数据驱动的SCAN +U参数化方法精确描述过渡金属氧化物三维热化学
Data-driven Approach to Parameterize SCAN+U for an Accurate Description of 3d Transition Metal Oxide Thermochemistry
摘要：
半局域DFT方法对过渡金属氧化物的相图存在明显的误差，这是由于对分子氧的描述不正确以及在具有强局域电子轨道的材料中存在较大的自相互作用误差造成的。基于DFT+U方法的经验和半经验修正可以减少这些误差，但修正项的参数化和验证仍然是一个持续的挑战。我们开发了一个系统的方法来确定的参数，并通过考虑跨一组过渡金属化合物的热化学数据的结果进行统计评估。我们考虑了三个相互关联的校正项：（1）恒定氧结合校正，（2）Hubbard-U校正，（3）DFT/DFT+U相容性校正。参数化表示为一个统一的优化问题。我们证明了这种方法的三维过渡金属氧化物，考虑一组目标的二元和三元氧化物。从文献中总共获得了37个测量的生成能量，通过系统枚举从生成能量导出的1，710个独特反应的反应能来增强数据集。为了确保可用数据的平衡数据集，使用聚类并适当加权，根据其相似性对反应进行分组。使用留一交叉验证（CV），一个标准的统计模型验证技术的参数化进行验证。我们将该方法应用于SCAN密度泛函。基于CV分数，二元（三元）氧化物形成能的误差减少了40%（75%）至0.10（0.03）eV/atom。这里展示的方法和工具可以应用于其他类型的材料或参数化校正，以优化DFT+U性能的其他目标物理特性。
英文摘要：
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.
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