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The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine- Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q G, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: a-A1N, β-A1N, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure. [ABSTRACT FROM AUTHOR]

Structural, electronic, vibrational, and dielectric properties of LaBGeO5 with the stillwellite structure are determined based on ab initio density functional theory. The theoretically relaxed structure is found to agree well with the existing experimental data with a deviation of less than 0.2%. Both the density of states and the electronic band structure are calculated, showing five distinct groups of valence bands. Furthermore, the Born effective charge, the dielectric permittivity tensors, and the vibrational frequencies at the center of the Brillouin zone are all obtained. Compared to existing model calculations, the vibrational frequencies are found in much better agreement with the published experimental infrared and Raman data, with absolute and relative1 firms values of 6.04 cm-1, and 1.81%, respectively. Consequently, numerical values for both the parallel and perpendicular components of the permittivity tensor are established as 3.55 and 3.71 (10.34 and 12.28), respectively, for the high-(low-)frequency limit. [ABSTRACT FROM AUTHOR]

We show that density functional theory within the RPA (random phase approximation for the exchange-correlation energy) provides a correct description of bond dissociation in H2 in a spin-restricted Kohn–Sham formalism, i.e., without artificial symmetry breaking. We present accurate adiabatic connection curves both at equilibrium and beyond the Coulson–Fisher point. The strong curvature at large bond length implies important static (left–right) correlation, justifying modern hybrid functional constructions but also demonstrating their limitations. Although exact at infinite separation and accurate near the equilibrium bond length, the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths. Going beyond the RPA by including the exact exchange kernel (RPA+X), we find a similar repulsion. We argue that this deficiency is due to the absence of double excitations in adiabatic linear response theory. Further analyzing the H2 dissociation limit we show that the RPA+X is not size consistent, in contrast to the RPA. [ABSTRACT FROM AUTHOR]

The linear-response Sham-Schlüter equation can be used to calculate an exchange-correlation potential starting from a given approximation for the self-energy. The asymptotic behavior of these potentials is, however, much debated, a recent work suggesting that they could blow up in finite systems. Here we investigate the asymptotic behavior of the linear-response Sham-Schlüter potentials in the GW and second-order approximations for the self-energy. We show that these potentials do not diverge, and that the correlation potential itself has a -α/(2r[SUP4]) tail (under appropriate conditions), where a depends on the self-energy. We also provide further justification for the quasiparticle approximation to the linear-response Sham-Schlüter equation, that is much simpler to solve while likely being of comparable accuracy. Calculations for real molecules or solids using this approximation should be within the reach of present computers. [ABSTRACT FROM AUTHOR]

The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose for insulators a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expression using a tight-binding model, analytically from the present theory and numerically from the large-size limit of a finite cluster, with excellent numerical agreement. [ABSTRACT FROM AUTHOR]

Using density functional theory, we investigate the structural, vibrational, and dielectric properties of titanium oxides and silicates, which have attracted considerable attention in the framework of the quest for alternative high-κ materials. For the oxides, three crystalline phases of titanium dioxide are considered. The first two are hypothetical; they are obtained by similarity with the cubic and tetragonal structure of zirconia ZrO2 or hafnia HfO2. The third is the rutile, a crystal that occurs naturally. For the silicates, we analyze a hypothetical TiSiO4 structure constructed by analogy with crystalline ZrSiO4 and HfSiO4 (zircon and hafnon). [ABSTRACT FROM AUTHOR]

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Presents calculations of the cohesive energy and bulk moduli of two hypothetical, negatively curved carbon networks. Finds that both have a cohesive energy smaller than that of graphite but significantly greater than that of C60. Stability of fullerenes; Euler's theorem; More.

The electron-phonon interaction plays a crucial role in many fields of physics and chemistry. Nevertheless, its actual calculation by means of modern many-body perturbation theory is weakened by the use of model Hamiltonians that are based on parameters difficult to extract from the experiments. Such shortcoming can be bypassed by using density-functional theory to evaluate the electron-phonon scattering amplitudes, phonon frequencies, and electronic bare energies. In this work, we discuss how a consistent many-body diagrammatic expansion can be constructed on top of density-functional theory. In that context, the role played by screening and self-consistency when all the components of the electron-nucleus and nucleus-nucleus interactions are taken into account, is paramount. A way to avoid overscreening is notably presented. Finally, we derive cancellation rules as well as internal consistency constraints in order to draw a clear, sound, and practical scheme to merge the many-body perturbation and density-functional theory. [ABSTRACT FROM AUTHOR]

The search for new materials based on computational screening relies on methods that accurately predict, in an automatic manner, total energy, atomic-scale geometries, and other fundamental characteristics of materials. Many technologically important material properties directly stem from the electronic structure of a material, but the usual workhorse for total energies, namely density-functional theory, is plagued by fundamental shortcomings and errors from approximate exchange-correlation functionals in its prediction of the electronic structure. At variance, the GW method is currently the state-of-the-art ab initio approach for accurate electronic structure. It is mostly used to perturbatively correct density-functional theory results, but is, however, computationally demanding and also requires expert knowledge to give accurate results. Accordingly, it is not presently used in high-throughput screening: fully automatized algorithms for setting up the calculations and determining convergence are lacking. In this paper, we develop such a method and, as a first application, use it to validate the accuracy of G0W0 using the PBE starting point and the Godby-Needs plasmon-pole model (G0W0GN@PBE) on a set of about 80 solids. The results of the automatic convergence study utilized provide valuable insights. Indeed, we find correlations between computational parameters that can be used to further improve the automatization of GW calculations. Moreover, we find that G0W0GN@PBE shows a correlation between the PBE and the G0W0GN@PBE gaps that is much stronger than that between GW and experimental gaps. However, the G0W0GN@PBE gaps still describe the experimental gaps more accurately than a linear model based on the PBE gaps. With this paper, we hence show that GW can be made automatic and is more accurate than using an empirical correction of the PBE gap, but that, for accurate predictive results for a broad class of materials, an improved starting point or some type of self-consistency is necessary. [ABSTRACT FROM AUTHOR]

The renormalization of the band structure at zero temperature due to electron-phonon coupling is explored in diamond, BN, LiF, and MgO crystals. We implement a dynamical scheme to compute the frequency-dependent self-energy and the resulting quasiparticle electronic structure. Our calculations reveal the presence of a satellite band below the Fermi level of LiF and MgO. We show that the renormalization factor (Z), which is neglected in the adiabatic approximation, can reduce the zero-point renormalization (ZPR) by as much as 40%. Anharmonic effects in the renormalized eigenvalues at finite atomic displacements are explored with the frozen-phonon method. We use a nonperturbative expression for the ZPR, going beyond the Allen-Heine-Cardona theory. Our results indicate that high-order electron-phonon coupling terms contribute significantly to the zero-point renormalization for certain materials. [ABSTRACT FROM AUTHOR]

The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g., density-functional theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janak's theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janak's theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principles context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the density-functional perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion approximation. For the two different numerical approaches without non-rigid-ion terms, the agreement is better than 7 μeV in the case of diamond, which represent an agreement tof ive significant digits. The magnitude of the non-rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies. [ABSTRACT FROM AUTHOR]