Local hybrid functionals with position-dependent exact-exchange admixture have been implemented in the noncollinear spin form into a two-component X2C code and are evaluated for the hyperfine coupling tensors of a series of 3d, 4d, and 5d transition-metal complexes. One aim is to see if the potential of local hybrid functionals toward an improved balance between core-shell and valence-shell spin polarization, recently identified in nonrelativistic computations on 3d complexes (Schattenberg, C.; Maier, T. M.; Kaupp, M. J. Chem. Theory Comput. 2018, 14, 5653-5672), can be extended to the hyperfine couplings of heavier metal centers. The correctness of the two-component implementation is first established by comparison to previous computations for 3d systems with or without notable spin-orbit contributions to their hyperfine tensors, and the good performance of a standard "t-LMF" local mixing function is confirmed. However, when moving to 4d and 5d metal centers, the performance of such local mixing functions deteriorates. This is likely due to their violation of the homogeneous coordinate scaling condition in the high-density limit, which is particularly important for the core shells of heavier atoms. A local mixing function that respects this high-density limit performs notably better for heavier metal centers. However, it brings in much too high exact-exchange admixtures for the 3d systems and is too inflexible to simultaneously provide reasonable chemical accuracy in other areas. These results point to the ongoing need to develop improved local mixing functions and local hybrid functionals that exhibit favorable properties in different areas of space defined by very high and much lower electron densities.

中文翻译：

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使用局部混合泛函的超精细耦合的非共线相对论两成分X2C计算。高密度坐标缩放限制的重要性。

具有位置依赖的精确交换混合物的局部混合功能已以非共线自旋形式实现为两组分X2C代码，并针对一系列3d，4d和5d过渡金属配合物的超精细耦合张量进行了评估。一个目标是观察局部混合功能是否有潜力改善核-壳和价-壳自旋极化之间的平衡，最近在3d络合物的非相对论计算中确定了这种作用（Schattenberg，C .; Maier，TM; Kaupp，MJ Chem。 Theory Comput。2018，14，5653-5672），可以扩展到较重金属中心的超精细耦合。首先，通过与之前对3d系统的计算进行比较来确定两部分实现的正确性，而对于3d系统，其超精细张量具有或不具有明显的自旋轨道贡献，并确认了标准“ t-LMF”局部混合功能的良好性能。但是，当移动到4d和5d金属中心时，这种局部混合功能的性能会下降。这可能是因为它们违反了高密度极限中的均匀坐标缩放条件，这对于重原子的核壳特别重要。遵守此高密度限制的局部混合函数对于较重的金属中心的性能要好得多。但是，它为3d系统带来了太多的精确交换掺合料，并且过于僵化而无法在其他领域同时提供合理的化学准确性。