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Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general "hidden" scale invariance of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Griineisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant inverse power-law (IPL) pair interactions. However, crystal packings of several transition metals (V, Cr, Mn, Fe, Nb, Mo, Ta, W, and Hg), most post-transition metals (Ga, In, Sn, and Tl), and the metalloids Si and Ge cannot be explained by the IPL assumption. The virial-energy correlation coefficients of iron and phosphorous are shown to increase at elevated pressures. Finally, we discuss how scale invariance explains the Griineisen equation of state and a number of well-known empirical melting and freezing rules. [ABSTRACT FROM AUTHOR]

The equation of motion for the Green function is combined with the Bethe-Salpeter equation for the scattering amplitude yielding a concise and formally closed system of three equations that encapsulates the essence of Green function theory. Two of the three equations formally resemble a Dyson-like relation. We prove that this formally simple set is exactly equivalent to Hedin's equations. Our derivation therefore constitutes an alternative to Hedin's derivation which is based on functional derivatives. Furthermore, we briefly discuss how approximations can be introduced as a hierarchy of approximations to the four-point Green function. [ABSTRACT FROM AUTHOR]

The band lineup, or alignment, of semiconductors is investigated via first-principles calculations based on density functional theory (DFT) and many-body perturbation theory (MBPT). Twenty-one semiconductors including C, Si, and Ge in the diamond structure, BN, A1P, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, and GaN and ZnO in the wurtzite structure are considered in view of their fundamental and technological importance. Band alignments are determined using the valence and conduction band offsets from heterointerface calculations, the ionization potential (IP) and electron affinity (EA) from surface calculations, and the valence band maximum and conduction band minimum relative to the branch point energy, or charge neutrality level, from bulk calculations. The performance of various approximations to DFT and MBPT, namely the Perdew-Burke-Ernzerhof (PBE) semilocal functional, the Heyd-Scuseria-Emzerhof (HSE) hybrid functional, and the GW approximation with and without vertex corrections in the screened Coulomb interaction, is assessed using the GWΓ1 approximation as a reference, where first-order vertex corrections are included in the self-energy. The experimental IPs, EAs, and band offsets are well reproduced by GWΓ1 for most of the semiconductor surfaces and heterointerfaces considered in this study. The PBE and HSE functionals show sizable errors in the IPs and EAs, in particular for group II-VI semiconductors with wide band gaps, but are much better in the prediction of relative band positions or band offsets due to error cancellation. The performance of the GW approximation is almost on par with GWΓ1 as far as relative band positions are concerned. The band alignments based on average interfacial band offsets for all pairs of 17 semiconductors and branch point energies agree with explicitly calculated interfacial band offsets with small mean absolute errors of both ∼0.1 eV, indicating a good overall transitivity of the band offsets. The alignment based on IPs from selected nonpolar surfaces performs comparably well in the prediction of band offsets at most of the considered interfaces. The maximum errors are, however, as large as 0.3, 0.4, and 0.7 eV for the alignments based on the average band offsets, branch point energies, and IPs, respectively. This margin of error should be taken into account when performing materials screening using these alignments. [ABSTRACT FROM AUTHOR]

We derive a finite-basis-set correction for quasiparticle (QP) energies in the G W approximation and many-body correlation energies in the random phase approximation. Since the correction requires only knowledge of the ground-state density distribution, it is straightforward to implement in any plane-wave code and significantly improves convergence at negligible computational cost. The expression also indicates that QP energies might converge to the wrong value using the projector augmented wave (PAW) method since the overlap densities of occupied orbitals and high-energy, plane-wave-like orbitals are inaccurately described. The error is shown to be related to the incompleteness of the partial waves inside the atomic spheres. It can be avoided by adopting norm-conserving partial waves. G0W0 and GW0 results based on such norm-conserving PAW potentials are presented for a large set of semiconductors and insulators. Accurate extrapolation procedures to the infinite-basis-set limit and infinite-k-point limit are discussed in detail. [ABSTRACT FROM AUTHOR]

