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开展的。尽管如此，如果与足够高质量的量子化学计算一起使用来准确描述化学反应，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不使用导数的内插方案。在该方案中，我们结合了内插移动最小二乘法和Shepard格式(IMLS/Shepard)。我们将本方案应用于O-H_2、OH-H_2、H_2-H_2和Li-H_2体系。我们还考察了Betten和Collins提出的贝叶斯方法的效果。在O Ha系统中，对于相同数目的插值点，IMLS/Shepard格式的最优结果具有与Shepard格式相似的均方根误差。因此，IMLS/Shepard格式比Shepard格式有很大的优势，因为Shepard格式需要高达二阶导数的势能面。另一方面，对于OH-H_2体系，对于RMS、平均绝对误差和中位数绝对误差，比O-H_2体系更紧密的权函数是有利的。贝叶斯方法在Shepard结果的基础上改进了IMLS/Shepard结果。总体而言，我们已经展示了本方案的优势，它在从头计算中不需要任何导数。

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.