Development and Applications of Density Functional Methods for Large Systems

杜克大学的杨伟涛教授获得了化学系化学理论、模型和计算方法项目的奖励。杨博士的研究重点是研究电子在化学体系中的分布或电子结构。当原子结合(或结合)形成分子和固体时，原子中的电子会重新排列它们的位置。这种定位决定了这些体系特有的化学性质，在研究许多具有挑战性的科学问题时很重要。具体地说，杨博士基于一种名为密度泛函理论的数学方法，使用运动方程对化学体系的电子结构进行建模。这一理论已经成功地应用于广泛的化学研究中，如对化学反应速度进行建模、太阳能转换、燃料电池设计和药物开发；然而，仍然有一些重要领域，包括涉及带电或暂态系统的研究，密度泛函理论包含的近似会导致重大误差。杨博士的项目专注于分析这些误差，并对当前使用的近似进行系统的修正，从而使电子结构的密度泛函理论更加准确和可靠。这项研究在密度泛函理论方面的进展可能会在生物、化学、物理、工程、纳米科学和纳米技术等广泛的计算建模问题中找到应用。该项目有助于培养未来几代理论和计算化学研究人员。作为SEED项目的一部分，杨博士还邀请科学、技术、工程和数学领域的少数族裔学生参与他的研究项目。电子结构的密度泛函理论(DFT)对量子力学在化学中许多有趣和具有挑战性的问题的应用产生了重大影响。基于广义梯度近似(GGA)的近似泛函在形式和性能方面都取得了很大的进展，从亚GGA和超GGA到结合微扰理论的泛函和随机位相近似。有了这些发展，密度泛函近似的精度在许多化学和物理问题上都有了显著的提高，甚至对于非常具有挑战性的远程van der Waals吸引点问题也是如此。然而，DFT中的突出挑战依然存在，这些挑战阻碍了DFT的广泛和强有力的应用。常用的近似泛函具有显著的离域误差，偏离了分数电荷的精确线性条件，导致了应用中的许多不准确。这些泛函也不能描述静态或强相关性。克服这些误差的必要条件用分数电荷和分数自旋表示。杨博士的研究小组对常用泛函进行了修正，以满足这些限制，从而推进了DFT的前沿。研究工作集中于通过局部轨道定标修正消除离域误差，并通过局部轨道定标修正和多参考DFT减少静态修正误差。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。

Professor Weitao Yang of Duke University is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry. Dr. Yang's research focuses on studying the distributions of electrons in, or the electronic structures of, chemical systems. The electrons present in atoms rearrange their positions when atoms combine (or bond) to form molecules and solids. This positioning determines the characteristic chemical properties of these systems and is important when studying many challenging problems in science. Specifically, Dr. Yang models the electronic structure of chemical systems using equations of motion based on a mathematical method called density functional theory. This theory has been applied successfully in a wide array of chemical studies such as modeling the speed of chemical reactions, solar energy conversion, fuel cell design and the development of pharmaceuticals; however, there are still important areas, including studies involving charged or transitory systems, where density functional theory contains approximations which lead to significant errors. Dr. Yang's project focuses on analyzing these errors and developing systematic corrections to the approximations in current use, thus making the density functional theory of electronic structure more accurate and robust. The advances in density functional theory from this research may find applications to a wide range of computational modeling problems in biology, chemistry, physics, engineering, nanoscience and nanotechnology. The project contributes to the development of future generations of theoretical and computational chemistry researchers. Dr. Yang also engage students from underrepresented minorities in science, technology, engineering and mathematics in his research project as part of Project SEED.The density functional theory (DFT) of electronic structure has had a significant impact on the application of quantum mechanics to many interesting and challenging problems in chemistry. Much progress has been made in both the forms and the performance of the approximate functionals based on the so-called generalized gradient approximation (GGA), ranging from meta-GGA and hyper-GGA to functionals incorporating perturbation theory and the random phase approximation. With all these developments, the accuracy of density functional approximations has been significantly improved for many chemical and physical problems, even for the very challenging problem of long-range van der Waals attractions. However, outstanding challenges in DFT remain and these challenges prevent the broad and robust application of DFT. Commonly used approximate functionals have significant delocalization error, with deviations from the exact linearity condition for fractional charges, leading to many inaccuracies in applications. These functionals also fail to describe static or strong correlation. Necessary conditions for overcoming these errors have been expressed in terms of fractional charges and fractional spins. Dr. Yang's research group derives corrections to commonly used functionals to satisfy these constraints, thus advancing the frontiers of DFT. Research efforts focus on eliminating delocalization error with localized orbital scaling corrections and reducing static correction errors with both localized orbital scaling corrections and multireference DFT.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.