Where Does the Density Localize? Convergent Behavior for Global Hybrids, Range Separation, and DFT+U

TL;DR

This study compares the effects of DFT+U, hybrid, and range-separated hybrid methods on electron density delocalization in transition metal complexes, revealing consistent charge loss at metal centers and increased magnetic moments across various conditions.

Contribution

It demonstrates that different delocalization correction methods have similar impacts on electron density and highlights the need for approaches that separately address density and energetic errors.

Findings

All methods cause charge loss at metal centers and charge gain at ligands.

Charge loss is mainly from minority spin electrons, increasing magnetic moments.

Optimal correction parameters for density and magnetic properties differ from those for energetic error correction.

Abstract

Approximate density functional theory (DFT) suffers from many-electron self- interaction error, otherwise known as delocalization error, that may be diagnosed and then corrected through elimination of the deviation from exact piecewise linear behavior between integer electron numbers. Although paths to correction of energetic delocalization error are well- established, the impact of these corrections on the electron density is less well-studied. Here, we compare the effect on density delocalization of DFT+U, global hybrid tuning, and range- separated hybrid tuning on a diverse test set of 32 transition metal complexes and observe the three methods to have qualitatively equivalent effects on the ground state density. Regardless of valence orbital diffuseness (i.e., from 2p to 5p), ligand electronegativity (i.e., from Al to O), basis set (i.e., plane wave versus localized basis set), metal (i.e., Ti, Fe, Ni) and spin state, or tuning method, we consistently observe substantial charge loss at the metal and gain at ligand atoms (ca. 0.3-0.5 e or more). This charge loss at the metal is preferentially from the minority spin, leading to increasing magnetic moment as well. Using accurate wavefunction theory references, we observe that a minimum error in partial charges and magnetic moments occur at higher tuning parameters than typically employed to eliminate energetic delocalization error. These observations motivate the need to develop multi-faceted approximate-DFT error correction approaches that separately treat density delocalization and energetic errors in order to recover both correct density and magnetization properties.