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

用于计算旋转振动谱和非弹性速率常数的新迭代、张量和配置方法

• 批准号: RGPIN-2019-04357
• 负责人: Carrington, Tucker
• 金额: $ 7.65万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=714114
• 关键词: New; iterative; tensor; collocation; methods

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.

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。