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学部化学理论、模型和计算方法项目的奖项。杨博士的研究重点是研究化学系统中的电子分布或电子结构。当原子结合（或成键）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非常重要。具体来说，杨博士使用基于密度泛函理论的数学方法的运动方程来模拟化学系统的电子结构。这一理论已成功地应用于广泛的化学研究，如模拟化学反应的速度，太阳能转换，燃料电池设计和药物的开发；然而，仍然有重要的领域，包括涉及带电或暂态系统的研究，其中密度泛函理论包含导致显着误差的近似。杨博士的项目重点是分析这些误差，并对目前使用的近似值进行系统修正，从而使电子结构的密度泛函理论更加准确和稳健。本研究在密度泛函理论方面所取得的进展，可广泛应用于生物、化学、物理、工程、纳米科学和纳米技术等领域的计算建模问题。该项目有助于未来几代理论和计算化学研究人员的发展。他还在SEED项目的研究项目中吸引来自科学、技术、工程和数学领域的少数族裔学生。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。基于所谓的广义梯度近似（GGA）的近似泛函在形式和性能方面都取得了很大进展，从元-GGA和超-GGA到结合微扰理论和随机相位近似的泛函。随着所有这些发展，密度泛函近似的准确性已经大大提高了许多化学和物理问题，甚至是非常具有挑战性的远距离范德华引力问题。然而，DFT中仍然存在突出的挑战，这些挑战阻碍了DFT的广泛和稳健应用。常用的近似泛函具有明显的离域误差，与分数电荷的精确线性条件存在偏差，导致应用中的许多不准确性。这些函数也不能描述静态或强相关性。用分数电荷和分数自旋表示了克服这些误差的必要条件。杨博士的研究小组对常用的泛函进行了修正，以满足这些限制，从而推进了DFT的前沿。研究主要集中在利用轨道定域标度修正消除离域误差和利用轨道定域标度修正和多参考DFT同时减少静校正误差。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。

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.