Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations

The self-consistent evaluation of Hubbard parameters using linear-response theory is crucial for quantitatively predictive calculations based on Hubbard-corrected density-functional theory. Here, we extend a recently-introduced approach based on density-functional perturbation theory (DFPT) for the calculation of the on-site Hubbard U to also compute the inter-site Hubbard V. DFPT allows to reduce significantly computational costs, improve numerical accuracy, and fully automate the calculation of the Hubbard parameters by recasting the linear response of a localized perturbation into an array of monochromatic perturbations that can be calculated in the primitive cell. In addition, here we generalize the entire formalism from norm-conserving to ultrasoft and projector-augmented wave formulations, and to metallic ground states. After benchmarking DFPT against the conventional real-space Hubbard linear response in a supercell, we demonstrate the effectiveness of the present extended Hubbard formulation in determining the equilibrium crystal structure of LiₓMnPO₄ (x=0,1) and the subtle energetics of Li intercalation.

基于哈伯德修正的密度泛函理论（Hubbard-corrected density-functional theory）开展定量预测性计算时，借助线性响应理论对哈伯德参数（Hubbard parameters）进行自洽评估至关重要。本文将近期提出的基于密度泛函微扰理论（density-functional perturbation theory, DFPT）的局域哈伯德U参数计算方法，拓展至可同时计算格点间哈伯德V参数。密度泛函微扰理论可显著降低计算成本、提升数值精度，并可通过将局域微扰的线性响应转化为可在原胞中计算的单色微扰阵列，实现哈伯德参数计算的全自动化。此外，本文将整套形式体系从守恒赝势（norm-conserving）框架推广至超软赝势（ultrasoft）与投影缀加波（projector-augmented wave, PAW）方法，并适配金属基态体系。在采用超胞内传统实空间哈伯德线性响应方法对DFPT进行基准测试后，本文验证了所提出的扩展哈伯德形式体系在确定LiₓMnPO₄（x=0,1）的平衡晶体结构，以及解析锂插层过程的精细能量学特征方面的有效性。