The random phase approximation (RPA) to the correlation energy is among the most promising methods to obtain accurate correlation energy differences from diagrammatic perturbation theory at modest computational cost. We show here that a cubic system size scaling can be readily obtained, which dramatically reduces the computation time by one to two orders of magnitude for large systems. Furthermore, the scaling with respect to the number of k points used to sample the Brillouin zone can be reduced to linear order. In combination, this allows accurate and very well-converged single-point RPA calculations, with a time complexity that is roughly on par or better than for self-consistent Hartree-Fock and hybrid-functional calculations. The present implementation enables new applications. Here, we apply the RPA to determine the energy difference between diamond Si and β-tin Si, the energetics of the Si self-interstitial defect and the Si vacancy, the latter with up to 256 atom supercells. We show that the RPA predicts Si interstitial and vacancy energies in excellent agreement with experiment. Si self-interstitial diffusion barriers are also in good agreement with experiment, as opposed to previous calculations based on hybrid functionals or range-separated RPA variants. [ABSTRACT FROM AUTHOR]

We propose an approach for computing the Gibbs free energy difference between phases of a material. The method is based on the determination of the average force acting on interfaces that separate the two phases of interest. This force, which depends on the Gibbs free energy difference between the phases, is computed by applying an external harmonic field that couples to a parameter which specifies the two phases. Validated first for the Lennard-Jones model, we demonstrate the flexibility, efficiency, and practical applicability of this approach by computing the melting temperatures of sodium, magnesium, aluminum, and silicon at ambient pressure using density functional theory. Excellent agreement with experiment is found for all four elements, except for silicon, for which the melting temperature is, in agreement with previous simulations, seriously underestimated. [ABSTRACT FROM AUTHOR]

Linear optical properties can be accurately calculated using the Bethe-Salpeter equation. After introducing a suitable product basis for the electron-hole pairs, the Bethe-Salpeter equation is usually recast into a complex non-Hermitian eigenvalue problem that is difficult to solve using standard eigenvalue solvers. In solid-state physics, it is therefore common practice to neglect the problematic coupling between the positive- and negative-frequency branches, reducing the problem to a Hermitian eigenvalue problem [Tamm-Dancoff approximation (TDA)]. We use time-inversion symmetry to recast the full problem into a quadratic Hermitian eigenvalue problem, which can be solved routinely using standard eigenvalue solvers even at a finite wave vector q. This allows us to access the importance of the coupling between the positive- and negative-frequency branch for prototypical solids. As a starting point for the Bethe-Salpeter calculations, we use self-consistent Green's-function methods (GW), making the present scheme entirely ab initio. We calculate the optical spectra of carbon (C), silicon (Si), lithium fluoride (LiF), and the cyclic dimer Li2F2 and discuss why the differences between the TDA and the full solution are tiny. However, at finite momentum transfer q, significant differences between the TDA and our exact treatment are found. The origin of these differences is explained. [ABSTRACT FROM AUTHOR]

We study the canted magnetic state in Sr2IrO4 using fully relativistic density functional theory (DFT) including an on-site Hubbard U correction. A complete magnetic phase diagram with respect to the tetragonal distortion and the rotation of IrO6 octahedra is constructed, revealing the presence of two types of canted to collinear magnetic transitions: a spin-flop transition with increasing tetragonal distortion and a complete quenching of the basal weak ferromagnetic moment below a critical octahedral rotation. Moreover, we put forward a scheme to study the anisotropic magnetic couplings by mapping magnetically constrained noncollinear DFT onto a general spin Hamiltonian. This procedure allows for the simultaneous account and direct control of the lattice, spin, and orbital interactions within a fully ab initio scheme. We compute the isotropic, single site anisotropy and Dzyaloshinskii-Moriya (DM) coupling parameters, and clarify that the origin of the canted magnetic state in Sr2IrO4 arises from the structural distortions and the competition between isotropic exchange and DM interactions. [ABSTRACT FROM AUTHOR]

We present lattice constants and cohesive energies of alkali, alkaline earth, and transition metals using the correlation energy evaluated within the adiabatic-connection fluctuation-dissipation (ACFD) framework in the random phase approximation (RPA) and compare our ündings to results obtained with the meta-GGA functional revTPSS and the gradient corrected PBE (Perdew-Burke-Emzerhof) functional and the PBEsol functional (PBE reparametrized for solids), as well as a van der Waals (vdW) corrected functional optB88-vdW. Generally, the RPA reduces the mean absolute error in the lattice constants by about a factor 2 compared to the other functionals. Atomization energies are also on par with the PBE functional, and about a factor 2 better than with the other functionals. The study confirms that the RPA describes all bonding situations equally well including van der Waals, covalent, and metallic bonding. [ABSTRACT FROM AUTHOR]

