Density Functional Theory of Electronic Structure

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、化学物质和材料的计算机模型。为了做到这一点，PI将重点关注将一个原子与另一个原子结合在一起形成分子和材料的“粘合剂”：交换相关能。在这项研究中，PI将为这种“胶水”开发更精确的近似值，这仍然允许在计算机上进行有效的模拟。Kohn-Sham密度泛函理论广泛应用于物理、化学和材料科学，用于预测原子、分子和材料的存在及其性质。该理论从量子力学的第一性原理出发，从包括“胶”贡献在内的非相互作用电子辅助系统构建多电子系统的基态能量和电子密度，便于实际计算。确切的交换相关能必须近似。广泛的预测近似本身应该基于第一性原理，并且足够准确地预测复杂材料和系统中竞争状态之间的小能量差。该项目的策略是通过结合交换相关能的精确通用密度泛函的更多数学性质来实现更精确但可计算的通用近似，即通过满足更精确的约束，通过拟合更合适的近似可以精确或高度精确的系统，并通过在广泛的系统范围内仔细测试和验证新的近似。对社会的长期实际利益可能包括新的药物、化学品、材料或设备。该研究项目培养研究生和更高级的研究人员作为密度泛函和电子结构理论的开发者、验证者和用户。它将进一步吸引本科生和高中生参与科学发现的兴奋。PI还将与TUteach的学生和管理人员以及其他对坦普尔物理感兴趣的个人合作，在坦普尔组织一年一度的高中物理日，重点关注受邀的高中物理教师。技术概述：材料研究部和化学部为该奖项提供资金，支持理论研究、计算和教育，以开发更准确和预测的交换相关能密度函数，同时保持相对计算效率的优势。这些函数将被设计为满足已知的精确函数的精确约束。一个更平滑和更完善的SCAN（强约束和适当规范）元广义梯度近似将被开发，作为适当的规范，不仅使用均匀的电子气体，而且使用许多真实原子。此外，PI的目标是继续开发一种广义的Perdew-Zunger自相互作用校正，以改进SCAN，在所有单电子密度下都应该精确，而不会失去对多电子密度的精度。这些先进的功能将在SCAN已经成功的许多系统上进行测试，包括液态水、固体结构能差、人工分子和高温超导材料，以及少数已知失败的系统，如一些大块过渡金属和合金，以及其他复杂或强相关的系统。远程范德华校正的改进，以及随机相位近似的自相互作用校正，也将进行和验证。理解是什么构成了函数预测，应该指导通过机器学习开发密度函数近似的新兴努力。这个建议的智力价值在于，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在合理的计算成本下得到广泛和准确的预测，从而使它们在许多应用中有用，不仅对密度泛函已经可靠的简单分子和材料，而且对更复杂或强相关的分子和材料也有用。特别是改进的功能对于高通量搜索具有所需性能的新材料至关重要。不同状态之间的微小能量差异可以使复杂的材料在人类的控制下很容易地从一种状态和功能切换到另一种状态和功能。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.