New computational methods for studying the quantum dynamics of systems with five and more atoms

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The properties of molecules (their shape and size, the way they vibrate) are governed by quantum mechanics. According to quantum mechanics, the energy of a molecule can take only certain values. These values may be determined by solving an equation called the Schroedinger equation (SE). Using solutions of the SE one can deduce properties of molecules and interpret experimental results. The subject of this proposal is the solution of the SE associated with the vibration and rotation of small molecules. The SE is generally solved by representing the state of the molecule (a function from which one can calculate all observable properties) in terms of a set of known functions, called basis functions. It is difficult to solve because the number of basis functions required is very large. If a large number of basis functions is necessary the computer memory required and the calculation time are large. The more nuclei a molecule has the larger the number of basis functions required. We propose methods of coping with very large sets of basis functions. The ideas I propose are necessary for studying molecules with five or more atoms: established methods are not adequate. We will study, for example, methane. Methane is of interest in astrophysics and in atmospheric science. In the earth's atmosphere methane is a greenhouse gas. The greenhouse effect is the rise in temperature that the Earth experiences because gases in the atmosphere trap energy from the sun. Greenhouse gases cause the earth to warm up, like the inside of a car parked in the sun. Understanding methane better may help us to know to what extent methane is responsible for global warming. Using similar ideas we will calculate rates of reactions. From such rates one can understand the chemistry that takes places in the atmosphere. In the long term, it will be possible to use the methods we develop to understand proton transfer reactions in biological molecules. In the course of doing this research, graduate students will be trained in computational chemistry, numerical analysis and computers. Because computational science is important for maintaining health and prosperity it is critical that Canada train scientists to develop and use modern numerical methods and modern computers.