Density Functional Theory of the Electronic Structure of Molecules

该项目由NSF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·皮尔逊的软硬酸碱概念(HSAB)的理论公式。在这项工作的一个方面，Kohn-Sham轨道是由给定的电子密度直接确定的。一个主要目标是开发一种改进的交换相关DFT泛函。为此，将对局部泛函和非局部泛函的解析性质进行数学分析，例如尖点条件和坐标标度条件。密度泛函理论为计算物质的电子结构提供了一种替代薛定谔方程从头算解的方法。密度泛函理论的历史可以追溯到20世纪20年代由托马斯、费米和狄拉克在量子理论最早期的S所做的工作。在过去的二十年里，密度泛函计算被广泛应用于预测金属和其他晶体的电子性质，但直到最近几年，密度泛函计算才变得足够准确，可以广泛应用于分子。由于新的交换相关泛函的发展，这一进步成为可能，使大分子的计算时间减少了至少十分之一。本项目的重点是基本数学方面的分析，只是正在进行的几个正在进行的研究项目之一，这些项目寻求开发更精确的泛函。许多科学家预计，有一天，在分子量子理论的所有应用中，新的DFT方法将取代昂贵得多的从头计算。如果是真的，这将是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.