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

TL;DR

This paper investigates how ligand field strength influences two types of delocalization errors in density functional theory, revealing generally inverse relationships and ligand additivity effects that can inform error correction strategies.

Contribution

It demonstrates the relationship between global and local delocalization errors and shows ligand additivity effects across complexes, aiding error correction in DFT calculations.

Findings

Inverse relationship between global and local curvatures across complexes

Ligand substitution effects on delocalization are additive

Ligand additivity enables error inference for complex geometries

Abstract

Despite its widespread use, the predictive accuracy of density functional theory (DFT) is hampered by delocalization errors, especially for correlated systems such as transition-metal complexes. Two complementary tuning strategies have been developed to reduce delocalization error: eliminating the global curvature with respect to charge addition or removal, and computing a linear response Hubbard U as a measure of local curvature at the metal center at fixed charge and applying it to the transition-metal complex in a DFT+U framework. We investigate the relationship between the two measures of delocalization error as we manipulate the ligand field strength by varying 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 with varying ligand fields, 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 two quantities seldom coincide. The observation of ligand additivity suggests opportunities for evaluating errors on homoleptic complexes to infer corrections for lower-symmetry complexes.