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

提议的研究是在理论化学和解决原子在分子和反应过程中的运动。原子的运动很容易计算和理解，如果它们保持非常接近平衡几何。然而，真正的化学涉及到大振幅运动和化学键的形成和断裂。为了详细地理解原子的运动，我们必须应用量子力学定律，用基函数表示波函数（可以计算所有可观测属性的函数），并使用线性代数方法计算可观测值，从而求解Schrödinger方程。计算是困难的，因为所需的函数数量，因此要操作的矩阵和向量的大小很大。我将开发新的思路来选择更好的基函数，以减少所需函数的数量。从Schrödinger方程的解可以推断出分子的性质并解释实验结果。**我们的工作将为理解大气中的分子如何吸收和发射辐射提供必要的信息，这对模拟全球变暖很重要。理解和应对全球变暖是我们这个时代最重要的问题之一。我们将研究温室气体分子（臭氧、水二聚体、甲烷）和天体物理学中感兴趣的分子（如CH5+）。温室效应是由于大气中的气体捕获了来自太阳的能量，导致地球温度升高。更好地了解温室气体将有助于我们了解它们是如何吸收热量的，从而了解它们在多大程度上导致了全球变暖。水是一种重要的温室气体，了解水二聚体的光谱可能很重要。这在实验室中是困难的，因为水单体和二聚体的光谱重叠。水二聚体也是理解氢键的原型系统，这在许多生物分子中都很重要。我们还将研究在燃烧中起重要作用的丙炔基。我们建议开发的新技术将使科学家能够理解氢键分子（例如水二聚体）中原子的运动。氢键在自然界中起着非常重要的作用。例如，DNA的结构是由氢键决定的。现有的研究原子运动的计算方法不适用于氢键分子。我们还将开发计算速率常数的方法。要模拟任何复杂的反应系统，就需要所涉及的基本反应的速率常数。发展出精确可靠的方法来计算这种速率常数，将使人们能够更可靠地模拟（例如）燃烧和大气化学。**我们开发的计算方法，既适用于分离分子（光谱学），也适用于反应（速率常数），都与分子的运动有关。它们将帮助化学家分析和理解实验室数据。我们开发的数值方法在其他科学和工程领域也可能有用。例如，我们用来计算速率常数的方程也用于研究分子的电导率。**在进行这项研究的过程中，HQP将接受计算化学、数值分析和计算机科学方面的培训，并从众多国际合作提供的机会中获益。由于计算科学对维持健康和繁荣至关重要，因此加拿大必须培训科学家开发和使用现代数值方法和现代计算机。

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.