Intricacies of DFT+U, Not Only in a Numeric Atom Centered Orbital Framework

Abstract

We implemented the popular Hubbard density-functional theory + U (DFT+U) method in its spherically averaged form in the all-electron, fullpotential DFT code FHI-aims. There, electronic states are expressed on a basis of highly localized numeric atomic orbitals (NAO), which straightforwardly lend themselves as projector functions for the DFT+U correction, yielding the necessary occupations of the correlated Hubbard subspace at no additional cost. We establish the efficacy of our implementation on the prototypical bulk NiO and obtain the well-known band gap opening effect of DFT+U. As a more stringent, real world test system, we then study polaron formation at the rutile TiO 2 (110) surface, where our results are in line with both experimental data as well as hybrid functional calculations. At this TiO 2 test system, yet in the bulk, we analyze some of the intricacies of using the DFT+U correction in a localized, numeric atomic orbital basis set. Specifically, we find that multiple localized radial basis functions of the same angular momentum can lead to highly erroneous predictions of ground-state properties. We also demonstrate a number of remedies to this problem. Finally, we highlight the critical influence of the exact choice of projector functions on DFT+U results using a number of projector functions of different spatial extent and composed of linear combinations of NAO basis functions. All of our efforts serve to highlight that, contrary to its deceptive ease of use, the DFT+U is far from the "black-box" approach it is sometimes made out to be.

Machine learning the Hubbard U parameter in DFT+U using Bayesian optimization

“…We note that all DFT+U results presented here are based on the implementation of the Dudarev formalism in VASP. Different DFT+U implementations may yield different results 30 .…”

Investigating Polaron Formation in Anatase and Brookite TiO2 by Density Functional Theory with Hybrid-Functional and DFT + U Methods

“…21,22 In addition, it depends heavily on the implementation in the DFT code. 42 Thus, we cannot directly compare the absolute values of U , which are taken from different DFT codes. Nevertheless, it can be used as a reasonable model for qualitatively comparing results with those from available theoretical or experimental studies.…”

Electrode and Electrolyte Materials From Atomistic Simulations: Properties of LixFEPO4 Electrode and Zircon-Based Ionic Conductors

“…In the most recent contribution we computed the MUO 4 compounds with M = Ni, Fe, Co, Cd, and found that only by using the correct projectors for estimation of occupation of d orbitals, e.g., Wannier functions, we could reproduce experimentally seen structural distortions (Murphy et al, 2021). The problem arises from the fact that with the standard DFT+U approach, when using atomic orbitals as projectors, the total occupancy of the d or f states of interest is much higher than the actual one (Kick et al, 2019;Murphy et al, 2021). As illustrated in Table 3, in our case it gives ∼1.3 excess electrons for Fe(III) and ∼0.5 for Fe(II).…”

“…In a series of papers we have shown that standard DFT approach often fails for such cases and these compounds must be carefully computed, including proper accounting for the correlation effects (Beridze and Kowalski, 2014;Blanca-Romero et al, 2014;Kowalski et al, 2015;Li and Kowalski, 2018). These simulations must be performed with methods beyond the standard DFT+U approach and include derivation of the Hubbard U parameter and careful choice of projectors for estimation of occupancy of d− and f − levels within the DFT+U scheme (Maxisch and Ceder, 2006;Kvashnina et al, 2018;Kick et al, 2019). In particular, we apply the linear response method (Cococcioni and de Gironcoli, 2005) with Wannier orbitals as representation of d or f states (Kvashnina et al, 2018) and here we will demonstrate impact of these procedures on the estimation of formation enthalpies and solubility limits of Li x FePO 4 compound.…”