Density Functional Theory of the Electronic Structure of Molecules

该项目由美国国家科学基金会理论和计算化学计划支持，继续罗伯特·帕尔在密度泛函理论（DFT）相关领域的研究，以及拉尔夫·皮尔森的硬、软酸碱概念（HSAB）的理论公式。在这项工作的一个方面，Kohn-Sham轨道是直接由给定的电子密度确定的。主要目标是开发改进的交换相关DFT函数。为此，将对局部泛函和非局部泛函的解析性质，如尖点条件和坐标标度条件进行数学分析。密度泛函理论为计算物质的电子结构提供了一种替代从头解薛定谔方程的方法。DFT的历史可以追溯到托马斯、费米和狄拉克在20世纪20年代量子理论早期的工作。在过去的二十年里，DFT计算被广泛应用于预测金属和其他晶体的电子特性，但直到最近几年，DFT计算才变得足够精确，可以普遍应用于分子。这一进步是由于新的交换相关函数的发展而成为可能的，它将大分子的计算时间减少了至少十倍。目前的项目强调对基本数学方面的分析，只是几个正在进行的研究项目之一，这些研究项目寻求开发更精确的函数。许多科学家预计，新的DFT方法有一天将取代更昂贵的从头计算，在大约80%的分子量子理论应用中。如果这是真的，这将构成我们设计新材料能力的重大进步。

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.