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

我们的研究项目是理论化学，涉及分子中的原子运动和分子碰撞过程。我们将开发和应用新的方法来计算和理解分子的光谱和碰撞过程中的能量转移速率。当原子接近平衡几何或量子效应可以忽略不计时，原子的运动很容易理解。真正的化学包括大振幅运动。量子效应在许多过程中都很重要，例如酶催化中的质子隧穿。为了详细地理解原子的运动，人们必须应用量子力学的定律，这就需要使用计算机来解Schrödinger方程。从它的解可以计算分子的性质和碰撞过程。例如，从光谱可以确定分子的大小和形状以及它们的键的硬度。计算是困难的，因为要操作的矩阵和向量很大。我的HQP和我将开发创新的张量和稀疏网格的想法，以减少矩阵和向量的大小。我们将继续开发我们的想法，以避免需要在一个完整的多维网格中存储电位。我们开发的计算方法将用于研究在燃烧中起重要作用的分子。这将为提高效率和减少排放提供必要的信息。同样的方法将用于提取所需的信息，以了解大气中的分子如何吸收和发射辐射，这对于模拟全球变暖非常重要。光谱和能量传递过程都揭示了行星大气和星际介质的组成和物理性质的信息。我们开发的研究碰撞的方法可以被修改以应用于复杂的反应系统。精确可靠的速率常数计算方法的发展将使人们能够更可靠地模拟（例如）燃烧和大气化学。我们开发的最先进的计算方法将帮助化学家分析和理解实验室数据。我们正在开发的用于插值函数和求解微分方程的新工具也适用于许多科学和工程领域。例如，它们可以用来研究飞机机翼周围的空气流动、洋流、建筑物的振动、发动机和发电厂的燃烧过程、体内化学物质的运输等。它们与天气预报、机器学习和最优控制理论中使用的方法有关。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。

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.