The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements

The adsorption of benzene on metal surfaces is an important benchmark system for hybrid inorganic/organic interfaces. The reliable determination of the interface geometry and binding energy presents a significant challenge for both theory and experiment. Using the Perdew-Burke-Ernzerhof (PBE), PBE+vdW (van der Waals) and the recently developed PBE+vdW surf (densityfunctional theory with vdW interactions that include the collective electronic response of the substrate) methods, we calculated the structures and energetics for benzene on transition-metal surfaces: Cu, Ag, Au, Pd, Pt, Rh and Ir. Our calculations demonstrate that vdW interactions increase the binding energy by more than 0.70 eV for physisorbed systems (Cu, Ag and Au) and by an even larger amount for strongly bound systems (Pd, Pt, Rh and Ir). The collective response of the substrate electrons captured via the vdW surf method plays a significant role for most substrates, shortening the equilibrium distance by 0.25 Å for Cu and decreasing the binding energy by 0.27 eV for Rh. The reliability of our results is assessed by comparison with calculations using the random-phase approximation including renormalized single excitations, often hard to interpret, or even lacking. For example, due to the relative difficulty of controlling and measuring weakly bound systems, no experimental adsorption height has been reported so far for Bz physisorbed on noble metals. The only experimentally deduced adsorption height, to the best of our knowledge, was determined for the disordered Bz chemisorbed on the Pt(111) surface at a coverage close to or less than one [36].The binding energy, which reflects the strength of the interaction between an adsorbate and the substrate, is another key parameter for the description of HIOS. Experimental binding energies are mainly obtained by temperature-programmed desorption (TPD) [22][23][24][25]27] and microcalorimetry measurements [32,[37][38][39]. TPD is the most extensively used method for determining the kinetic and thermodynamic parameters of desorption processes and decomposition reactions. The desorbing molecular species are selected by their mass, while the amount of adsorbate is determined by integrating the peaks of the desorption spectrum. The Redhead formula is typically used to calculate the adsorption energy based on three parameters: the desorption temperature, the heating rate and a pre-exponential factor [40]. The wide range of empirical pre-exponential factors (10 13 -10 19 s −1 ) that are typically used for molecular desorption may cause a notable uncertainty in the determined binding energy [41][42][43]. TPD experiments have been carried out to study the interaction of Bz with the Cu [13], Ag [24] and Au surfaces [29]. However, special attention must be paid to the interpretation of TPD spectra for the Pd, Pt and Rh surfaces, because the adsorbed Bz molecules may decompose during heating, in particular at low coverage [44]. Here, we revisit the adsorption energies from the measured TPD spectra for Bz on Cu(111), A...

van der Waals (vdW) energy corrected density-functional theory [Phys. Rev. Lett. 102, 073005 (2009)] is applied to study the cohesive properties of ionic and semiconductor solids (C, Si, Ge, GaAs, NaCl, and MgO). The required polarizability and dispersion coefficients are calculated using the dielectric function obtained from time-dependent density-functional theory. Coefficients for "atoms in the solid" are then calculated from the Hirshfeld partitioning of the electron density. It is shown that the Clausius-Mossotti equation that relates the polarizability and the dielectric function is accurate even for covalently-bonded semiconductors. We find an overall improvement in the cohesive properties of Si, Ge, GaAs, NaCl, and MgO, when vdW interactions are included on top of the Perdew-Burke-Ernzerhof or Heyd-Scuseria-Ernzerhof functionals. The relevance of our findings for other solids is discussed.

Accurate and careful benchmarking of different density-functional approximations (DFAs) represents an important source of information for understanding DFAs and how to improve them. In this work we have studied the lattice constants, cohesive energies, and bulk moduli of 64 solids using six functionals, representing the local, semi-local, and hybrid DFAs on the first four rungs of Jacob's ladder. The set of solids considered consists of ionic crystals, semiconductors, metals, and transition metal carbides and nitrides. To minimize numerical errors and to avoid making further approximations, the full-potential, all-electron FHI-aims code has been employed, and all the reported cohesive properties include contributions from zero-point vibrations. Our assessment demonstrates that current DFAs can predict cohesive properties with mean absolute relative errors of 0.6% for the lattice constant and 6% for both the cohesive energy and the bulk modulus over the whole database of 64 solids. For semiconducting and insulating solids, the recently proposed SCAN meta-GGA functional represents a substantial improvement over the other functionals. However, when considering the different types of solids in the set, all of the employed functionals exhibit some variance in their performance. There are clear trends and relationships in the deviations of the cohesive properties, pointing to the need to consider, for example, long-range van der Waals (vdW) interactions. This point is also demonstrated by consistent improvements in predictions for cohesive properties of semiconductors when augmenting GGA and hybrid functionals with a screened Tkatchenko-Scheffler vdW energy term.In this work, we explore the question of accuracy of DFAs on the first four rungs of Jacob's ladder proposed by Perdew and Schmidt [3,21], with each rung corresponding to more ingredients and contributions (besides the electron density) forming the DFA, ideally, leading to DFAs with improved accuracy. The local-density approximation (LDA) [2] represents the first rung of Jacob's ladder, considering only the density itself, and therefore it is a successful approximation for systems in which the electron density varies slowly, such as nearly free-electron metals, but is also surprisingly successful for less-uniform systems, such as molecules and semiconductors. However, there are many features that LDA fails to describe, with lattice constants typically being too small, up to 5% shorter than experiment, and cohesive energies (or atomization energies in molecules) that are very inaccurate, typically off by 20%-30% [19].Functionals based on the generalized gradient approximation (GGA) are on the next rung of the ladder, and represent an extension of the LDA functional by introducing the gradient of the electron density. They are also referred to as semi-local DFAs, and are successful in improving over LDA for certain properties. For example, they cure the overbinding problem of LDA and predict more accurate bond lengths. However, they show a tendency towards underb...