Ishida Toshimasa, Schatz George C
Research Center for Molecular-scale Nanoscience Center, Institute for Molecular Science, Okazaki 444-8585, Japan.
J Comput Chem. 2003 Jul 15;24(9):1077-86. doi: 10.1002/jcc.10252.
We recently proposed a local interpolation scheme, in which interpolant moving least squares (IMLS) and Shepard interpolation are employed to describe potential energy surfaces. This IMLS/Shepard scheme is used to interpolate quantum chemical potential energy surfaces for which analytical derivatives are not available. In this study, we apply the scheme to the highly exothermic O((1)D) + H(2) --> H + OH reaction and compare it with results based on Shepard interpolation using second-order Taylor expansions. An analytical surface is used to define the potential function so that errors in the interpolation function may accurately be determined. We find that the present scheme reproduces the correct reactive cross-sections more accurately than the Shepard scheme, and with rms errors for energy and gradients that are significantly smaller than those from Shepard interpolation. This occurs even though the present scheme does not utilize derivative and Hessian information, whereas the Shepard interpolation does. The Bayesian approach proposed by Bettens and Collins does not improve the IMLS/Shepard results significantly, although it does the Shepard-only approach. The accuracy of the IMLS/Shepard scheme is surprising, but can be explained by the more global nature of the interpolation.
我们最近提出了一种局部插值方案，其中采用插值移动最小二乘法（IMLS）和谢泼德插值来描述势能面。这种IMLS/谢泼德方案用于对无法获得解析导数的量子化学势能面进行插值。在本研究中，我们将该方案应用于高度放热的O((1)D) + H(2) --> H + OH反应，并将其与基于二阶泰勒展开的谢泼德插值结果进行比较。使用解析表面来定义势能函数，以便能够准确确定插值函数中的误差。我们发现，与谢泼德方案相比，本方案能更准确地再现正确的反应截面，并且能量和梯度的均方根误差明显小于谢泼德插值的误差。即便本方案未利用导数和海森矩阵信息，而谢泼德插值利用了这些信息，情况依然如此。贝滕斯和柯林斯提出的贝叶斯方法虽对仅使用谢泼德插值的方法有改进，但对IMLS/谢泼德结果的改进并不显著。IMLS/谢泼德方案的准确性令人惊讶，但可以通过插值更具全局性的特点来解释。
