Correcting density functional theory for accurate predictions of compound enthalpies of formation: Fitted elemental-phase reference energies

Abstract

Despite the great success that theoretical approaches based on density functional theory have in describing properties of solid compounds, accurate predictions of the enthalpies of formation (∆H f ) of insulating and semiconducting solids still remain a challenge. This is mainly due to incomplete error cancellation when computing the total energy differences between the compound total energy and the total energies of its elemental constituents. In this paper we present an approach based on GGA+U calculations, including the spin-orbit coupling, which involves fitted elemental-phase reference energies (FERE) and which significantly improves the error cancellation with compound total energies resulting in accurate values for the compound enthalpies of formation. We use an extensive set of 252 binary compounds with measured ∆H f values (pnictides, chalcogenides and halides) to obtain FERE energies and show that after the fitting, the 252 enthalpies of formation are reproduced with the mean absolute error MAE=0.054 eV/atom instead of MAE≈0.250 eV/atom resulting from pure GGA calculations. When applied to a set of 55 ternary compounds that were not part of the fitting set the FERE method reproduces their enthalpies of formation with MAE=0.048 eV/atom. Furthermore, we find that contributions to the total energy differences coming from the spin-orbit coupling can be, to a good approximation, separated into purely atomic contributions which do not affect ∆H f . The FERE method, hence, represents a simple and general approach, as it is computationally equivalent to the cost of pure GGA calculations and applies to virtually all insulating and semiconducting compounds, for predicting compound ∆H f values with chemical accuracy. We also show that by providing accurate ∆H f the FERE approach can be applied for accurate predictions of the compound thermodynamic stability or for predictions of Li-ion battery voltages.

Formation energies of group I and II metal oxides using random phase approximation

“…This is due to that the Hubbard U term applied to a metal oxide can not be applied to its corresponding bulk metal. An alternative way to obtain a meaningful U term for metals are proposed in the literature 30 , it is however, out of scope of current work. The second criterion thus excludes 3d transition metal oxides such as VO and NiO.…”

Strongly Enhanced Photovoltaic Performance and Defect Physics of Air‐Stable Bismuth Oxyiodide (BiOI)

“…The assessment was performed by using the fitted elemental-phase reference energies (FERE) approach for calculating the enthalpies of formation and a standard set of equations to determine the stability. [38] A map of the thermodynamically stable phases under different chemical potentials for Bi, I, and O is shown in Figure 2a, with the phase-stable region for BiOI indicated. The defect formation energies were calculated at the four extrema of this phase-stable region (Figure 2b).…”

Approaching chemical accuracy with density functional calculations: Diatomic energy corrections

“…Others have pointed out DFT's discrepancies with respect to experimental thermodynamics for certain classes of compounds, and have proposed various remedies [13][14][15][16][17] . For example, Stevanović et al fit one correction factor for each of fifty of the elements using experimental data from 252 binary compounds.…”

“…For example, Stevanović et al fit one correction factor for each of fifty of the elements using experimental data from 252 binary compounds. The fitted correction factors were then used to improve agreement between their calculations and experimental values for formation energies of chalcogenides and pnictides 15 . Wang et al 14 and Lee et al 17 followed a more conservative approach, fitting a correction factor to the O 2 molecule using a set of seven binary oxides.…”