Skala机器学习交换相关泛函在CP2K中的原生实现：用于分子和凝聚相计算的统一单中心重构
Native implementation of the machine-learned Skala exchange-correlation functional in CP2K: Unified one-centre reconstruction for molecular and condensed-phase calculations
- Center for Advanced Systems Understanding (CASUS)（高级系统理解中心）
- Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）
- Department of Chemistry, University of Zurich（苏黎世大学化学系）
- Institute of Artificial Intelligence, Technische Universität Dresden（德累斯顿工业大学人工智能研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
在CP2K中原生实现Skala机器学习交换相关泛函，通过统一单中心重构保持精度，全电子计算对DMC-ICE13相晶格能MAE为1.16 kJ/mol，带隙MAE为0.43 eV，但LC10显示晶格常数低估。
AI中文摘要：
我们使用CP2K的高斯和平面波（GPW）以及高斯和增强平面波（GAPW）方法，原生实现了机器学习Skala交换相关（XC）泛函。在泛函评估之前，对密度、密度梯度和动能密度进行联合单中心重构，可在全电子和赝势计算中保留混合梯度项以及平滑部分与原子局域贡献之间的非局域耦合。一种XC专用的GAPW表示在原子中心网格上解析快速变化的局域贡献，降低了赝势计算对平面波的需求。该实现包括布里渊区采样和点群对称性约化。在轨道基组足够灵活的情况下，它保持了先前GauXC公式的分子基准精度。全电子Skala-D3(BJ)计算对晶体CO₂、NH₃和尿素（涵盖色散、四极静电和氢键）的扩散蒙特卡洛参考值，平均绝对误差（MAE）为1.54 kJ mol⁻¹。对于全部十三个DMC-ICE13相，绝对晶格能的MAE为1.16 kJ mol⁻¹，相对于冰Ih的十二个相对能量的MAE为0.82 kJ mol⁻¹。在固定实验几何下，全电子/混合芯计算在15种材料集上给出的带隙MAE为0.43 eV，显著低于常用的半局域泛函，与广泛使用的杂化泛函相当。然而，LC10基准揭示了系统性地低估平衡晶格常数，表明存在结构过度束缚。该框架将分子Skala与凝聚相电子结构联系起来，并利用周期性多体参考数据支持未来发展。
英文摘要：
We implement the machine-learned Skala exchange-correlation (XC) functional natively in CP2K using its Gaussian and plane-wave (GPW) and Gaussian and augmented-plane-wave (GAPW) methods. A joint one-centre reconstruction of density, density gradients, and kinetic-energy density before functional evaluation preserves mixed gradient terms and nonlocal couplings between smooth and atom-local contributions in all-electron and pseudopotential calculations. An XC-specific GAPW representation resolves rapidly varying local contributions on atom-centred grids, reducing plane-wave requirements for pseudopotential calculations. The implementation includes Brillouin-zone sampling and point-group symmetry reduction. With sufficiently flexible orbital bases, it retains the molecular benchmark accuracy of our earlier GauXC formulation. All-electron Skala-D3(BJ) calculations yield a mean absolute error (MAE) of 1.54 kJ mol$^{-1}$ against diffusion Monte Carlo for crystalline CO$_2$, NH$_3$, and urea, spanning dispersion, quadrupolar electrostatics, and hydrogen bonding. For all thirteen DMC-ICE13 phases, the MAEs are 1.16 kJ mol$^{-1}$ for absolute lattice energies and 0.82 kJ mol$^{-1}$ for the twelve relative energies to ice Ih. At fixed experimental geometries, all-electron/mixed-core calculations give a band-gap MAE of 0.43 eV on a 15-material set, substantially below commonly used semilocal functionals and comparable to widely used hybrid functionals. The LC10 benchmark nevertheless reveals systematically underestimated equilibrium lattice constants, indicating structural overbinding. This framework connects molecular Skala to condensed-phase electronic structure and enables future development using periodic many-body reference data.
