Density Functional Theory of Electronic Structure

非技术总结材料研究部和化学部为该奖项提供资金，以支持理论研究、计算和教育，以开发更准确的分子、化学品和材料的计算机模型。为了做到这一点，PI将把重点放在将一个原子与另一个原子结合起来形成分子和材料的“胶水”上：交换关联能量。科恩-沙姆密度泛函理论在物理、化学和材料科学中被广泛应用，用来预测什么原子、分子和材料可以存在以及具有什么性质。该理论从量子力学的第一原理出发，由非相互作用电子的辅助系统构造了多电子系统的基态能量和电子密度，其中包含了胶的贡献，从而便于实际计算。准确的交换相关能量必须是近似的。广泛预测的近似本身应该以基本原理为基础，并且足够准确地预测复杂材料和系统中相互竞争的状态之间的微小能量差异。这个项目的策略是通过纳入交换关联能量的精确普适密度泛函的更多数学性质，即通过满足更精确的约束，通过适应其中的近似可以是精确的或高精度的更合适的系统，以及通过在广泛的系统上仔细地测试和验证新的近似，来实现更精确但可计算的通用近似。对社会的长期实际好处可能包括新的药物、化学品、材料或设备。这项研究计划培养研究生和更高级的研究人员，如密度泛函和电子结构理论的开发者、验证者和使用者。它还将进一步吸引本科生和高中生对科学发现的兴奋。PI还将与TU teach学生和管理人员以及其他对Temple物理感兴趣的个人合作，在Temple组织一年一度的高中物理日，重点是受邀的高中物理教师。技术总结材料研究部和化学部向该奖项提供资金，支持理论研究、计算和教育，为交换关联能量开发更准确和可预测的密度泛函，同时保持相对计算效率的优势。这些泛函将被设计成满足对精确泛函的已知精确约束。不仅使用均匀的电子气，而且使用许多真实的原子作为适当的范数，将发展出一个更平滑和更完善的扫描(强约束和适当范数)元广义梯度近似的版本。此外，PI的目标是继续发展广义Perdew-Zunger自作用校正，以改进扫描，该校正对所有单电子密度都应该是准确的，而不会损失对多电子密度的精度。这些高级泛函将在扫描成功的许多系统上进行测试，包括液态水、固体、人造分子和高温超导材料中的结构能量差，以及一些已知失败的系统，如一些大块过渡金属和合金，以及其他复杂或强关联的系统。对长程范德华修正的改进，以及对随机相位近似的自相互作用修正，也将被作出和验证。理解什么是泛函预测应该指导通过机器学习开发密度泛函近似的新兴努力。这一提议的智力价值在于，精确泛函的许多已知的数学性质应该使所得到的近似泛函以合理的计算成本广泛而准确地预测，从而使它们在许多应用中有用，不仅对于密度泛函已经可靠的简单分子和材料，而且对于更复杂或强关联的分子和材料。特别是，对于具有所需性能的新材料的高通量搜索，迫切需要改进的泛函。不同州之间的微小能量差异可以使复杂的材料在人类控制下很容易从一种状态和功能切换到另一种状态和功能。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。

NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Chemistry contribute funds to this award that supports theoretical research, computation, and education to develop more accurate computer modeling of molecules, chemicals, and materials. To do this, the PI will focus on the “glue” that binds one atom to another to form molecules and materials: the exchange-correlation energy. In this research, the PI will develop even more accurate approximations for this “glue” that still permit efficient simulation on computers.Kohn-Sham density functional theory is widely used in physics, chemistry, and materials science to predict what atoms, molecules, and materials can exist and with what properties. Starting from the first principles of quantum mechanics, this theory constructs the ground-state energy and electron density of a many-electron system from an auxiliary system of non-interacting electrons including the contribution from the "glue", facilitating practical computation. The exact exchange-correlation energy must be approximated. Widely predictive approximations should themselves be based upon first principles, and be accurate enough to predict the small energy differences between competing states in complex materials and systems. The strategy of this project is to achieve more accurate but computable general-purpose approximations by incorporating more of the mathematical properties of the exact universal density functional for the exchange-correlation energy, i.e., by satisfying more exact constraints, by fitting to more appropriate systems in which the approximation can be either exact or highly accurate, and by carefully testing and validating the new approximations over a wide range of systems. Long-term practical benefits to society could include new medicines, chemicals, materials or devices. This research program educates graduate students and more advanced researchers as developers, validators, and users of density functional and electronic structure theory. It will furthermore engage undergraduates and high-school students in the excitement of scientific discovery. The PI will also work with TUteach students and administrators along with other interested individuals in Temple Physics, to organize an annual High School Physics Day at Temple which would be focused on invited high school physics teachers.TECHNICAL SUMMARYThe Division of Materials Research and the Division of Chemistry contribute funds to this award that supports theoretical research, computation, and education to develop more accurate and predictive density functionals for the exchange-correlation energy, while retaining the advantage of relative computational efficiency. These functionals will be designed to satisfy the known exact constraints on the exact functional. A smoother and more perfected version of the SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation will be developed, using as appropriate norms not only the uniform electron gas but also many real atoms. Also, the PI aims to continue developing a generalized Perdew-Zunger self-interaction correction to the improved SCAN that should be exact for all one-electron densities without losing accuracy for many-electron densities. These advanced functionals will be tested on the many systems for which SCAN has succeeded, including liquid water, structural energy differences in solids, artificial molecules, and the high-temperature superconducting materials, and on the few for which it is known to fail, such as some bulk transition metals and alloys, as well as on additional complex or strongly-correlated systems. Improvements to long-range van der Waals corrections, and a self-interaction correction to the random phase approximation, will also be made and validated. Understanding what makes a functional predictive should guide the burgeoning effort to develop density functional approximations by machine learning. The intellectual merit of the proposal is that many known mathematical properties of the exact functional should make the resulting approximate functionals widely and accurately predictive, at reasonable computational cost, and thus make them useful for many applications, not only for the simpler molecules and materials for which density functionals are already reliable, but also for the more complex or strongly-correlated ones. In particular improved functionals are critically needed for high-throughput searches for new materials with desired properties. The small energy differences between different states can make a complex material easy to switch under human control from one state and functionality to another.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.