Formal and Computational Studies of Molecular Dynamics

9403416 Kouri University of Houston这个反应分子动力学理论的项目得到了NSF理论和计算化学计划的支持。 时间无关的波包（TIW）的量子力学方法将开发和实施到反应散射代码使用多项式表示的全绿色的运营商与吸收潜力和频谱密度运营商。 散射和束缚态费米子系统将被处理。 探讨了导出TIW Kohn型S-矩阵变分原理的可能性。 TIW方法将使用分布式近似函数来实现，以表示在离散点网格上评估的函数。 最近由Donald Kouri和大卫霍夫曼联合发明的TIW方法，提供了一种替代传统方法的方法，用于求解连续介质中散射态的与时间无关的薛定谔方程（S-矩阵形式主义）或求解随时间演化的波包的与时间相关的薛定谔方程。 新的TIW方法具有计算优势，这些。 Kohn先前已经推导出传统S矩阵计算的变分原理。 这个研究项目的主要目标之一是发展一个类似的变分原理TIW计算。 希望和期望的是，在正式的理论和计算方法的研究将显着提高我们的能力，使准确和详细的预测在气相中的分子过程。 这项技术未来可能的应用包括地球大气层臭氧消耗的计算机模型或喷气发动机和废物焚化炉中的高温燃烧过程。

9403416 Kouri Univ. of Houston This project in the theory of reactive molecular dynamics is supported by the NSF Theoretical and Computational Chemistry Program. The time-independent wavepacket (TIW) approach to quantum mechanics will be developed and implemented into reactive scattering codes using polynominal representations of the full Green's operators with absorbing potentials and the spectral density operator. Both scattering and bound-state Fermion systems will be treated. The possibility of deriving a TIW Kohn-type S-matrix variational principle will be explored. The TIW method will be implemented using distributed approximations functions to represent a function evaluated on a discrete grid of points. The TIW method, recently invented jointly by Donald Kouri and David Hoffman, offers an alternative to traditional methods of solving the time-independent Schroedinger equation for scattering states in the continuum (the S-matrix formalism) or solving the time-dependent Schroedinger equation for wavepackets that evolve in time. The new TIW method has computational advantages over each of these. Kohn has previously derived a variational principle for traditional S-matrix calculations. One of the major goals of this research project is the development of an analogous variational principle for TIW calculations. The hope and expectation is that this research in formal theory and computational methodology will significantly improve our ability to make accurate and detailed predictions of molecular processes in the gas phase. Possible future applications of this technology include computer models of ozone depletion in the earth's atmosphere or high temperature combustion processes in jet engines and waste incinerators.