We propose a scheme to construct predictive models for Hamiltonian matrices in atomic orbital representation from ab initio data as a function of atomic and bond environments. The scheme goes beyond conventional tight binding descriptions as it represents the ab initio model to full order, rather than in two-centre or three-centre approximations. We achieve this by introducing an extension to the atomic cluster expansion (ACE) descriptor that represents Hamiltonian matrix blocks that transform equivariantly with respect to the full rotation group. The approach produces analytical linear models for the Hamiltonian and overlap matrices. Through an application to aluminium, we demonstrate that it is possible to train models from a handful of structures computed with density functional theory, and apply them to produce accurate predictions for the electronic structure. The model generalises well and is able to predict defects accurately from only bulk training data.

我们提出了一种方案，用于从作为原子和键环境的函数的从头数据中的原子轨道表示中构建哈密顿矩阵的预测模型。该方案超越了传统的紧密绑定描述，因为它代表了从头算模型到完整的顺序，而不是两中心或三中心的近似值。我们通过引入原子簇扩展（ACE）描述符的扩展来实现这一点，该描述符表示哈密顿矩阵块，该矩阵块相对于整个旋转组进行等变变换。该方法为哈密顿矩阵和重叠矩阵生成分析线性模型。通过对铝的应用，我们证明可以从用密度泛函理论计算的少数结构中训练模型，并应用它们对电子结构产生准确的预测。该模型具有很好的泛化能力，并且能够仅从大量训练数据中准确预测缺陷。