When wurtzite ZnO is sliced perpendicular to the (0001) axis, two different polar surfaces, the (0001)-Zn and (0001)-O terminated surfaces, are formed. In a simple ionic picture, both surfaces are electrostatically unstable due to a diverging electrostatic energy. Although the ionic picture is an oversimplification, the surfaces adopt a modified surface structure to compensate for the polarity. In close collaboration with experiment, a hexagonal honeycomblike reconstruction has been suggested [J. V. Lauritsen et al., ACS Nano 5, 5987 (2011)]. The remarkable observation is that the (0001)-O surface behaves very differently than the (0001)-Zn surface. Here, we present a detailed density functional theory investigation of the (000i)-O surface, including a systematic investigation of H and Zn coverage as well as an investigation of various surface reconstructions. The difference between the two polar surfaces is explained by the different bonding preferences of Zn and O atoms: as a d element, Zn atoms are more flexible in their bond formation than O atoms. [ABSTRACT FROM AUTHOR]

Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete-basis-set (CBS) limit in methods utilizing plane-wave wave-function expansions. Simple analytic and numerical results from second-order M0ller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis-set Unncation when constructing many-electron wave functions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wave-function methods, from MP2 to coupled-cluster doubles theory and the random-phase approximation plus second-order screened exchange. Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the Orbitals of a general solid state system onto the HEG plane-wave basis and thereby allow application of these methods to more reaHstic physical problems. We demonstrate this explicitly for solid and molecular lithium hydride. [ABSTRACT FROM AUTHOR]

The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized-gradient-approximation (MGGA) and its revised version, the revTPSS, are implemented self-consistently within the framework of the projector-augmented-wave (PAW) method, using a plane wave basis set. Both TPSS and revTPSS yield accurate atomization energies for the molecules in the AE6 set, better than those of the standard Perdew-Burke-Ernzerhof (PBE) generalized-gradient-approximation. For lattice constants and bulk moduli of 20 diverse solids, revTPSS performs much better than PBE, and on average as well as PBEsol and Armiento-Mattsson (AM05), GGAs designed for solids. The latter two overestimate the atomization energies for molecules to an unacceptable degree. However, the revTPSS presents only a slight improvement over PBEsol for the prediction of cohesive energies for solids, and some deterioration with respect to PBE. We also study the magnetic properties of Fe, for which both TPSS and revTPSS predict the right ground-state solid phase, the ferromagnetic body-centered-cubic (bcc) structure, with an accurate magnetic moment. [ABSTRACT FROM AUTHOR]

Water monomer adsorption on graphene is examined with state-of-the-art electronic structure approaches. The adsorption energy determinations on this system from quantum Monte Carlo and the random-phase approximation yield small values of <100 meV. These benchmarks provide a deeper understanding of the reactivity of graphene that may underpin the development of improved more approximate methods enabling the accurate treatment of more complex processes at wet-carbon interfaces. As an example, we show how dispersion-corrected density functional theory, which we show gives a satisfactory description of this adsorption system, predicts that water undergoes ultra-fast diffusion on graphene at low temperatures. [ABSTRACT FROM AUTHOR]

Using the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) metageneralized gradient approximation, a computationally efficient semilocal functional, we studied the desorption energies of the molecule CO on the (111) surfaces of transition metals as well as the surface energies and lattice constants of the underlying transition metals. Due to its ability to distinguish single-orbital regions from regions of high orbital overlap, revTPSS improves all three properties over the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation. No generalized gradient approximation matches this performance, which has been regarded as unreachable by semilocal approximations. [ABSTRACT FROM AUTHOR]

A scheme to incorporate nonlocal polarizations into the dynamical mean-field theory (DMFT) and a tailor-made way to determine the effective interaction for DMFT are systematically investigated. Applying it to the two-dimensional Hubbard model, we find that nonlocal polarizations induce a nontrivial filling-dependent antiscreening effect for the effective interaction. The present scheme combined with density functional theory offers an ab initio way to derive effective on-site interactions for the impurity problem in DMFT. We apply it to SrVO3 and find that the antiscreening competes with the screening caused by the off-site interaction. [ABSTRACT FROM AUTHOR]