2016: Reproducibility of DFT calculations (Lejaeghere et al)
Lejaeghere et al.$^1$ compared the calculated values for the equation of states for 71 elemental crystals from 15 different widely used DFT codes employing 40 different potentials. They defined a single parameter, Δ, which allowed the comparison of EOS calculated with different codes, giving a simple route to evaluating the reproducibility of DFT. Δ was defined as the root-mean-square energy difference between the equations of state of the two codes, averaged over all crystals in a purely elemental benchmark set.
The key result from this paper is that modern DFT codes now achieve a precision which is comparable to high-precision experiments; a delta value which is better than 1 meV/atom. This precision applies across various basis sets: plane waves, augmented plane waves, and numerical orbitals. It also applies to all-electron, PAW, and both ultra-soft and norm-conserving pseudopotential calculations. The work demonstrates that the precision of DFT implementations can be determined and also shows that the pseudopotential approach using recent libraries are precise in comparison with all-electron results.
The summary table from the paper is shown below; the numbers given are the RMS value for Δ across all 71 elements and colour indicates overall reliability.
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