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，涉及分子中原子的运动和分子碰撞过程中的原子运动。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。真正的化学包括大幅度的运动。量子效应在许多过程中都是重要的，例如在酶催化中的质子隧穿。为了在详细的水平上理解原子的运动，人们必须应用量子力学定律，这就需要使用计算机来求解薛定谔方程。从它的解可以计算分子的性质和碰撞过程。例如，根据光谱可以确定分子的大小和形状以及它们的键的硬度。因为要处理的矩阵和向量很大，所以计算很困难。我和我的HQP将开发创新的张量和稀疏网格想法，以减少矩阵和向量的大小。我们将继续开发我们的想法，以消除在完整的多维网格上存储潜力的需要。 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。同样的方法将被用来提取了解大气中分子如何吸收和发射辐射所需的信息，这对建立全球变暖模型非常重要。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进行修改，以将其应用于复杂的反应体系。精确、可靠的计算速率常数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、体内的化学物质运输等。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培训。由于计算科学对保持健康和繁荣很重要，加拿大培训科学家开发和使用现代数值方法和现代计算机至关重要。

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.