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.

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