Development and application of new methods for computing rovibrational spectra and rate constants

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The proposed research is in theoretical chemistry and addresses the motion of atoms in molecules and during reactions. The motion of atoms is easy to calculate and understand if they remain confined very close to an equilibrium geometry. Real chemistry, however, involves large amplitude motion and the making and breaking of bonds. To understand, at a detailed level, the motion of atoms, one must apply the laws of quantum mechanics and solve the Schrödinger equation by representing wavefunctions (functions from which one can calculate all observable properties) in terms of basis functions and using methods of linear algebra to compute observables. The calculations are difficult because the required number of functions and therefore the size of the matrices and vectors to be manipulated is large. I shall develop new ideas for choosing better basis functions, to reduce the number of functions required. From solutions of the Schrödinger equation one can deduce properties of molecules and interpret experimental results. Our work will provide information necessary for understanding how molecules in the atmosphere absorb and emit radiation, which is important for modelling global warming. Understanding and combating global warming is one of the most important problems of our time. We will study greenhouse gas molecules (ozone, water dimer, methane) and molecules of interest in astrophysics (e.g. CH5+). The greenhouse effect is the rise in temperature that the Earth experiences because gases in the atmosphere trap energy from the sun. A better understanding of greenhouse gases will help us to know how they absorb heat and hence to what extent they are responsible for global warming. Water is an important greenhouse gas and understanding the spectrum of water dimer may be important. This is difficult in the lab because the spectra of water monomer and dimer overlap. The water dimer is also prototype system for understanding hydrogen bonding, which is important in many biological molecules. We shall also study the propargyl radical which is important in combustion. The new techniques we propose developing will enable scientists to understand the motion of atoms in hydrogen bonded molecules (e.g. water dimer). Hydrogen bonds play a very important role in nature. For example, the structure of DNA is determined by hydrogen bonds. Established computational methods for studying the motion of atoms are inadequate for hydrogen bonded molecules. We will also develop methods to calculate rate constants. To model any complex reacting system one requires rate constants for the elementary reactions that are implicated. The development of accurate, dependable methods to calculate such rate constants would enable one to model (for example) combustion and atmospheric chemistry much more reliably. The computational methods we develop, both those applied to isolated molecules (spectroscopy) and those applied to reactions (rate constants) relate to the motion of molecules. They will help chemists to analysis and understand laboratory data. Numerical methods we develop may also be useful in other areas of science and engineering. E.g., the equations we use to compute rate constants are also used to study conductivity of molecules. In the course of doing this research, HQP will be trained in computational chemistry, numerical analysis and computer science and profit from opportunities provided by numerous international collaborations. Because computational science is important for maintaining health and prosperity it is critical that Canada train scientists to both develop and use modern numerical methods and modern computers.