DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green’s functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.

Defect levels are a problem for standard implementations of density-functional theory and the error also influences the energetics. We demonstrate that the HSE06 functional, which describes the electronic structure of all group-IV semiconductors well (including Ge), gives highly accurate charge transition levels, too, if the defect wave function is host related\char22{}independent of localization. The degree of fulfilling the generalized Koopmans' theorem shows the reliability of the results and the highest-occupied eigenvalue always seems to give the correct vertical ionization energy.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners.

Due to its wide band gap and availability as a single crystal, $\beta -\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ has potential for applications in many areas of micro/optoelectronics and photovoltaics. Still, little is as yet known about its intrinsic defects, which may influence carrier concentrations and act as recombination centers. From a theoretical point of view, the problem is that standard (semi)local approximations of density functional theory usually cannot handle wide band-gap oxides, while results of tuned hybrid functional calculations so far have shown little quantitative coincidence with experimental data on $\beta -\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$. Here, we show a method for selecting the optimal hybrid, which reproduces not only the band gap, but also satisfies the generalized Koopmans’ theorem. Unless the screening is strongly orbital/direction dependent in the given material, such an optimal hybrid can reproduce the whole $GW$ band structure quite accurately. With the optimized functional, and introducing a modification into the charge correction process, we are able to give a consistent description of observed carrier trapping by intrinsic defects in $\beta -\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$. With the exception of gallium interstitials, which can act as shallow donors, all other intrinsic defects are deep. Gallium vacancies are the main compensating acceptors in $n$-type samples, while both oxygen interstitials and vacancies act as hole traps, in addition to small hole polarons. Considering the limitations imposed by a medium-sized (160-atom) supercell in an ionic solid, the calculated adiabatic and vertical transitions are in good agreement with available experimental data.

Metal oxides are extremely challenging for defect calculations within density-functional theory because of the underestimation of the band gap and of the polaronic effects due to spurious electron self-interaction in the standard (semi)local implementations. We show here that\char22{}similarly to Group-IV semiconductors\char22{}the HSE06 screened hybrid functional provides not only a good description of the ground-state properties and an accurate gap of TiO2 modifications, but fulfills the generalized Koopmans' theorem for host-related defect states\char22{}independent of localization. This means that the total energy has the correct dependence on the fractional occupation number, lending credibility to the calculated optical and thermodynamic charge transition levels for acceptors (Al, Ga, In, Sc, and Y on Ti site) and donors (Nb on Ti site, and interstitial H). We find deep, localized hole polarons in anatase and electron polarons in rutile. Therefore, p-type doping in anatase and n-type doping in rutile are counteracted by carrier self-trapping. Donors in anatase and the acceptors in rutile give rise to effective masslike states, but the latter are deeper. In fact, the polaron bound at In in anatase is about as deep as the effective masslike state induced by In in rutile. The shallow state in anatase and the deep one in rutile for the Nb donor, as well as the deep state for Al in anatase, agree well with experimental observations.