Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA and Department of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
Independent Researcher, Toronto, Ontario M9B0E3, Canada.
J Chem Phys. 2023 Jan 28;158(4):044109. doi: 10.1063/5.0134442.
We wish to describe a potential energy surface by using a basis of permutationally invariant polynomials whose coefficients will be determined by numerical regression so as to smoothly fit a dataset of electronic energies as well as, perhaps, gradients. The polynomials will be powers of transformed internuclear distances, usually either Morse variables, exp(-r/λ), where λ is a constant range hyperparameter, or reciprocals of the distances, 1/r. The question we address is how to create the most efficient basis, including (a) which polynomials to keep or discard, (b) how many polynomials will be needed, (c) how to make sure the polynomials correctly reproduce the zero interaction at a large distance, (d) how to ensure special symmetries, and (e) how to calculate gradients efficiently. This article discusses how these questions can be answered by using a set of programs to choose and manipulate the polynomials as well as to write efficient Fortran programs for the calculation of energies and gradients. A user-friendly interface for access to monomial symmetrization approach results is also described. The software for these programs is now publicly available.
我们希望通过使用由置换不变多项式构成的基来描述一个势能面，其系数将通过数值回归来确定，以便平滑地拟合电子能数据集，以及可能的梯度。多项式将是转化后的核间距离的幂次，通常是 Morse 变量 exp(-r/λ)，其中 λ 是一个常数范围超参数，或者是距离的倒数 1/r。我们要解决的问题是如何创建最有效的基，包括 (a) 保留或丢弃哪些多项式，(b) 需要多少个多项式，(c) 如何确保多项式正确地在大距离处再现零相互作用，(d) 如何确保特殊对称性，以及 (e) 如何有效地计算梯度。本文讨论了如何通过一组程序来回答这些问题，这些程序可以选择和操作多项式，以及编写高效的 Fortran 程序来计算能量和梯度。还描述了一种用户友好的接口，用于访问单项式对称化方法的结果。这些程序的软件现在已经公开可用。
