AI 中文总结
该研究针对周期固体的RDMFT计算难题，构建基组无关的RDMFT并提出平面波迭代极小化实现方案，经多体系基准测试及应用验证，其算法可靠稳健，SPG方法性能优于EBI。
AI 中文摘要
约化密度矩阵泛函理论（RDMFT）为强关联体系提供了超越Kohn-Sham密度泛函理论的途径，但周期固体的实际计算仍难以实现。我们以与基组无关的方式构建了扩展体系的RDMFT，并提出了一种采用迭代极小化的周期体系平面波实现方案，通过现有自适应压缩交换机制评估非局域交换关联泛函。在N可表示性约束下，自然占据数通过谱投影梯度（SPG）方法或一阶隐式显式（EBI）映射进行优化，而自然轨道则通过复Stiefel流形上的黎曼优化进行更新。对H₂、硅、钠等典型体系以Hartree-Fock泛函进行基准测试，结果显示SPG可复现收敛的杂化参考值，而EBI在占据数接近0或1时会停滞。采用幂函数和Müller函数时，SPG相比EBI能得到更低的能量和更稳定的收敛性。对分数电荷LiH、解离的H₂和N₂分子以及硅的状态方程的应用表明，该实现方案所提出的算法可靠且稳健。
英文摘要
Reduced density matrix functional theory (RDMFT) offers a route beyond Kohn-Sham density functional theory for strongly correlated systems, yet practical calculations for periodic solids are still out of reach. We formulate RDMFT for extended systems in a basis-independent way and present a planewave implementation using iterative minimization for periodic solids, evaluating nonlocal exchange-correlation functionals through the existing adaptive compressed exchange machinery. Natural occupations are optimized under N-representability constraints with a spectral projected gradient (SPG) method or an first-order explicit-by-implicit (EBI) map, while natural orbitals are updated by Riemannian optimization on the complex Stiefel manifolds. Benchmarks on typical systems of \ce{H2}, silicon, and sodium with the Hartree-Fock functional show that SPG reproduces converged hybrid references, whereas EBI can stall when occupations approach $0$ or $1$. With the power and Müller functionals, SPG yields lower energies and more stable convergence than EBI. Applications to fractionally charged \ce{LiH}, dissociating \ce{H2} and \ce{N2} molecules, and equation of state of silicon show that the algorithm presented in this implementation is reliable and robust.
Comments17 pages, 6 figures
