New iterative, tensor, and collocation methods for computing ro-vibrational spectra and inelastic rate constants

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Our research program is in theoretical chemistry and concerns the motion of atoms in molecules and during collisions of molecules. We shall develop and apply new methods for computing and understanding spectra of molecules and the rate of energy transfer during collisions. The motion of atoms is easy to understand when they are close to an equilibrium geometry or when quantum effects are negligible. Real chemistry involves large amplitude motion. Quantum effects are important in many processes, e.g., proton tunnelling in enzyme catalysis. To understand, at a detailed level, the motion of atoms, one must thus apply the laws of quantum mechanics and this requires using computers to solve the Schrödinger equation. From its solutions one can calculate properties of molecules and collision processes. For example, from spectra one determines the size and shape of molecules and the stiffness of their bonds. The calculations are difficult because the matrices and vectors to be manipulated are large. My HQP and I shall develop innovative tensor and sparse-grid ideas for reducing the size of the matrices and vectors. We shall continue to exploit our ideas for obviating the need to store the potential on a full multidimensional grid. Computational methods we develop will be used to study molecules that play an important role in combustion. This will provide information necessary for improving efficiency and reducing emissions. The same methods will be used to extract information required to understand how molecules in the atmosphere absorb and emit radiation, which is important for modelling global warming. Both spectra and energy transfer processes reveal information about the composition and physical properties of planetary atmospheres and the interstellar medium. The methods we develop for studying collisions can be modified to apply them to complex reacting systems. The development of accurate, dependable methods to calculate rate constants will enable one to model (for example) combustion and atmospheric chemistry much more reliably. The state-of-the-art computational methods we develop will help chemists to analyse and understand laboratory data. The new tools we are developing for interpolating functions and solving differential equations are also applicable in many areas of science and engineering. For example, they could be used to study the flow of air around plane wings, ocean currents, vibrations of buildings, combustion processes in engines and power plants, the transport of chemicals in the body, etc. They are related to methods used in weather prediction, machine learning, and optimal control theory. In the course of doing this research, HQP will be trained in computational chemistry, numerical analysis and computer science. 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.