耦合簇方程的鲁棒高效求解器
A robust and efficient solver for coupled cluster equations
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中文总结 AI 辅助
该研究针对耦合簇方程求解问题，将预处理牛顿-克雷洛夫方法推广到任意规范，得到鲁棒高效的求解框架，其性能优于基于不动点迭代的方法，有望成为求解耦合簇方程的新标准。
中文摘要 AI 辅助
耦合簇（CC）方程最常通过不动点（FP）迭代求解，但在局域关联CC等非规范规范下，FP迭代可能收敛缓慢甚至发散。水平移位、直接迭代子空间反演（DIIS）等实用修复措施常可改善收敛性，但本质上仍属于启发式方法且依赖规范。Yang等人证明预处理牛顿-克雷洛夫（PNK）方法可为规范CC提供显著的壁钟时间优势。本工作通过将能量分母替换为规范不变公式，将预条件子推广到任意规范，结合基于克雷洛夫的近似雅可比反演，所得框架无需水平移位，可在各种规范和具有挑战性的化学体系中实现鲁棒高效的收敛。数值结果表明，在一系列分子体系中，PNK始终优于精心优化的基于FP的方法，使所提出的PNK方法成为求解CC方程的有前景的新标准。
英文摘要
The coupled-cluster (CC) equations are most frequently solved via fixed-point (FP) iterations. However, when formulated in a non-canonical gauge, as in local correlation CC, the FP iteration may converge slowly or even diverge. Practical fixes, such as level-shifting and a direct inversion of iterative subspace (DIIS), often improve the convergence, but remain fundamentally heuristic and gauge dependent. {\it Yang et al.}~demonstrated that preconditioned Newton--Krylov (PNK) methods provide substantial wall-time advantage for canonical CC. In this work, we generalize the preconditioner to arbitrary gauges by replacing the energy denominator with a gauge-invariant formulation. Combined with Krylov-based approximate Jacobian inversion, the resulting framework removes the need for level-shifting and yields robust and efficient convergence across various gauges and challenging chemical systems. Our numerical results indicate that PNK consistently outperforms carefully optimized FP-based approaches across a range of molecular systems, positioning the proposed PNK method as a promising new standard for solving the CC equations.
