Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error

TL;DR

This paper introduces a molecular orbital (MO)-based DFT+U method that effectively eliminates delocalization error across various transition-metal complexes, improving accuracy and transferability over traditional atomic orbital (AO)-based approaches.

Contribution

The authors develop a transferable MO-based DFT+U correction that overcomes limitations of standard AO-based DFT+U in reducing delocalization error in transition-metal chemistry.

Findings

MO-based DFT+U recovers exact conditions where AO-based DFT+U fails.

The approach eliminates delocalization error across different ligand strengths and metal configurations.

It demonstrates high transferability in diverse transition-metal complexes.

Abstract

While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AO) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases where standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on a range of ligand field strengths (i.e., from H_2O to CO), electron configurations (i.e., from Sc to Fe to Zn), and spin states (i.e., low-spin and high-spin) in representative transition-metal complexes.