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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.

Quantitative predictions of defect properties in semiconductors using density functional theory have been crippled by two issues: the supercell approximation, which has incorrect boundary conditions for an isolated defect, and approximate functionals, that drastically underestimate the band gap. I describe modifications to the supercell method that incorporate boundary conditions appropriate to point defects, identify a common electron reservoir for net charge for all defects, deal with defect banding, and incorporate bulk polarization. The computed level spectrum for an extended set of silicon defects spans the experimental gap, i.e., exhibits no band gap problem, and agrees remarkably well with experiment.

We apply density functional theory (DFT) and the DFT+U technique to study the adsorption of transition metal porphine molecules on atomistically flat Au(111) surfaces. DFT calculations using the Perdew-Burke-Ernzerhof exchange correlation functional correctly predict the palladium porphine (PdP) low-spin ground state. PdP is found to adsorb preferentially on gold in a flat geometry, not in an edgewise geometry, in qualitative agreement with experiments on substituted porphyrins. It exhibits no covalent bonding to Au(111), and the binding energy is a small fraction of an electronvolt. The DFT+U technique, parametrized to B3LYP-predicted spin state ordering of the Mn d-electrons, is found to be crucial for reproducing the correct magnetic moment and geometry of the isolated manganese porphine (MnP) molecule. Adsorption of Mn(II)P on Au(111) substantially alters the Mn ion spin state. Its interaction with the gold substrate is stronger and more site-specific than that of PdP. The binding can be partially reversed by applying an electric potential, which leads to significant changes in the electronic and magnetic properties of adsorbed MnP and approximately 0.1 A changes in the Mn-nitrogen distances within the porphine macrocycle. We conjecture that this DFT+U approach may be a useful general method for modeling first-row transition metal ion complexes in a condensed-matter setting.

We investigate the structural properties and energy levels of simple intrinsic defects in gallium arsenide. The first-principles calculations (1) apply boundary conditions appropriate to charge defects in supercells and enable quantitatively accurate predictions of defect charge transitions with a supercell approximation, (2) are demonstrated to be converged with respect to cell size and (3) assess the sensitivity to model construction to Ga pseudopotential construction (3d core or 3d valence) and density functionals (local density or generalized gradient approximation). With these factors controlled, we present the first quantitatively reliable survey of defect levels in GaAs, reassess the available literature and begin to decipher the complexity of GaAs defect chemistry. The computed defect level spectrum spans the experimental GaAs band gap, defects exhibit multiple bistabilities with (sometimes overlapping) negative-U systems, express more extensive charge states than previously anticipated and collectively suggest that our atomistic understanding of GaAs defect physics needs to be reassessed.