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Computational materials science

Which is a correct tendency of the results of standard DFT calculations using LDA or GGA exchange-correlation functionals?

  1. AThey tend to overestimate the band gaps of semiconductors and insulators compared with experiment; for silicon GGA gives about 2 eV
  2. BThey tend to underestimate the band gaps of semiconductors and insulators compared with experiment; for silicon GGA gives about 0.6 eV
  3. CBesides the ground state at 0 K, they give finite-temperature free energies and melting points directly from a single structural optimization
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Answer: B. They tend to underestimate the band gaps of semiconductors and insulators compared with experiment; for silicon GGA gives about 0.6 eV

It is well known that with LDA or GGA, a band gap read from the difference of eigenvalues of the Kohn–Sham equations comes out smaller than experiment. For silicon, GGA gives about 0.6 eV, roughly half the experimental 1.12 eV, so the statement that they overestimate gets the trend backwards. When accurate values are needed, hybrid functionals or the GW approximation are used. On the other hand, quantities tied to the total energy of the ground state, such as lattice parameters, elastic moduli and formation energies, are obtained with good accuracy for many materials. Ordinary DFT is a calculation of the ground state at 0 K, so obtaining finite-temperature properties requires combining it with calculations of lattice vibrations (phonons) or molecular dynamics. Standard functionals also describe van der Waals forces poorly, so corrections are added for layered materials and adsorption.

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