Development and Applications of Density Functional Methods for Large Systems

在化学系化学理论、模型和计算方法（CTMC）项目的支持下，杜克大学杨伟涛教授将开发密度泛函理论的方法，用于准确预测大型复杂系统的能量、电荷分布和光谱学。所提出的发展应该在生物、化学、物理、工程和纳米科学与技术的计算建模领域有广泛的应用。杨和他的研究小组将通过发表原创研究成果和公开分发软件包来传播通过这些研究获得的知识和技术。拟议的工作将有助于为未来一代理论和计算化学研究人员发展人力资源，并将通过SEED项目扩大科学、技术、工程和数学方面的参与。在这个奖项下，杨伟涛和他的研究小组将对普通密度泛函近似进行修正，以满足分数电荷和分数自旋的关键约束。常用的近似泛函具有主要的系统误差：离域误差（偏离凸行为中分数电荷的精确线性条件）和强/静态相关误差（违反分数自旋的恒定条件）。克服这些误差的必要条件用分数电荷、分数自旋和它们的组合来表示。密度泛函理论面临的突出挑战仍然是满足这些条件并克服相关的系统误差。杨和他的团队将重点研究以下三个方向：(1)利用轨道定域尺度校正消除离域误差；(2)探索从基态密度泛函理论计算中获得激发态能量信息的基本原理；(3)利用轨道定域尺度校正和基于线性响应理论的多参考密度泛函理论减少静校正误差。由于杨团队计划将在这项工作中开发的计算软件免费提供给科学界，因此这项工作的广泛科学影响将得到加强。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。

With support from the Chemical Theory, Models and Computational Methods (CTMC) program in the Division of Chemistry, Professor Weitao Yang of Duke University will develop methods in density functional theory for accurate prediction of energy, charge distributions and optical spectroscopy for large and complex systems. The proposed developments should have broad application in a wide range of computational modeling in biology, chemistry, physics, engineering and nano- science and technology. Yang and his research group will disseminate the knowledge and technology gained through these studies through publication of original research work and the public distribution of software packages. The proposed work will contribute to the development of human resources, for the future generation of theoretical and computational chemistry researchers, and will broaden participation in science, technology, engineering and mathematics through Project SEED. Under this award, Weitao Yang and his research group will develop corrections to common density functional approximations to satisfy key constraints on fractional charges and fractional spins. Commonly used approximate functionals have major systematic errors: the delocalization error, as the deviation from the exact linearity condition for fractional charges in a convex behavior, and the strong/static correlation error, as the violation of the constancy condition for fractional spins. Necessary conditions for overcoming these errors have been expressed in terms of fractional charges, fractional spins and their combination. Outstanding challenges in density functional theory remain to satisfy these conditions and overcome the associated systematic errors. Yang and his group will focus on the following three directions: (1) eliminating delocalization error with localized orbital scaling correction, (2) exploring the fundamental principles of obtaining excited state energetic information from ground state density functional theory calculations, and (3) reducing static correction error with localized orbital scaling correction and with multireference density functional theory based on the linear response theory. The broad scientific impact of the work will be enhanced as the Yang team plans to make the computational software developed in this work freely available to the scientific community.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.