Correlating Symmetry-Projected States

关联对称投影状态

• 批准号: 2153820
• 负责人: Gustavo Scuseria
• 金额: $ 50.82万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-06-15 至 2025-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2153820&HistoricalAwards=false
• 关键词: Correlating; Symmetry; Projected; States

With support from the Chemical Theory, Models and Computational Methods (CTMC) program in the Division of Chemistry, Gustavo Scuseria of Rice University is developing methods for the description of strong correlations. Strong correlations occur when the behavior of chemical systems is determined by the interaction between electrons, instead of by the attraction of the electrons to atomic nuclei. Such correlations are not present in every chemical system, but they appear in a wide range of important applications. Examples include molecular magnetism, which is important for applications such as data storage and quantum computing, and enyzmatic reactions containing metal atoms, such as those responsible for nitrogen fixation, the process by which nitrogen is converted into ammonia. Unfortunately, conventional computational methods have been developed under the assumption that strong correlation is not present. This means that strong correlations are difficult to describe with traditional approaches and are typically treated by computationally costly brute-force approaches that depend on the user’s insight into the problem. Tools will be developed by Scuseria and his group that are designed to overcome these difficulties. Computational methods that can reliably treat strong correlation will be valuable for the computational community as a whole, and will enable myriad important applications. This project will also involve education and outreach activities to help recruit and train new members of the workforce.To solve the difficulties in describing strong correlations, Scuseria and his group will begin with symmetry-projected techniques, which permit the mean-field description of the system to spontaneously break symmetry and extract the component of the broken-symmetry state that has good quantum numbers. All of this is expected to be done with a computational cost that is comparable to or slightly higher than that of standard mean-field methods. However, while symmetry-projected mean-field methods are often qualitatively accurate for strongly-correlated systems already, they lack dynamic correlations and are by no means quantitative. Scuseria will develop a “project then correlate” approach that formulates standard correlated wave function techniques to work directly on the projected mean-field state. The hope is that this combination of two well-established methods will work much better than its components under strong correlation. Students mentored within the scope of this project will gain state-of-the-art expertise in molecular electronic structure theory and quantum mechanics more broadly.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.

在化学系化学理论、模型和计算方法（CTMC）项目的支持下，莱斯大学的Gustavo Scuseria正在开发描述强相关性的方法。当化学系统的行为由电子之间的相互作用而不是电子对原子核的吸引力决定时，就会出现强相关性。这种相关性并不存在于每个化学系统中，但它们出现在广泛的重要应用中。例子包括分子磁性，这对数据存储和量子计算等应用很重要，以及含有金属原子的酶反应，例如负责固氮的那些，氮转化为氨的过程。不幸的是，传统的计算方法已经开发的假设下，强相关性不存在。这意味着强相关性很难用传统方法来描述，并且通常由计算成本高的蛮力方法来处理，这取决于用户对问题的洞察力。Scuseria和他的团队将开发旨在克服这些困难的工具。能够可靠地处理强相关性的计算方法对于整个计算界来说都是有价值的，并且将使无数重要的应用成为可能。为了解决描述强相关性的困难，Scuseria和他的团队将开始使用平均场投影技术，该技术允许系统的对称性自发破缺，并提取对称性破缺状态中具有良好量子数的分量。所有这一切都预计将完成与计算成本是可比的，或略高于标准的平均场方法。然而，虽然投影平均场方法对于强相关系统通常是定性准确的，但它们缺乏动态相关性，并且绝不是定量的。Scuseria将开发一种“项目，然后相关”的方法，制定标准的相关波函数技术，直接对预计的平均场状态。希望这两种成熟方法的结合将比其在强相关性下的组成部分更好地工作。在本项目范围内指导的学生将获得分子电子结构理论和量子力学更广泛的最先进的专业知识。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。