Density Functional Theory of the Electronic Structure of Molecules

该项目得到了NSF理论和计算科学中心的支持。 化学计划，继续罗伯特帕尔在相关领域的研究 密度泛函理论（DFT），和理论公式， Ralph Pearson的软硬酸碱（HSAB）概念。 在一个 这项工作的一个方面，科恩-沙姆轨道是直接从一个 给定电子密度。 一个主要目标是开发一种改进的 交换相关DFT泛函 为此，一个数学 分析局部和非局部泛函的分析性质，如 作为尖点条件和坐标标度条件， 出去 密度泛函理论提供了一个替代从头算解决方案 薛定谔方程的计算电子 mater的结构DFT的历史可以追溯到托马斯的工作， 费米和狄拉克在20世纪20年代量子理论的早期。 在过去的二十年里，DFT计算已被广泛应用于 预测金属和其他晶体的电子性质，但只有 近年来，DFT计算变得足够精确， 允许对分子的一般应用。 这一进步，使之成为可能， 新的交换相关泛函的发展，减少了 大分子的计算时间至少缩短了十倍。 的 本项目，其重点是分析基本的 数学方面，只是几个正在进行的研究项目之一， 它试图发展出更精确的泛函。 许多科学家 预计新的DFT方法有一天会取代更多的 昂贵的从头计算在约80%的所有应用， 分子量子理论 如果这是真的， 我们设计新材料的能力。

This project, supported by the NSF Theoretical and Computational Chemistry Program, continues research by Robert Parr in the related areas of density functional theory (DFT), and the theoretical formulation of Ralph Pearson's concept of hard and soft acids and bases (HSAB). In one aspect of this work the Kohn-Sham orbitals are determined directly from a given electron density. A major goal is the development of an improved exchange-correlation DFT functional. To this end, a mathematical analysis of analytic properties of local and non-local functionals, such as cusp conditions and coordinate scaling conditions, will be carried out. Density functional theory provides an alternative to ab initio solution of the Schroedinger equation for the computation of the electronic structure of mater. The history of DFT dates back to work by Thomas, Fermi, and Dirac in the 1920's in the earliest days of quantum theory. In the past two decades, DFT calculations have been widely applied to predict the electronic properties of metals and other crystals, but only in recent years have DFT calculations become sufficiently accurate to permit general application to molecules. This advance, made possible by the development of new exchange-correlation functionals, reduces computation time for large molecules by at least a factor of ten. The present project, with its emphasis on analysis of fundamental mathematical aspects, is just one of several ongoing research projects which seek to develop even more accurate functionals. Many scientists anticipate that new DFT methods will one day replace the much more expensive ab initio calculations in about 80% of all applications of molecular quantum theory. If true, this will constitute a major advance in our ability to design new materials.