Comparison of performance of van der Waals-corrected exchange-correlation functionals for interlayer interaction in graphene and hexagonal boron nitride

Exchange-correlation functionals with corrections for van der Waals interactions (PBE-D2, PBE-D3, PBE-D3(BJ), PBE-TS, optPBE-vdW and vdW-DF2) are tested for graphene and hexagonal boron nitride, both in the form of bulk and bilayer. The characteristics of the potential energy surface, such as the barrier to relative sliding of the layers and magnitude of corrugation, and physically measurable properties associated with relative in-plane and out-of-plane motion of the layers including the shear modulus and modulus for axial compression, shear mode frequency and frequency of out-of-plane vibrations are considered. The PBE-D3(BJ) functional gives the best results for the stackings of hexagonal boron nitride and graphite that are known to be ground-state from the experimental studies. However, it fails to describe the order of metastable states of boron nitride in energy. The PBE-D3 and vdW-DF2 functionals, which reproduce this order correctly, are identified as the optimal choice for general studies. The vdW-DF2 functional is preferred for evaluation of the modulus for axial compression and frequency of out-of-plane vibrations, while the PBE-D3 functional is somewhat more accurate in calculations of the shear modulus and shear mode frequency. The best description of the latter properties, however, is achieved also using the vdW-DF2 functional combined with consideration of the experimental interlayer distance. In the specific case of graphene, the PBE-D2 functional works very well and can be further improved by adjustment of the parameters.Comment: 22 pages, 4 figue

Readability of PBE reporting

The standardisation of Public Benefit Entities reporting has developed since 1992. Beneficial PBE reporting requires representations of position and performance, congruent with the Qualitative Characteristics of the conceptual framework. Non-regulation, optional adoption and sector-neutral standards led to issues of erroneous, complicated and misleading language in past reports. After calls for change, sector specific regulations and a tier system was introduced to address negative impacts on PBE reporting, and catering to different PBE types or users. This study aims to investigate if current reporting is meeting expected outcomes of regulation, specifically: Has the 2015 adoption of sector-specific standards impacted the readability of New Zealand PBE's annual reports? Data was collected by a convenience sample of PBE compliant annual reports and the corresponding sector-neutral report. These reports were converted, cleaned and measured for readability (by applying Flesch Reading Ease, Flesch Kincaid Grade Level and passive sentences measures). The resulting data was analysed with a Paired t-Test for a significant difference. FRE results indicated 93% of reports were tougher than ‘slightly difficult to read’. Most reports indicated a difference of one point or more, 53% of reports improved, while, 33% of reports declined after implementing the PBE regulations. This study concludes sector specific standards have not resulted in a consistent, statistically significant, difference in PBE for any readability measures studied. The use of jargon and the lack of specificity in readability measures are possible limitations of this research. However, for PBE’s to deliver efficient annual reports for users, further changes may be needed

Systematic investigation of a family of gradient-dependent functionals for solids

Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and combinations thereof. Several of these variations are proposed here for the first time. On a test set of 60 solids we perform a system-by-system analysis for selected functionals and a full statistical analysis for all of them. The impact of restoring the gradient expansion and of tightening the Lieb-Oxford bound is discussed, and confronted with previous results obtained from other codes, functionals or test sets. No functional is uniformly good for all investigated systems, but surprisingly, and pleasingly, the simplest possible modifications to PBE turn out to have the most beneficial effect on its performance. The atomization energy of molecules was also considered and on a testing set of six molecules, we found that the PBE functional is clearly the best, the others leading to strong overbinding

Automation methodologies and large-scale validation for GWGW, towards high-throughput GWGW calculations

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 {\em 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 work we develop such a method and, as a first application, use it to validate the accuracy of $G_0W_0$ using the PBE starting point, and the Godby-Needs plasmon pole model ($G_0W_0^\textrm{GN}$@PBE), on a set of about 80 solids. The results of the automatic convergence study utilized provides 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 $G_0W_0^\textrm{GN}$@PBE shows a correlation between the PBE and the $G_0W_0^\textrm{GN}$@PBE gaps that is much stronger than that between $GW$ and experimental gaps. However, the $G_0W_0^\textrm{GN}$@PBE gaps still describe the experimental gaps more accurately than a linear model based on the PBE gaps.Comment: 12 pages, 11 figure

Ideal, Defective, and Gold--Promoted Rutile TiO2(110) Surfaces: Structures, Energies, Dynamics, and Thermodynamics from PBE+U

Extensive first principles calculations are carried out to investigate gold-promoted TiO2(110) surfaces in terms of structure optimizations, electronic structure analyses, ab initio thermodynamics calculations of surface phase diagrams, and ab initio molecular dynamics simulations. All computations rely on density functional theory in the generalized gradient approximation (PBE) and account for on-site Coulomb interactions via inclusion of a Hubbard correction, PBE+U, where U is computed from linear response theory. This approach is validated by investigating the interaction between TiO2(110) surfaces and typical probe species (H, H2O, CO). Relaxed structures and binding energies are compared to both data from the literature and plain PBE results. The main focus of the study is on the properties of gold-promoted titania surfaces and their interactions with CO. Both PBE+U and PBE optimized structures of Au adatoms adsorbed on stoichiometric and reduced TiO2 surfaces are computed, along with their electronic structure. The charge rearrangement induced by the adsorbates at the metal/oxide contact are also analyzed and discussed. By performing PBE+U ab initio molecular dynamics simulations, it is demonstrated that the diffusion of Au adatoms on the stoichiometric surface is highly anisotropic. The metal atoms migrate either along the top of the bridging oxygen rows, or around the area between these rows, from one bridging position to the next along the [001] direction. Approximate ab initio thermodynamics predicts that under O-rich conditions, structures obtained by substituting a Ti5c atom with an Au atom are thermodynamically stable over a wide range of temperatures and pressures.Comment: 20 pages, 12 figures, accepted for publication in Phys. Rev.

Adsorption of Cu, Ag, and Au atoms on graphene including van der Waals interactions

We performed a systematic density functional study of the adsorption of copper, silver, and gold adatoms on graphene, especially accounting for van der Waals interactions by the vdW-DF and the PBE+D2 methods. In particular, we analyze the preferred adsorption site (among top, bridge, and hollow positions) together with the corresponding distortion of the graphene sheet and identify diffusion paths. Both vdW schemes show that the coinage metal atoms do bind to the graphene sheet and that in some cases the buckling of the graphene can be significant. The results for silver are at variance with those obtained with GGA, which gives no binding in this case. However, we observe some quantitative differences between the vdW-DF and the PBE+D2 methods. For instance the adsorption energies calculated with the PBE+D2 method are systematically higher than the ones obtained with vdW-DF. Moreover, the equilibrium distances computed with PBE+D2 are shorter than those calculated with the vdW-DF method