Mathematical Studies in Quantum Mechanics

该数学项目的首席研究员和研究生将研究分子的量子力学及其在化学和物理中的应用。一个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，因为它们在典型温度下容易形成和断裂。由于氢键长而弱，即使使用高性能计算机，它们也提出了理论上的挑战。该项目的另一个高优先级目标是研究一种被广泛使用的计算化学技术，称为Moller-Plesset微扰理论，该技术对某些分子不起作用。研究将集中在失效的机制和如何在这些失效发生时获得正确的结果。该项目的其他目标包括质子转移反应的研究，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。这个项目研究的数学是理解分子和化学反应的基础。它专注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。该项目的大部分工作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。

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.