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Density functional theory (DFT) methods for calculating the quantum mechanical ground states of condensed matter systems are now a common and significant component of materials research. The growing importance of DFT reflects the development of sufficiently accurate functionals, efficient algorithms and continuing improvements in computing capabilities. As the materials problems to which DFT is applied have become large and complex, so have the sets of calculations necessary for investigating a given problem. Highly versatile, powerful codes exist to serve the practitioner, but designing useful simulations is a complicated task, involving intricate manipulation of many variables, with many pitfalls for the unwary and the inexperienced. We discuss several of the most important issues that go into designing a meaningful DFT calculation. We emphasize the necessity of investigating these issues and reporting the critical details.

Germanium telluride undergoes rapid transition between polycrystalline and amorphous states under either optical or electrical excitation. While the crystalline phases are predicted to be semiconductors, polycrystalline germanium telluride always exhibits p-type metallic conductivity. We present a study of the electronic structure and formation energies of the vacancy and antisite defects in both known crystalline phases. We show that these intrinsic defects determine the nature of free-carrier transport in crystalline germanium telluride. Germanium vacancies require roughly one-third the energy of the other three defects to form, making this by far the most favorable intrinsic defect. While the tellurium antisite and vacancy induce gap states, the germanium counterparts do not. A simple counting argument, reinforced by integration over the density of states, predicts that the germanium vacancy leads to empty states at the top of the valence band, thus giving a complete explanation of the observed p-type metallic conduction.

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The Heyd-Scuseria-Ernzerhof (HSE) density functionals are popular for their ability to improve the accuracy of standard semilocal functionals such as Perdew-Burke-Ernzerhof (PBE), particularly for semiconductor band gaps. They also have a reduced computational cost compared to hybrid functionals, which results from the restriction of Fock exchange calculations to small inter-electron separations. These functionals are defined by an overall fraction of Fock exchange and a length scale for exchange screening. We systematically examine this two-parameter space to assess the performance of hybrid screened exchange (sX) functionals and to determine a balance between improving accuracy and reducing the screening length, which can further reduce computational costs. Three parameter choices emerge as useful: "sX-PBE" is an approximation to the sX-LDA screened exchange density functionals based on the local density approximation (LDA); "HSE12" minimizes the overall error over all tests performed; and "HSE12s" is a range-minimized functional that matches the overall accuracy of the existing HSE06 parameterization but reduces the Fock exchange length scale by half. Analysis of the error trends over parameter space produces useful guidance for future improvement of density functionals.