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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=747813
• 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.

我们的研究计划是理论化学中的，涉及分子中原子和分子碰撞期间的运动。我们将开发并应用新方法来计算和理解分子的光谱以及碰撞过程中的能量传递速率。当原子接近相等的几何形状或量子效应可忽略不计时，原子的运动很容易理解。实际化学涉及大型放大器运动。量子效应在许多过程中很重要，例如酶催化中的质子隧穿。要了解原子的运动，必须应用量子力学定律，这需要使用计算机来求解Schrödinger方程。通过其溶液可以计算分子和碰撞过程的特性。例如，从光谱中确定分子的大小和形状及其键的刚度。这些计算很困难，因为要操纵的物质和向量很大。我和我的HQP将开发创新的张量和稀疏网格的想法，以减少物品和向量的大小。我们将继续利用我们的想法，以消除将潜力存储在完整的多维网格上的需求。我们开发的计算方法将用于研究在组合中起重要作用的分子。这将提供提高效率和降低排放所必需的信息。将使用相同的方法来提取所需的信息，以了解大气中的分子如何吸收和发射辐射，这对于对全球变暖进行建模非常重要。光谱和能量传递过程都揭示了有关行星大气和星际介质的组成和物理特性的信息。我们开发的研究碰撞方法可以修改以将其应用于复杂的反应系统。计算速率常数的准确，依赖的方法的开发将使人们能够更可靠地建模（例如）燃烧和大气化学。我们开发的最新计算方法将帮助化学家分析和理解实验室数据。我们正在开发用于插值功能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，它们可用于研究平面机翼，洋流，建筑物的振动，发动机和发电厂的混合过程，体内化学物质的运输等。它们与天气预测，机器学习和最佳控制理论相关。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的培训。由于计算科学对于维持健康和繁荣很重要，因此至关重要的是，加拿大训练科学家既开发并使用现代数值方法和现代计算机。