[论文解读] Data-driven Approach to Parameterize SCAN+U for an Accurate Description of 3d Transition Metal Oxide Thermochemistry

Nongnuch Artrith, José Antonio Garrido Torres+2 more|arXiv (Cornell University)|Feb 1, 2021

Machine Learning in Materials Science参考文献 43被引用 5

一句话总结

本文提出一种数据驱动的统一优化框架，用于参数化SCAN+U泛函，以实现对3d过渡金属氧化物的精确热化学计算。通过整合1,710个衍生反应的生成能和反应能，该方法在留一法交叉验证下将生成能误差分别降低40%（二元体系）和75%（三元体系），分别达到0.10和0.03 eV/atom的精度。

ABSTRACT

Semi-local DFT methods exhibit significant errors for the phase diagrams of transition-metal oxides that are caused by an incorrect description of molecular oxygen and the large self-interaction error in materials with strongly localized electronic orbitals. Empirical and semiempirical corrections based on the DFT+U method can reduce these errors, but the parameterization and validation of the correction terms remains an on-going challenge. We develop a systematic methodology to determine the parameters and to statistically assess the results by considering thermochemical data across a set of transition metal compounds. We consider three interconnected levels of correction terms: (1) a constant oxygen binding correction, (2) Hubbard-U correction, and (3) DFT/DFT+U compatibility correction. The parameterization is expressed as a unified optimization problem. We demonstrate this approach for 3d transition metal oxides, considering a target set of binary and ternary oxides. With a total of 37 measured formation enthalpies taken from the literature, the dataset is augmented by the reaction energies of 1,710 unique reactions that were derived from the formation energies by systematic enumeration. To ensure a balanced dataset across the available data, the reactions were grouped by their similarity using clustering and suitably weighted. The parameterization is validated using leave-one-out cross-validation (CV), a standard technique for the validation of statistical models. We apply the methodology to the SCAN density functional. Based on the CV score, the error of binary (ternary) oxide formation energies is reduced by 40% (75%) to 0.10 (0.03) eV/atom. The method and tools demonstrated here can be applied to other classes of materials or to parameterize the corrections to optimize DFT+U performance for other target physical properties.

研究动机与目标

• 为解决DFT在3d过渡金属氧化物中因d电子强烈局域化而产生的大自相互作用误差。
• 通过统一的优化框架系统性地参数化DFT+U校正。
• 提高对二元和三元氧化物生成焓预测的准确性。
• 通过聚类和加权反应选择确保数据集的平衡表示。
• 通过严格的留一法交叉验证验证参数化结果。

提出的方法

• 该方法将DFT+U参数化表述为一个统一的优化问题，结合三项校正项：氧结合能、Hubbard-U参数以及DFT与DFT+U之间的兼容性。
• 使用包含37个实验测得的生成焓的数据集，并通过系统枚举氧化物化合物生成1,710个独特的反应能。
• 利用聚类方法根据结构相似性对反应进行分组，以确保数据集中各类相的平衡表示。
• 根据聚类规模为每个反应分配权重，以防止对过度代表相的偏差。
• 采用最小二乘拟合程序优化参数，以最小化与实验生成焓的偏差。
• 通过留一法交叉验证进行验证，以评估预测精度和泛化能力。

实验结果

研究问题

• RQ1 统一的、数据驱动的方法能否提升DFT+U在3d过渡金属氧化物中的准确性？
• RQ2 联合校正（氧结合能、U参数、兼容性）如何影响热化学预测误差？
• RQ3 为实现最小生成能误差，各项校正项之间应如何达到最优平衡？
• RQ4 聚类与加权采样能否提升模型在多样化氧化物相中的鲁棒性？
• RQ5 交叉验证在多大程度上验证了参数化SCAN+U泛函的预测能力？

主要发现

• 该方法将二元氧化物生成能的平均绝对误差降低40%，达到0.10 eV/atom的精度。
• 对于三元氧化物，误差降低75%，达到0.03 eV/atom，显著提升了准确性。
• 留一法交叉验证证实了模型的鲁棒性和泛化能力。
• 引入1,710个独特反应的反应能数据，增强了数据集的平衡性与预测能力。
• 统一的优化框架实现了可迁移的参数化，适用于其他材料或物理性质。