AI 中文总结
本文评估了多种KS-DFT泛函对第二至第四周期原子自旋密度矩的预测，发现与CCSD相比存在显著偏差，其中QTP00泛函在全局自旋密度和超精细耦合常数上表现最佳。
AI 中文摘要
量化开壳层分子的磁性是化学中的一项常见任务，并且越来越多地通过使用Kohn-Sham密度泛函理论（KS-DFT）进行计算机模拟来完成。先前的工作表明，少数泛函对于一种此类性质——超精细耦合常数（HFCCs）——的预测准确性是可能的，这意味着这些近似必须在原子核处产生准确的自旋密度。然而，这些泛函能否全局预测出与严格从头算耦合簇理论（如CCSD）质量相当的自旋密度，这一点是可疑的，尽管自旋密度是KS-DFT的基本量。本工作旨在通过评估第二、第三和第四周期原子的自旋密度矩，$\langle r^n \rangle = \int ρ(r)r^n dτ$，$n=-2,\cdots,2,3$，来探讨这一问题，以将各种KS-DFT泛函与CCSD进行比较。我们的结果大致表明，所测试的泛函在距原子核1 Bohr以内的区域中，相对于CCSD自旋密度存在显著偏差，且大多数误差发生在原子核的紧邻区域。我们发现某些泛函对单个$α$/$β$自旋密度存在极端误差的证据，尽管在形成相应的全局自旋密度后，其中几个最终受益于显著的误差抵消。然而，在所有误差指标上，CAM-B3LYP与基于相关轨道理论条件的量子理论项目（QTP）族DFT泛函之间的比较表明，QTP00更准确地再现了全局自旋密度以及HFCCs，通常提供与CCSD更一致的结果。与先前的工作一致，我们还证实了PBE0和TPSS族泛函在HFCCs上的成功，进一步发现这两种近似通常产生的自旋密度属于最佳之列。
英文摘要
Quantifying the magnetic properties of open-shell molecules is a common task in chemistry and is increasingly performed in silico using Kohn-Sham density functional theory (KS-DFT). Previous work demonstrates that the predictive accuracy of a few functionals for one such property - hyperfine coupling constants (HFCCs) - is possible, implying that such approximations must yield accurate spin-densities at the nucleus. However, the ability of such functionals to globally predict accurate spin-densities of comparable quality to rigorous ab initio coupled cluster theory, for example, is dubious, despite this being a fundamental quantity for KS-DFT. This work intends to explore the matter by evaluating moments of the spin-density, $\langle r^n \rangle = \int ρ(r)r^n dτ$, $n=-2,\cdots,2,3$, for second-, third-, and fourth-row atoms to compare various KS-DFT functionals against CCSD. Our results broadly indicate that the tested functionals experience significant deviations with respect to CCSD spin-densities in regions up to 1 Bohr away from the nuclei, with most errors occurring in the immediate vicinity of the nucleus. We find evidence of extreme errors by some functionals for individual $α$/$β$ spin-densities, although several ultimately end up benefiting from significant error cancellation once the corresponding global spin-density is formed. Nevertheless, a comparison between CAM-B3LYP and the Quantum Theory Project (QTP)-family of DFT functionals based on Correlated Orbital Theory conditions across all error metrics demonstrates that QTP00 more accurately reproduces the global spin-density as well as HFCCs, generally offering results in better agreement with CCSD. In line with previous work, we also corroborate the success of PBE0 and the TPSS-family of functionals for HFCCs, further finding that both approximations generally yield spin-densities that are amongst the best.
