We present a method based on interpolating moving least-squares (IMLS) that is designed for efficient and accurate local fitting of discrete energy values to provide global representations of potential energy surfaces (PESs) for many-atom systems. We have demonstrated the method with one-, two-, and three-dimensional fits of the NH_2 → N_2 + H PES. To allow for extensive fitting and testing, the analytical PES developed by Koizumi et al. [Koizumi, H.; Schatz, G. C.; Walch, S. P. J. Chem. Phys. 1991, 95, 4130] was used to generate energy values. Unlike the modified Shepard method this approach does not require derivatives, thus it can be used to fit energies computed using highest-level quantum chemistry methods for which forces are not directly obtainable. This fitting scheme accurately describes the PES, is not computationally time-consuming, can be improved by using higher degrees and larger number of basis functions, and is straightforward to apply. Extension to many-dimensional PESs seems promising.
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机译：我们提出了一种基于插值移动最小二乘（IMLS）的方法，该方法旨在有效，准确地对离散能量值进行局部拟合，以为多原子系统提供势能面（PES）的全局表示。我们已经证明了该方法具有NH_2→N_2 + H PES的一维，二维和三维拟合。为了进行广泛的安装和测试，Koizumi等人开发了分析型PES。 [小泉，H; Schatz，G. C .; Walch，S.P. J. Chem。物理1991，95，4130]用于产生能量值。与改进的Shepard方法不同，此方法不需要导数，因此可以用于拟合使用无法直接获得力的最高级别量子化学方法计算出的能量。该拟合方案准确地描述了PES，不耗费计算时间，可以通过使用更高的度数和更多数量的基函数进行改进，并且易于直接应用。扩展到多维PES似乎很有希望。
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