Response calculations in density functional theory aim at computing the change in ground-state density induced by an external perturbation. At finite temperature these are usually performed by computing variations of orbitals, which involve the iterative solution of potentially badly-conditioned linear systems, the Sternheimer equations. Since many sets of variations of orbitals yield the same variation of density matrix this involves a choice of gauge. Taking a numerical analysis point of view we present the various gauge choices proposed in the literature in a common framework and study their stability. Beyond existing methods we propose a new approach, based on a Schur complement using extra orbitals from the self-consistent-field calculations, to improve the stability and efficiency of the iterative solution of Sternheimer equations. We show the success of this strategy on nontrivial examples of practical interest, such as Heusler transition metal alloy compounds, where savings of around 40% in the number of required cost-determining Hamiltonian applications have been achieved.
翻译:密度功能理论的反应计算旨在计算由外部扰动引起的地面状态密度变化。在有限的温度下,这些变化通常通过轨道变化的计算来进行,其中涉及可能条件恶劣的线性系统的迭代解决方案, Sternheimer 方程式。由于轨道变化的许多组产生密度矩阵的相同变量,因此需要选择量度。从数字分析角度出发,我们在一个共同框架内提出文献中所提议的各种测量选择,并研究其稳定性。除了现有的方法外,我们提议采用新的方法,利用自一致的实地计算产生的额外轨道补充Schur,以提高Sternheimer方程式迭代解决方案的稳定性和效率。我们展示了这一战略在实际感兴趣的非三轨实例上的成功,例如Heusler金属转换合金化合物,在其中节省了大约40%的成本确定汉密尔顿式应用量。