessary to compute the important energies and properties of molecules and materials. Because electrons are indistinguishable with pairwise interactions, however, the wave function as the basic variable of quantum mechanics can be replaced by the two-electron reduced density matrix (2-RDM). With support from the NSF, Mazziotti and his research group are building upon their recent advances in 2-RDM methods with an emphasis on developing and improving 2-RDM methods for treating ground and excited states as well as time-dependent quantum systems. Several significant advances in the direct calculation of the 2-RDM for strongly correlated systems are being pursued including: (1) a low-scaling 2-RDM method, which can strongly correlate hundreds of orbitals, corresponding to wave functions that are intractable by conventional methods, and (2) a steady-state 2-RDM method that can determine the conductance of a molecule or material even in the presence of strong electron correlation. The research has important applications to modeling and predicting the electronic energies and properties including conductivity of a wide range of large strongly correlated molecular systems.

芝加哥大学的大卫马齐奥蒂获得了化学理论、模型和计算方法项目的资助，以开发量子化学的新方法。发现新的分子和材料是从太阳捕获能量或对抗人体疾病的最佳选择，需要详细了解它们的电子分布。然而，电子是非常小的粒子;事实上，它们的质量比单个氢原子小1000倍。因此，电子服从量子力学定律。就像薛定谔那只著名的猫，它同时处于半死不活的状态，电子可以同时处于两种或两种以上的物理状态。当分子中的电子占据的状态比电子的数量多得多时，分子中的电子被科学家描述为强相关（或纠缠）。强关联电子存在于一些最迷人的分子和材料中，从固氮的过渡金属催化剂到高温超导体中的氧化铜平面。尽管强关联电子的重要性，然而，用量子力学定律描述它们的计算成本传统上随着电子的数量呈指数级增加，这极大地限制了理论化学和物理学可描述的强关联系统的数量。在这个项目中，Mazziotti和他的研究小组正在进一步开发一种新的方法来研究强相关分子，其中能量和性质被计算为剩余电子中电荷“海洋”中仅两个电子的函数。这些所谓的双电子约化密度矩阵（2-RDM）方法能够有效和准确地处理强相关的分子，当系统变大时，计算成本不会呈指数增长。最近，2-RDM方法已被应用到几个有趣的和非常不同类型的化学系统，例如，模型的能量有效释放萤火虫生物发光。 Mazziotti和他的研究小组目前正在努力将2-RDM方法扩展到更大的分子系统以及时间依赖性现象，这对从材料到医学的研究中描述分子具有重要意义。 Mazziotti还为高中生制作了一份名为E = mc 2的杂志，该杂志发表了学生的研究。该杂志提供了一个论坛，鼓励高中生追求数学科学的职业生涯。多电子波函数包含的信息比计算分子和材料的重要能量和性质所需的信息要多得多。然而，由于电子在成对相互作用下是不可区分的，作为量子力学基本变量的波函数可以用双电子约化密度矩阵（2-RDM）代替。在NSF的支持下，Mazziotti和他的研究小组正在建立他们在2-RDM方法方面的最新进展，重点是开发和改进用于处理基态和激发态以及时间依赖量子系统的2-RDM方法。在直接计算强相关系统的2-RDM方面，正在取得一些重大进展，包括：（1）低尺度2-RDM方法，其可以强关联数百个轨道，对应于常规方法难以处理的波函数，以及（2）稳态2-RDM方法，其甚至可以在强电子相关存在下确定分子或材料的电导。该研究对于模拟和预测大范围强关联分子系统的电子能量和性质包括电导率具有重要的应用价值。