A procedure is proposed to produce intermolecular potential energy surfaces from limited data. The procedure involves generation of geometrical configurations using a Latin hypercube design, with a maximin criterion, based on inverse internuclear distances. Gaussian processes are used to interpolate the data, using over-specified inverse molecular distances as covariates, greatly improving the interpolation. Symmetric covariance functions are specified so that the interpolation surface obeys all relevant symmetries, reducing prediction errors. The interpolation scheme can be applied to many important molecular interactions with trivial modifications. Results are presented for three systems involving ${CO}_2$, a system with a deep energy minimum ($HF-HF$), and a system with 48 symmetries (${CH}_4-{\mathrm{N}}_2$). In each case, the procedure accurately predicts an independent test set. Training this method with high-precision $abinitio$ evaluations of the ${CO}_2-CO$ interaction enables a parameter-free, first-principles prediction of the ${CO}_2-CO$ cross virial coefficient that agrees very well with experiments.

中文翻译：

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使用高斯过程对分子间电位进行插值

提出了产生分子间潜能的方法 活力有限数据的表面。该过程涉及基于反核间距离，使用具有最大值准则的拉丁超立方体设计生成几何构型。高斯过程 可以使用超规定的反分子距离作为协变量来对数据进行插值，从而极大地改善了 插值。 指定对称协方差函数，以便 插补表面遵守所有相关的对称性，减少了预测误差。这插补 该方案可以应用于许多重要的分子 互动经过微不足道的修改。提出了涉及以下三个系统的结果${CØ}_{\mathrm{2个}}$，具有深层次的系统 活力 最低限度 （$HF-HF$），以及一个具有48个对称性的系统（${CH}_4-{\mathrm{ñ}}_{\mathrm{2个}}$）。在每种情况下，该过程均可准确预测独立的测试集。高精度训练此方法$\mathrm{一个}b\mathrm{一世}ñ\mathrm{一世}Ť\mathrm{一世}Ø$ 的评价 ${CØ}_{\mathrm{2个}}-CØ$ 相互作用 启用无参数的第一性原理预测 ${CØ}_{\mathrm{2个}}-CØ$ 交叉维里系数与实验非常吻合。