Correlating Symmetry-Projected States

在化学系化学理论、模型和计算方法(CTMC)计划的支持下，莱斯大学的古斯塔沃·斯库里亚正在开发描述强相关性的方法。当化学体系的行为由电子之间的相互作用而不是由电子对原子核的吸引决定时，就会发生强关联。这种关联并不存在于每个化学体系中，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程序很重要，以及包含金属原子的谜式反应，如负责固氮的反应，即氮被转化为氨的过程。不幸的是，传统的计算方法是在不存在强相关性的假设下发展起来的。这意味着很难用传统方法来描述强相关性，并且通常通过依赖于用户对问题的洞察力的计算代价高昂的暴力方法来处理。斯库塞里亚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将对整个计算界具有价值，并将使无数重要的应用成为可能。这个项目还将包括教育和推广活动，以帮助招募和培训劳动力的新成员。为了解决描述强关联的困难，斯库塞里亚和他的团队将从对称投影技术开始，这种技术允许系统的平均场描述自发地破坏对称性，并提取具有良好量子数的破坏对称态的分量。所有这一切都有望用与标准平均场方法相当或略高的计算成本来完成。然而，尽管对称投影平均场方法对于已经存在的强关联系统通常是定性准确的，但它们缺乏动态关联，也绝不是定量的。斯库塞里亚将开发一种“计划然后关联”的方法，制定标准的关联波函数技术，直接对投影的平均场状态进行工作。人们希望，这两种久负盛名的方法的结合，在强相关性下的效果将远远好于其组成部分。在本项目范围内指导的学生将获得更广泛的分子电子结构理论和量子力学方面的最先进的专业知识。该奖项反映了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。

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.