AI 中文总结
本文提出一种结合并行化、密度拟合近似及混合导数方案的可扩展框架，通过有限磁场微分实现高效精确的DFT水平NMR屏蔽计算，为后续高级量子化学方法扩展奠定基础。
AI 中文摘要
绝对核磁共振屏蔽常数和相对化学位移是二阶导数响应性质，是解释核磁共振（NMR）谱的基础，可为各类化学体系的结构和电子环境提供关键见解。然而，它们的准确计算常受限于需特定方法的解析响应实现，对于非变分相关波函数方法（通常无法获取解析二阶导数）而言，这一挑战尤为突出。本文提出一种可扩展框架，通过对基于复数值含规范不变原子轨道（GIAO）的自洽场（SCF）计算进行有限磁场微分来计算NMR屏蔽张量。结合混合MPI与OpenMP并行化、基于密度拟合（RI）近似的库仑（J）和交换（K）实现，以及混合数值/解析导数计算方案，针对不同规模的实际化学体系，相较于现有最先进的解析实现，该框架在杂化密度泛函理论（DFT）NMR屏蔽计算中实现了优异的效率。通过严格误差分析推导的最优步长进行前向微分，可保持远小于实验不确定度或固有DFT误差的良好数值误差。结果表明，经密度拟合加速的有限磁场计算可非常精确地获取DFT级别的NMR屏蔽常数，为未来扩展至更高级量子化学方法提供了可扩展的基础。
英文摘要
Absolute nuclear magnetic shielding constants and relative chemical shifts are second-derivative response properties that underpin the interpretation of Nuclear Magnetic Resonance (NMR) spectra and provide critical insights into the structural and electronic environments of diverse chemical systems. However, their accurate computation is often constrained by the need for method-specific, analytical response implementation, and therefore is particularly challenging for non-variational, correlated wavefunction methods where analytical second derivatives are frequently unavailable. Here we present a scalable framework that computes NMR shielding tensors through finite magnetic field differentiation of complex-valued, gauge-including atomic-orbital (GIAO) based self-consistent field (SCF) calculations. By combining hybrid MPI and OpenMP parallelization and resolution-of-identity (RI) approximation-based Coulomb (J) and Exchange (K) implementation and mixed numerical/analytical derivatives computational scheme, we achieve very good efficiency for hybrid density functional theory (DFT) NMR shielding, relative to existing state-of-the-art analytic implementations across realistic chemical systems of various sizes. Forward differentiation with optimal step sizes derived from rigorous error analysis retains favorable numerical errors much smaller than experimental uncertainty or intrinsic DFT errors. The results demonstrate that RI-accelerated finite magnetic field calculations can obtain DFT-level NMR shielding constants very precisely, providing a scalable foundation for extensions to more advanced quantum chemistry methods in future work.
