使用具有高斯形式节点函数的 Shepard 插值对小分子团进行势能面建模。

Modelling potential energy surfaces for small clusters using Shepard interpolation with Gaussian-form nodal functions.

机构信息

Department of Chemistry, Princeton University, Princeton, USA.

出版信息

Phys Chem Chem Phys. 2019 Feb 20;21(8):4513-4522. doi: 10.1039/c8cp07640e.

Abstract

The potential energy surface (PES) of a chemical system is an analytical function that outputs the potential energy of the system when a nuclear configuration is given as input. The PESs of small atmospheric clusters have theoretical as well as environmental significance. A common method used to generate analytical PESs is the Shepard interpolation, where the PES is a weighed sum of Taylor series expansions (nodal functions) at ab initio sample points. Based on this, in this study we present a new method based on the Shepard interpolation, where the nodal functions are composed of a symmetric Gaussian term and an asymmetric exponential term in each dimension. Corresponding sampling methods were also developed. We tested the method on several atmospheric bimolecular clusters and achieved root mean square errors (RMSE) below 0.13 kJ mol-1 in 150 samples for Ar-rigid H2O and Ne-rigid CO2, and below 0.39 kJ mol-1 in 1800 samples for rigid N2-rigid CO2.

摘要

化学体系的势能面（PES）是一个分析函数，当给定核构型作为输入时，它会输出体系的势能。小的大气团簇的 PES 具有理论和环境意义。一种常用的生成分析 PES 的方法是 Shepard 插值，其中 PES 是在从头算样本点的泰勒级数展开（节点函数）的加权和。基于此，在本研究中，我们提出了一种基于 Shepard 插值的新方法，其中节点函数由每个维度中的对称高斯项和不对称指数项组成。还开发了相应的采样方法。我们在几个大气双分子团簇上测试了该方法，对于 Ar-刚性 H2O 和 Ne-刚性 CO2，在 150 个样本中达到了低于 0.13 kJ mol-1 的均方根误差（RMSE），对于刚性 N2-刚性 CO2，在 1800 个样本中达到了低于 0.39 kJ mol-1 的 RMSE。