Formal and Computational Studies in Molecular Dynamics

休斯顿大学的Don Kouri得到了形式和计算研究的理论和计算化学计划的支持，该计划专注于反应散射的与时间无关的波包反应-产物去耦合(TIW-RPD)方法，并探索分布近似泛函(DAFS)的使用。TIW-RPD方法将被用来开发和测试近似，以扩大可以计算可靠截面的反应系统的范围。将探索DAFS在多分辨率分析中的使用，并可能在数字信号处理中应用。将继续开发和应用一种算法来构造足够精确的量子势，以便能够直接求解Bohmian动力学方程，目标是使该方法能够应用于三维反应原子-硅原子散射计算。建立和求解基本量子力学方程的新的数学和计算方法的发展和应用与分子碰撞动力学有关，并因此与所有化学反应有关。在这样一个高度专业化的领域进行研究可能会产生更广泛的影响。例如，数据压缩出现在科学、工程和医学的所有领域。这在化学问题中尤其重要，例如减少拟合势能面所需的数据量，以及减少求解微分方程所需的网格点数量。为治疗反应散射而开发的工具现在显示出在医学和地球物理成像以及通信数字化方面的希望。

Don Kouri of the University of Houston is supported by the Theoretical and Computational Chemistry Program for formal and computational studies focusing on the time-independent wave packet reactant-product decoupling (TIW-RPD) approach to reactive scattering and on the exploration of the use of distributed approximating functionals (DAFs). TIW-RPD methods will be used to develop and test approximations for enlarging the range of reactive systems for which reliable cross sections can be computed. DAFs will be explored for use in multi-resolution analysis with likely applications in digital signal processing. Development and applications of an algorithm for constructing sufficiently accurate quantum potentials to enable the direct solution of the Bohmian dynamics equations will be pursued, with the goal of enabling the method to be applied to three-dimensional reactive atom-diatom scattering calculations. The development and application of new mathematical and computational methods for formulating and solving fundamental quantum mechanical equations is relevant to molecular collision dynamics, and consequently to all chemical reactions. Research in such a highly specialized area can lead to more general impacts. For example, data compression arises in all areas of science, engineering, and medicine. It is especially important in chemical problems such as reducing the amount of data needed to fit potential energy surfaces, and reducing the number of grid points needed to solve differential equations. Tools developed for treating reactive scattering are now showing promise for medical and geophysical imaging, and digitization in communications.