Development and applications of an interpolation scheme of potential energy surfaces which can be combined with latest ab initio methodologies

从头算动力学是随着高速计算机的发展而进行的。但是，如果使用量子化学计算来精确描述化学反应，这种方法仍然非常需要CPU。因此，我们开发了一种在从头计算中使用无导数的插值方案。在该方案中，我们将插值移动最小二乘法与Shepard方案（IMLS/Shepard）相结合。我们将该方案应用于O+ H_2、OH+H_2、H_2+ H_2和Li+ H_2体系。我们还研究了Bettens和Collins提出的贝叶斯方法的效果。在O+ Ha系统中，当插入点数目相同时，IMLS/Shepard方案的最佳结果与Shepard方案的均方根误差大小相近。因此，与Shepard格式相比，IMLS/Shepard格式具有很大的优势，因为Shepard格式需要对势能面进行高达二阶导数。另一方面，对于OH+ H_2体系，相对于O+ H_2体系，更严格的权函数对于均方根、平均绝对误差和中位数绝对误差都是有利的。除了Shepard结果外，贝叶斯方法还改进了IMLS/Shepard结果。总的来说，我们已经证明了该方案的优点，它不需要从头计算任何导数。

Ab initio dynamics are carried out as development of high-speed computers. Still this approach is still very CPU demanding if used with quantum chemical cal culations of sufficient quality to describe chemical reactions accurately. Thus, we developed an interpolation scheme using no derivatives in ab initio calculations. In this scheme, we combine interpolant moving least squares method and Shepard scheme (IMLS/Shepard). We applied the present scheme to O+ H_2, OH+H_2, H_2+ H_2 and Li+ H_2 systems. We also investigate the effect of Bayesian approach proposed by Bettens and Collins. In O+ Ha system, the best result of IMLS/Shepard scheme was shown to have similar magnitude of rms errors to that of Shepard scheme for the same number of interpolant points. Thus, IMLS/Shepard has great advantage in comparison with Shepard scheme because Shepard scheme requires up to second derivatives of potential energy surfaces. On the other hand, for the OH+ H_2 system, tighter weight functions than for O+ H_2 system was favorable as for all of rms, mean absolute, and median absolute errors. Bayesian approach improved IMLS/Shepard results in addition to Shepard results. Overall, we have showed the advantage of the present scheme, which does not require any derivatives in ab initio calculations.