AI 中文总结
提出一种自适应几何精修工作流，根据梯度成本与拓扑可靠性选择笛卡尔或内坐标，结合稀疏秩测试与二次化映射，实现近线性扩展并减少困难极小值的迭代次数。
AI 中文摘要
我们提出了一种几何精修工作流，该工作流能适应能量-梯度评估的成本以及分子拓扑的可靠性。初始的笛卡尔计算和连续成键诊断决定了是从投影笛卡尔坐标开始，还是从化学自适应的内坐标开始。化学感知生成局部的冗余测量；稀疏秩和条件数测试将它们组合成非冗余的、对称自适应的坐标；一个通用的优化器使用选定的表示，配合常驻或外部计算器。对于廉价的梯度，投影笛卡尔路线限制了坐标开销；单个受监控的内坐标步长即可提供化学可解释性。当梯度昂贵且拓扑已认证时，对称自适应的内坐标减少了昂贵的能量-梯度调用。二次化映射改善了局部的非谐情况，而混合的笛卡尔/内坐标图表则覆盖了不确定或复杂的拓扑。局部稀疏算子和常驻的力场及紧束缚计算器将两条路线扩展到大型系统。相同的笛卡尔计算器契约支持多能级能量和梯度组合。所测量的坐标流水线和循环的常驻紧束缚更新在测试的尺寸范围内显示出近线性缩放；这一陈述适用于那些合格的组件，而非任意的电子结构计算或冷启动。对于已认证的、可直接分离的内坐标图表，优化器可以使用化学设计的莫尔斯或高斯映射来二次化局部步长问题。二次化分支使用简短的几何局部历史，而离域图表保持不变。这减少了困难极小值处的迭代次数，而不改变电子势或坐标图表。
英文摘要
We present a geometry-refinement workflow that adapts to the cost of an energy--gradient evaluation and the reliability of molecular topology. An initial Cartesian calculation and continuous bonding diagnostics determine whether to begin in projected Cartesian coordinates or in chemically adapted internal coordinates. Chemical perception generates local redundant measurements; sparse rank and conditioning tests combine them into nonredundant, symmetry-adapted coordinates; and a common optimizer uses the selected representation with resident or external calculators. For inexpensive gradients, the projected Cartesian route limits coordinate overhead; a single monitored internal-coordinate step can then provide chemical interpretability. When gradients are costly and topology is certified, symmetry-adapted internal coordinates reduce expensive energy--gradient calls. A quadraticized map improves localized anharmonic cases, while mixed Cartesian/internal charts cover uncertain or complex topologies. Local sparse operators and resident force-field and tight-binding calculators extend both routes to large systems. The same Cartesian calculator contract supports multilevel energy and gradient composition. The measured coordinate pipeline and recurrent resident tight-binding update show near-linear scaling over the tested size ranges; this statement applies to those qualified components, not to arbitrary electronic-structure calculations or cold starts. For certified, directly separable internal charts, the optimizer can use chemically designed Morse or Gaussian maps to quadraticize the local step problem. The quadraticized branch uses a short geometry-local history, while delocalized charts remain unchanged. This reduces iterations in difficult minima without changing the electronic potential or coordinate chart.
