Mathematical Studies in Quantum Mechanics

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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.