Ligand Additivity and Divergent Trends in Two Types of Delocalization Errors from Approximate Density Functional Theory

The predictive accuracy of density functional theory (DFT) is hampered by delocalization errors, especially for correlated systems such as transition-metal complexes. Two complementary strategies have been developed to reduce delocalization error: eliminating the global curvature with change in charge, and applying a linear response Hubbard U as a measure of local curvature at a metal center at fixed charge in a DFT+U framework. We investigate the relationship between the two delocalization error measures as the ligand field strength is varied with the number of strong-field ligands in a series of heteroleptic complexes or by geometrically constraining the metal–ligand bond length in homoleptic octahedral complexes. We show that across these sets of complexes an inverse relationship generally exists between global and local curvatures. We find that effects of ligand substitution on both measures of delocalization are typically additive, but the quantities seldom coincide.密度泛函理论（DFT）的预测精度常受到离域误差的制约，对于过渡金属配合物等关联体系而言尤为显著。目前已开发出两种互补策略以降低离域误差：一是通过电荷变化消除全局曲率，二是在DFT+U框架下，将线性响应Hubbard U作为固定电荷下金属中心局域曲率的表征量。我们通过调控一系列异配配合物中的强场配体数目，或是对同配八面体配合物的金属-配体键长施加几何约束以改变配体场强度，探究了两种离域误差表征手段之间的关联。研究表明，在上述配合物体系中，全局曲率与局域曲率之间普遍存在反比关系。我们发现，配体取代对两种离域误差表征量的影响通常具有可加性，但二者的数值极少能够完全一致。