Performance of various density-functional approximations for cohesive properties of 64 bulk solids

Abstract

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...

Effect of dispersion corrections on ab initio predictions of graphite and diamond properties under pressure

“…The effect of those functionals developed to describe vdW binding have also been applied to diamond and other ionic or semiconducting solids. In the considered cases, an improved agreement with experimental data has been found [32][33][34][35][36][37][38].…”

“…However, we find that the zero-point energy varies by less than 1.3% when calculated with LDA, TS+SCS, and the MBD (at 0.17 meV/C). Similarly, Zhang et al found that the effect of the specific functional on the zero-point energy was negligible when considering a database of bulk solids [38]. We find that the vdW-corrected functionals actually increase in error compared to LDA when the contribution of zero-point motion is included.…”

Density Functional Model for van der Waals Interactions: Unifying Many-Body Atomic Approaches with Nonlocal Functionals

“…In practical calculations, the evaluation of the kinetic energy density is the computationally most demanding part of MBD-NL, but this means that its cost is still only a fraction of a single self-consistent cycle of a regular meta-GGA KS-DFT calculation. (Zhang et al, 2018). Each distribution is normalized to 62 (a.…”

“…For molecular crystals, -point grids with density of at least 0.8 Å in reciprocal space were used for all DFT and MBD calculations. For hard solids, we have used the -point density from (Zhang et al, 2018). All molecular and crystal geometries were taken directly from the respective benchmark sets without any relaxation.…”

“…The scale encoded by the color multiplies the equilibrium distance between the centers of mass of two given monomers. (b) Set of 64 hard solids(Zhang et al, 2018). The color encodes the class of a solid: transition metals (TM), main-group metals (MM), semiconductors (SC), transition-metal carbides and nitrides (TMCN), and ionic crystals (IC).…”