发表机构
Texas A&M University; Texas A&M University at Qatar; Ankara University; Hamad Bin Khalifa University（得克萨斯农工大学; 得克萨斯农工大学卡塔尔分校; 安卡拉大学; 哈马德·本·哈利法大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究机器学习交换关联改进向密度泛函紧束缚的继承性，发现反转移现象，明确不同体系的继承规律，提出转移比可用于参数化前的低成本预测试。
AI 中文摘要
机器学习得到的交换关联泛函可在近半局域计算成本下修正带隙，而密度泛函紧束缚（DFTB）方法可处理10^3至10^6个原子的体系；将二者结合的前提是，更优的母泛函能得到更优的参数化，但本文表明这一假设不成立。当前代泛函是轨道依赖的广义Kohn-Sham算子，而参数化通道基于乘性势，无法实现精确表示。利用转移比（母能级变化的留存分数），本文发现了反转移：四种共价半导体的转移比均为负值，使带隙向错误方向移动，这与分子代理模型和r²SCAN对照结果一致。最小基组的过带隙主要由 onsite 约定而非基组不完备性导致；修正 onsite 块可消除大部分过带隙，而添加一个d极化壳层可进一步缩小16%至40%，具体数值取决于空d能级的位置，该位置无法由自由原子本征值唯一确定。占据流形增强项、离子与闭壳层排斥势以及岩盐氧化物的带隙可继承，而元素和III-V共价网络既不继承带隙也不继承排斥势，氧化物网络仅继承排斥势。本文筛选了23种元素并发布了参数集，表明转移比可在任何参数化工作开展前作为低成本预测试。
英文摘要
Machine-learned exchange-correlation functionals correct band gaps at near-semilocal cost, while density-functional tight binding reaches the $10^3$-$10^6$-atom regime; combining them assumes that a better parent yields a better parameterization, but we show it does not. Current-generation functionals are orbital-dependent generalized Kohn-Sham operators, whereas the parameterization channel is built on a multiplicative potential, preventing exact representation. Using the transfer ratio, the surviving fraction of a parent-level change, we find anti-transfer: coherently negative ratios across four covalent semiconductors move the gap in the wrong direction, consistent with a molecular proxy and an r$^2$SCAN control. The minimal-basis overgap is dominated by the on-site convention rather than basis incompleteness; correcting the on-site block removes most of it, while one $d$-polarization shell closes a further $16$-$40%$, depending on the placement of the empty $d$ level, which no free-atom eigenvalue uniquely fixes. Occupied-manifold enhancements, ionic and closed-shell repulsive potentials, and rocksalt-oxide gaps inherit, whereas elemental and III-V covalent networks inherit neither gaps nor repulsive potentials and oxide networks inherit only the latter. We screen 23 elements and release the parameter sets, showing that the transfer ratio provides a cheap pre-test before any parameterization campaign.
