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

Abstract

Approximate density functional theory (DFT) suffers from many-electron selfinteraction 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 wellestablished, 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 rangeseparated 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.

Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost

“…Examining shapes and parameters of fit expressions across elements confirms that errors are generally the same shape but this also leads to observations consistent with earlier work on only delocalization error 38,44,[57][58][59][60] : heavier elements exhibit reduced convexity and concavity as the addition or removal of a single electron becomes a smaller fraction of total electron count (i.e., smaller coefficients in fits, Supporting Information Tables S3-S14).…”

Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering

“…[41][42][43] However, disadvantages for DFT+U remain in the fact that one must calculate [43][44] or tune the U parameter, which introduces empiricism. We have also shown that optimal U choice may be ambiguous, depending on whether one is aiming to reproduce accurate density properties 14 , recover piecewise linearity 45 , or reproduce spin-state ordering [41][42][43] .…”

Magnetic configurations of open-shell molecules on metals: The case of CuPc and CoPc on silver

“…This is consistent with the notion that higher-level methods, such as hybrid functionals, or the use of "DFT+U" or "DFT+Anderson impurity" methods [90,[101][102][103], are necessary to properly capture magnetic properties of molecular systems [58][59][60][61][62]104,105]; note that the latter two methodologies are also known to have their own intrinsic limitations for describing theoretically the properties of these systems [90,106]. Precedent for this statement can be found for the case of gas-phase transition-metal complexes, where it has been shown that with increasing amount of exact exchange, the ground-state charge density within the complexes localizes more in the ligand region than on the metal and the splitting between low-and high-spin states increases [107]. Indeed, due to the inclusion of exact exchange, hybrid functionals are able to better describe exchange-coupling effects between spin-parallel electrons, which are not fully captured by semilocal DFT functionals such as PBE [57][58][59][60][61]63].…”