约束密度泛函理论的阻尼子空间分裂算法
A Damped Subspace Splitting Algorithm for Constrained Density Functional Theory
AI总结：
针对CDFT离散优化问题的挑战，本文提出首个带严格收敛保证的单循环算法DASSP，其含三步迭代，数值实验显示该算法精度与效率俱佳，将推动大规模CDFT应用发展。
AI中文摘要：
约束密度泛函理论（CDFT）为描述电子激发态和电荷定域态提供了强大的框架，这些态是广泛物理和化学现象的基础。然而，CDFT计算产生的离散优化问题仍然具有挑战性，因为其同时存在斯蒂费尔（Stiefel）流形约束和额外的非凸二次约束。现有算法要么无法高精度地满足二次约束，要么由于双循环迭代结构面临收敛问题。本文中，我们首先利用固有的旋转不变性并引入非线性子空间对齐约束，推导了一种将两组约束解耦的子空间分裂重述。基于该重述，我们提出了一种名为DASSP的单循环交替方向乘子法（ADMM）。据我们所知，DASSP是首个用于CDFT计算且具有严格收敛保证的算法。DASSP的每次迭代包含谱极小化步、投影梯度步和阻尼对偶上升步，所有步骤均可高效实现。在合成和实际CDFT问题上的数值结果表明，DASSP能达到高可行性精度，且在不牺牲鲁棒性的情况下展现出良好的效率。我们期望这项工作将为可靠高效的大规模CDFT应用铺平道路。
英文摘要：
Constrained density functional theory (CDFT) provides a powerful framework for describing electronically excited and charge-localized states, which underlie a broad range of physical and chemical phenomena. However, the discretized optimization problems arising from CDFT calculations remain challenging, owing to the presence of both the Stiefel manifold constraint and additional nonconvex quadratic constraints. Existing algorithms either fail to enforce the quadratic constraints with high accuracy or face convergence issues due to double-loop iterative structures. In this paper, we first derive a subspace-splitting reformulation that decouples the two groups of constraints, by exploiting the inherent rotation invariance and introducing a nonlinear subspace alignment constraint. Based on this reformulation, we propose a single-loop damped alternating direction method of multipliers, called DASSP. To the best of our knowledge, DASSP is the first algorithm for CDFT calculations with rigorous convergence guarantees. Each iteration of DASSP comprises a spectral minimization step, a projected gradient step, and a damped dual ascent step, all of which admit efficient implementations. Numerical results on synthetic and realistic CDFT problems demonstrate that DASSP attains high feasibility accuracy and exhibits favorable efficiency without compromising robustness. We expect that this work will pave the way toward reliable and efficient large-scale CDFT applications.
