Mardirossian Narbe, Head-Gordon Martin
Department of Chemistry, University of California, Berkeley and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
J Chem Phys. 2014 May 14;140(18):18A527. doi: 10.1063/1.4868117.
The limit of accuracy for semi-empirical generalized gradient approximation (GGA) density functionals is explored by parameterizing a variety of local, global hybrid, and range-separated hybrid functionals. The training methodology employed differs from conventional approaches in 2 main ways: (1) Instead of uniformly truncating the exchange, same-spin correlation, and opposite-spin correlation functional inhomogeneity correction factors, all possible fits up to fourth order are considered, and (2) Instead of selecting the optimal functionals based solely on their training set performance, the fits are validated on an independent test set and ranked based on their overall performance on the training and test sets. The 3 different methods of accounting for exchange are trained both with and without dispersion corrections (DFT-D2 and VV10), resulting in a total of 491 508 candidate functionals. For each of the 9 functional classes considered, the results illustrate the trade-off between improved training set performance and diminished transferability. Since all 491 508 functionals are uniformly trained and tested, this methodology allows the relative strengths of each type of functional to be consistently compared and contrasted. The range-separated hybrid GGA functional paired with the VV10 nonlocal correlation functional emerges as the most accurate form for the present training and test sets, which span thermochemical energy differences, reaction barriers, and intermolecular interactions involving lighter main group elements.
通过对各种局域、全局杂化和范围分离杂化泛函进行参数化，探索了半经验广义梯度近似（GGA）密度泛函的精度极限。所采用的训练方法在两个主要方面与传统方法不同：（1）不是统一截断交换、同自旋相关和异自旋相关泛函的非均匀性校正因子，而是考虑了高达四阶的所有可能拟合；（2）不是仅根据训练集性能选择最优泛函，而是在独立测试集上验证拟合，并根据它们在训练集和测试集上的整体性能进行排名。对三种不同的交换处理方法分别在有无色散校正（DFT-D2和VV10）的情况下进行训练，共得到491508个候选泛函。对于所考虑的9种泛函类别中的每一种，结果都说明了在提高训练集性能和降低可转移性之间的权衡。由于所有491508个泛函都经过统一训练和测试，这种方法使得每种类型泛函的相对优势能够得到一致的比较和对比。与VV10非局域相关泛函配对的范围分离杂化GGA泛函，在涵盖热化学能差、反应势垒以及涉及较轻主族元素的分子间相互作用的当前训练集和测试集中，成为最精确的形式。
