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Computational materials science

Which statement about the ideas behind density functional theory (DFT) is correct?

  1. ABased on the electron density determining the ground-state energy, it solves the Kohn–Sham equations and treats electron interactions with an approximate exchange-correlation functional
  2. BIt fits the form of an interatomic potential to experimental data and solves Newton's equations of motion for the atoms, so the electronic states never appear anywhere in the calculation
  3. CIt obtains the wave functions of all electrons exactly, without any exchange-correlation approximation, so it predicts any property of any material with the same accuracy as experiment does
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Answer: A. Based on the electron density determining the ground-state energy, it solves the Kohn–Sham equations and treats electron interactions with an approximate exchange-correlation functional

The wave function of many electrons has too many variables to be solved as it is. DFT takes the electron density as its main variable, based on the Hohenberg–Kohn theorem that the ground-state energy is determined by the electron density, a function of only three dimensions. In practice, the Kohn–Sham equations, in which fictitious non-interacting electrons move in an effective potential, are solved repeatedly until the electron density no longer changes (a self-consistent calculation). The complicated interactions between electrons are gathered into the exchange-correlation functional, for which approximations such as LDA and GGA are used, so the results are not exact and their accuracy differs with the material and property. Solving equations of motion with an empirical interatomic potential is classical molecular dynamics.

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More Computational materials science questions

  1. Which is a correct tendency of the results of standard DFT calculations using LDA or GGA exchange-correlation functionals?
  2. A 108-atom supercell (with periodic boundary conditions) of a metal calculated with DFT has a total energy of −405.00 eV. Removing one atom to create one vacancy and relaxing the structure gives −400.10 eV. Which is closest to the vacancy formation energy calculated as E_v = E(N−1) − [(N−1)/N]E(N)?
  3. In molecular dynamics, you want to integrate the equations of motion with a time step of 2 fs to calculate atomic motion over 1 ns. How many time steps are needed?
  4. Which statement about the interatomic potentials used in molecular dynamics is correct?
  5. Argon is described by the Lennard-Jones potential V(r) = 4ε[(σ/r)¹² − (σ/r)⁶] with σ = 0.34 nm. Which is closest to the interatomic distance r₀ at which the energy is a minimum?