Efficient Generation of Permutationally Invariant Potential Energy Surfaces for Large Molecules

An
efficient method is described for generating a fragmented, permutationally
invariant polynomial basis to fit electronic energies and, if available,
gradients for large molecules. The method presented rests on the fragmentation
of a large molecule into any number of fragments while maintaining
the permutational invariance and uniqueness of the polynomials. The
new approach improves on a previous one reported by Qu and Bowman
by avoiding repetition of polynomials in the fitting basis set and
speeding up gradient evaluations while keeping the accuracy of the
PES. The method is demonstrated for CH3–NH–CO–CH3 (N-methylacetamide) and NH2–CH2–COOH (glycine).

本文提出一种高效方法，用于生成碎片化的置换不变多项式基组，以拟合大型分子的电子能量；若存在梯度数据，亦可同时拟合梯度。该方法的核心思路是将大型分子拆分为任意数量的片段，同时确保多项式的置换不变性与唯一性。相较于Qu与Bowman此前报道的方法，本新方法实现了改进：避免了拟合基组内多项式的重复，在保证势能面（Potential Energy Surface, PES）精度的同时，加快了梯度的计算速度。本文通过CH3–NH–CO–CH3（N-甲基乙酰胺）与NH2–CH2–COOH（甘氨酸）两个体系验证了该方法的有效性。