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

分子的性质（它们的形状和大小，它们振动的方式）是由量子力学控制的。根据量子力学，分子的能量只能取一定的值。这些值可以通过求解一个叫做薛定谔方程（SE）的方程来确定。利用SE的解可以推导出分子的性质并解释实验结果。本提案的主题是与小分子的振动和旋转有关的SE的解决方案。SE通常是通过用一组已知函数（称为基函数）表示分子的状态（一个可以计算所有可观察性质的函数）来求解的。由于所需基函数的数量非常大，求解起来比较困难。如果需要大量的基函数，则所需的计算机内存和计算时间都很大。一个分子的原子核越多，所需的基函数的数量就越多。我们提出了处理非常大的基函数集的方法。我提出的想法对于研究有五个或更多原子的分子是必要的，现有的方法是不够的。比如，我们会学习甲烷。甲烷在天体物理学和大气科学中引起了人们的兴趣。地球大气中的甲烷是一种温室气体。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。温室气体导致地球变暖，就像停在阳光下的汽车内部一样。更好地了解甲烷可以帮助我们了解甲烷在多大程度上导致了全球变暖。我们用类似的方法来计算反应速率。根据这样的速率，人们可以了解大气中发生的化学反应。从长远来看，使用我们开发的方法来理解生物分子中的质子转移反应是可能的。在进行这项研究的过程中，研究生将接受计算化学、数值分析和计算机方面的训练。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 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.