Schattenberg Caspar Jonas, Lehmann Morten, Bühl Michael, Kaupp Martin
Institut für Chemie, Theoretische Chemie/Quantenchemie Sekretariat C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623, Berlin, Germany.
School of Chemistry, University of St. Andrews, Purdie Building, North Haugh, St Andrews KY16 9ST, Fife, U.K.
J Chem Theory Comput. 2022 Jan 11;18(1):273-292. doi: 10.1021/acs.jctc.1c00964. Epub 2021 Dec 30.
A wide range of density functionals from all rungs of Jacob's ladder have been evaluated systematically for a set of experimental 3d transition-metal NMR shifts of 70 complexes encompassing 12 × Ti, 10 × V, 10 × Cr, 11 × Mn, 9 × Fe, 9 × Co, and 9 × Ni shift values, as well as a diverse range of electronic structure characteristics. The overall 39 functionals evaluated include one LDA, eight GGAs, seven meta-GGAs (including their current-density-functional─CDFT─versions), nine global hybrids, four range-separated hybrids, eight local hybrids, and two double hybrids, and we also include Hartree-Fock and MP2 calculations. While recent evaluations of the same functionals for a very large coupled-cluster-based benchmark of main-group shieldings and shifts achieved in some cases aggregate percentage mean absolute errors clearly below 2%, the best results for the present 3d-nuclei set are in the range between 4 and 5%. Strikingly, the overall best-performing functionals are the recently implemented CDFT versions of two meta-GGAs, namely cM06-L (4.0%) and cVSXC (4.3%), followed by cLH14t-calPBE (4.9%), B3LYP (5.0%), and cLH07t-SVWN (5.1%), i.e., the previously best-performing global hybrid and two local hybrids. A number of further functionals achieve aggregate deviations in the range 5-6%. Range-separated hybrids offer no particular advantage over global hybrids. Due to the overall poor performance of Hartree-Fock theory for all systems except the titanium complexes, MP2 and double-hybrid functionals are unsuitable for these 3d-nucleus shifts and provide large errors. Global hybrid functionals with larger EXX admixtures, such as BHLYP or M06-2X, also perform poorly, and some other highly parametrized global hybrids also are unsuitable. For many functionals depending on local kinetic energy τ, their CDFT variants perform much better than their "non-CDFT" versions. This holds notably also for the above-mentioned M06-L and VSXC, while the effect is small for τ-dependent local hybrids and can even be somewhat detrimental to the agreement with experiment for a few other cases. The separation between well-performing and more poorly performing functionals is mainly determined by their results for the most critical nuclei Mn, Fe, and Co. Here either moderate exact-exchange admixtures or CDFT versions of meta-GGAs are beneficial for the accuracy. The overall deviations of the better-performing global or local hybrids are then typically dominated by the Cr shifts, where triplet instabilities appear to disfavor exact-exchange admixture. Further detailed analyses help to pinpoint specific nuclei and specific types of complexes that are challenges for a given functional.
针对一组包含70种配合物的实验性3d过渡金属核磁共振位移数据，系统评估了雅各布天梯各层级的多种密度泛函。这些配合物涵盖12种钛、10种钒、10种铬、11种锰、9种铁、9种钴和9种镍的位移值，以及各种电子结构特征。总共评估了39种泛函，包括1种局域密度近似（LDA）、8种广义梯度近似（GGA）、7种meta-GGA（包括其电流密度泛函——CDFT——版本）、9种全局杂化泛函、4种范围分离杂化泛函、8种局域杂化泛函和2种双杂化泛函，同时还包括哈特里 - 福克（Hartree - Fock）和二阶微扰理论（MP2）计算。虽然最近针对基于耦合簇的主族屏蔽和位移的非常大的基准对相同泛函进行的评估在某些情况下总百分比平均绝对误差明显低于2%，但对于当前的3d原子核数据集，最佳结果在4%至5%之间。引人注目的是，总体表现最佳的泛函是两种meta-GGA最近实现的CDFT版本，即cM06-L（4.0%）和cVSXC（4.3%），其次是cLH14t-calPBE（4.9%）、B3LYP（5.0%）和cLH07t-SVWN（5.1%），即之前表现最佳的全局杂化泛函和两种局域杂化泛函。还有一些其他泛函的总偏差在5% - 6%范围内。范围分离杂化泛函相对于全局杂化泛函没有特别优势。由于除钛配合物外，哈特里 - 福克理论对所有体系的总体表现较差，MP2和双杂化泛函不适用于这些3d原子核位移，会产生较大误差。具有较大精确交换混合比例的全局杂化泛函，如BHLYP或M06 - 2X，表现也很差，其他一些高度参数化的全局杂化泛函也不合适。对于许多依赖局部动能τ的泛函，其CDFT变体的表现远优于其“非CDFT”版本。上述的M06-L和VSXC尤其如此，而对于依赖τ的局域杂化泛函，这种影响较小，甚至在其他一些情况下可能对与实验结果的一致性略有不利。表现良好和表现较差的泛函之间的差异主要由它们对最关键的原子核锰、铁和钴的计算结果决定。在这里，适度的精确交换混合或meta-GGA的CDFT版本对提高准确性有益。表现较好的全局或局域杂化泛函的总体偏差通常由铬的位移主导，在铬的位移中，三重态不稳定性似乎不利于精确交换混合。进一步的详细分析有助于确定特定的原子核和特定类型的配合物，这些对给定的泛函来说是挑战。
