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：密度泛函理论中的响应计算旨在计算由外部微扰引起的基态密度变化。在有限温度下，这些计算通常通过计算轨道的变分来实现，这涉及迭代求解可能病态的线性系统——斯特恩海默方程。由于许多不同的轨道变分集合会产生相同的密度矩阵变分，因此需要选择一种规范。我们从数值分析的角度出发，将文献中提出的各种规范选择置于统一框架下研究其稳定性。在现有方法的基础上，我们提出了一种新方法——基于利用自洽场计算中的额外轨道进行舒尔补计算——以提高斯特恩海默方程迭代求解的稳定性与效率。我们在具有实际意义的非平凡算例（如赫斯勒过渡金属合金化合物）中展示了该策略的成功，其中所需成本主导型哈密顿量应用数量节省了约40%。