Correlating Symmetry-Projected States

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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.