Mathematical Studies in Quantum Mechanics

量子力学的数学研究

• 批准号: 0600944
• 负责人: George Hagedorn
• 金额: $ 24.38万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600944&HistoricalAwards=false
• 关键词: Mathematical; Studies; Quantum; Mechanics

The principal investigator and graduate students involved in this mathematical project will study the quantum mechanics of molecules with applications to chemistry and physics. A main goal is to develop new techniques for studying hydrogen bonds. These bonds play extremely important roles in biochemistry and the actions of many modern pharmaceuticals because they form and break easily at typical temperatures. Because hydrogen bonds are long and weak, they present theoretical challenges, even with the use of high performance computers. Another high priority goal of the project is to study a heavily used computational chemistry technique called Moller-Plesset perturbation theory that fails for some molecules. The research will concentrate on the mechanism of failure and how to obtain correct results when these failures occur. Additional goals of the project include studies of proton transfer reactions, certain effects of electron energy level crossings, and semiclassical analysis for the Dirac equation of relativistic quantum mechanics.brbrThis project studies the mathematics that underlies the understanding of molecules and chemical reactions. It concentrates on developing new theoretical and computational techniques for use by chemists and chemical physicists. Much of the project will concentrate on improving the understanding of hydrogen bonds. They play crucial roles in biological systems and the actions of many modern drugs.

参与这个数学项目的首席研究员和研究生将研究分子的量子力学，并将其应用于化学和物理。主要目标是开发研究氢键的新技术。这些键在生物化学和许多现代药物的作用中起着极其重要的作用，因为它们在典型的温度下很容易形成和断裂。由于氢键长而弱，即使使用高性能计算机，它们也存在理论挑战。该项目的另一个高优先级目标是研究一种被称为Moller-Plesset微扰理论的大量使用的计算化学技术，该理论对某些分子无效。研究将集中在故障的机制，以及如何获得正确的结果时，这些故障发生。该项目的其他目标包括研究质子转移反应、电子能级交叉的某些影响以及相对论量子力学狄拉克方程的半经典分析。brbr该项目研究理解分子和化学反应的数学基础。它致力于开发新的理论和计算技术，供化学家和化学物理学家使用。该项目的大部分内容将集中在提高对氢键的理解上。它们在生物系统和许多现代药物的作用中起着至关重要的作用。