This paper presents a novel Riemannian conjugate gradient method for the Kohn-Sham energy minimization problem in density functional theory (DFT), with a focus on non-metallic crystal systems. We introduce an energy-adaptive metric that preconditions the Kohn-Sham model, significantly enhancing optimization efficiency. Additionally, a carefully designed shift strategy and several algorithmic improvements make the implementation comparable in performance to highly optimized self-consistent field iterations. The energy-adaptive Riemannian conjugate gradient method has a sound mathematical foundation, including stability and convergence, offering a reliable and efficient alternative for DFT-based electronic structure calculations in computational chemistry.

翻译：本文针对密度泛函理论（DFT）中的Kohn-Sham能量最小化问题，提出了一种新颖的黎曼共轭梯度方法，重点研究非金属晶体体系。我们引入了一种能量自适应度量，对Kohn-Sham模型进行预处理，显著提升了优化效率。此外，通过精心设计的位移策略及多项算法改进，该方法的实现性能可与高度优化的自洽场迭代相媲美。能量自适应黎曼共轭梯度法具有坚实的数学基础，包括稳定性与收敛性分析，为计算化学中基于DFT的电子结构计算提供了一种可靠且高效的替代方案。