密度泛函理论中响应性质计算的数值稳定性与效率
Numerical stability and efficiency of response property calculations in density functional theory
AI总结：
本文从数值分析角度统一研究了密度泛函理论响应计算中Sternheimer方程求解的规范选择，并提出基于Schur补的新方法，利用额外轨道显著提升了迭代求解的稳定性与效率，在Heusler合金实例中节省约40%的Hamiltonian应用次数。
摘要：
密度泛函理论中的响应计算旨在计算由外部扰动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变分来执行，这涉及对可能病态的线性系统（即Sternheimer方程）的迭代求解。由于许多组轨道变分产生相同的密度矩阵变分，这涉及规范选择。从数值分析的角度出发，我们在一个统一框架中呈现文献中提出的各种规范选择，并研究其稳定性。超越现有方法，我们提出一种新方法，基于使用来自自洽场计算的额外轨道的Schur补，以提高Sternheimer方程迭代求解的稳定性和效率。我们在实际应用中的非平凡实例上展示了该策略的成功，例如Heusler过渡金属合金化合物，其中决定成本的Hamiltonian应用次数节省了约40%。
英文摘要：
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.
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