Charged defects are often studied within the periodic density functional theory (DFT), but this introduces strong finite-size artifacts. In this work, we develop an electrostatic image interaction correction (IIC) method based on the direct solution of the Poisson equation for charge models constructed directly from DFT calculations. These IICs are found to be detail-insensitive, depending almost entirely on bulk dielectric properties. As these IICs are not able to fully explain the observed finite-size scaling, we explore potential alignment in detail and introduce a novel decomposition to separate out different contributions. We find that the two main sources of potential alignment are defect image interactions and changes in the number of atoms present in the supercell. This first effect is accurately predicted by the periodic part of our IIC. The second contribution is unrelated to the IIC and justifies the common observation that the magnitude of finite-size dependence can strongly vary between vacancy and interstitial defects. It can be approximately predicted using atomic radius, but is strongly sensitive to the pseudopotential employed. Combined, these developments provide a new justification for known finite-size scaling rules. Our results suggest that for cubic supercells, the Lany-Zunger IIC, combined with simplified potential alignment between neutral systems, can yield accurate corrections in spite of the simplicity of the approach.

We introduce a new functional for simulating ground-state and time-dependent electronic systems within density-functional theory. The functional combines an expression for the exact Kohn-Sham (KS) potential in the limit of complete electron localization with a measure of the actual localization. We find accurate self-consistent charge densities, even for systems where the exact exchangecorrelation potential exhibits non-local dependence on the density, such as potential steps. We compare our results to the exact KS potential for each system. The self-interaction correction is accurately described, avoiding the need for orbital-dependent potentials.PACS numbers: 71.15. Mb, 73.63.Nm, Density-functional theory (DFT) [1] is the most widely used tool for the simulation of many-electron systems in numerous fields of physics, chemistry and materials science. Its success hinges on approximations [2,3] to the exchange-correlation (xc) part of the Kohn-Sham (KS) functional, which perform well across a range of groundstate systems. However, these approximations become much less secure in the presence of strong correlation [4,5] and/or current flow [6][7][8][9][10]. Particular attention has been given to improving the time-dependent xc potential, used within time-dependent DFT (TDDFT) [11], where the use of adiabatic functionals of the electron density ignores the role of currents and memory effects.In this Letter we demonstrate that electron localization, driven by the Coulomb interaction and the Pauli principle, can form a powerful ingredient in approximations for the KS potential. The electron localization function (ELF), L(x), as in Ref. 12, provides a useful indicator of localization: L = 1 is complete localization, i.e. the chance of finding one electron in the vicinity of another is zero. L(x) ranges from 0 to 1, and a homogeneous electron gas (HEG) has L = 0.5.Our starting point is the KS potential of Refs. 13 and 14, originally derived for a system of two spinful electrons in their spin-zero ground state. We observe that the logic applies exactly to any one-electron system, and, indeed, in a general system, to all regions of space where the electron density is dominated by any one Kohn-Sham orbital [15]. For such a region the KS equations may be approximated as [16] − 1 2 2 + V KS √ n = ε k √ n for the dominant orbital φ k , where n ≈ |φ k | 2 in the region, yielding the ground-state KS potential, which we term the single orbital approximation (SOA),(Here the zero of energy in the KS system is at ε k .) We begin by considering Eq. 1 as an approximation to the universal KS functional. We find that the SOA not only works well for the strongly localized orbital regions, but also accounts for non-local features and corrects selfinteraction in the KS potential in regions of low localization. We compare the SOA to the exact KS potential for a variety of ground-state and time-dependent systems that exhibit non-local behavior in the xc potential. We then extend our approach by combining the SOA with a potential suited to d...

Predicting the degree of localization and calculating the trapping energies of polarons in insulators by density functional theory (DFT) is challenging. Hybrid functionals are often reparametrized to obtain accurate results and the a priori selection of these parameters is still an open question. Here we test the accuracy of several range-separated hybrid functionals, all reparametrized to produce an accurate band gap, by calculating the charge transition levels (CTLs) of experimentally well-studied hole polaron defect centers in MgO. We show that the functional with screened long-range exact exchange is moderately but consistently more accurate than functionals which do not include long-range exact exchange. We provide evidence that the source of the improved accuracy is the eigenvalue associated with the valence band maximum of the bulk material. We discuss the extent to which this accuracy relates to Koopmans' compliance of the defect energy level.

Density Functional Theory (DFT) with Generalized Gradient Approximation (GGA) functionals is commonly used to predict defect properties in 2D transition metal dichalcogenides (TMDs). Since GGA functionals often underestimate bandgaps of semiconductors and incorrectly describe the character of electron localization in defects and their level positions within the band-gap, it is important to assess the accuracy of these predictions. To this end, we used the non-local density functional PBE0-TC-LRC to calculate the properties of a wide range of intrinsic defects in monolayer WS2. The properties, such as geometry, in-gap states, charge transition levels, electronic structure and the electron/hole localization of the lowest formation energy defects are discussed in detail. They are broadly similar to those predicted by the GGA PBE functional but exhibit numerous quantitative differences caused by the degree of electron and hole localization in charged states. For some anti-site defects, more significant differences are seen, with both changes in defect geometries (differences of up to 0.5 Å) as well as defect level positions within the band gap of WS2. This work provides an insight into the performance of functionals chosen for future DFT calculations of transition metal dichalcogenides with respect to the desired defect properties.