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

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 and6%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 augmentingGGAand hybrid functionals with a screened Tkatchenko–
Scheffler vdW energy term.