DFT: Plane Wave¶
QuantumATK can model the electronic properties of periodic quantum systems within the framework of density functional theory (DFT) using a plane-wave (PW) basis set. For closed and open systems, QuantumATK can also use the DFT-LCAO calculator, as discussed in DFT: LCAO. The DFT: Plane Wave calculator is not suitable for open systems, because it assumes periodic boundary conditions when solving the Kohn–Sham equations.
The key parameter in the self-consistent DFT-PW calculation of the Kohn–Sham equations is the electron density. The electron density then sets up an effective potential, which is given by the Hartree, exchange-correlation, and external potential. Knowing the effective potential allows us to obtain the Kohn–Sham Hamiltonian.
The PlaneWaveCalculator provides a description of electronic structure using DFT in combination with norm-conserving pseudopotentials or PAW potentials [Blo94]. This method is based on an expansion of the single-particle wave functions in a basis of plane-wave functions to solve the Kohn–Sham equations, instead of the LCAO basis set. The description for the mathematical formalism of the DFT-PW calculator and PAW potentials can be found in the QuantumATK reference paper by Smidstrup et al. [SMV+19] and the work by Blöchl [Blo94], respectively.
Unlike the DFT: LCAO calculator, the DFT: Plane Wave calculator does not support the XC+U mean-field Hubbard term and DFT-1/2 method yet, as well as some of QuantumATK analysis objects, which are available for the DFT-LCAO calculator.
|[Blo94]||(1, 2) P. E. Blöchl. Projector augmented-wave method. Phys. Rev. B, 50:17953–17979, Dec 1994. URL: https://link.aps.org/doi/10.1103/PhysRevB.50.17953, doi:10.1103/PhysRevB.50.17953.|
|[SMV+19]||S. Smidstrup, T. Markussen, P. Vancraeyveld, P. Wellendorffi, J. Schneider, T. Gunst, B. Verstichel, D. Stradi, P. A. Khomyakov, U. G. Vej-Hanseni, M.-E. Lee, S. T. Chill, F. Rasmussen, G. Penazzi, F. Corsetti, A. Ojanperä, K. Jensen, M. L. N. Palsgaard, U. Martinez, A. Blom, M. Brandbyge, and K. Stokbro. Quantumatk: an integrated platform of electronic and atomic-scale modelling tools. Journal of Physics: Condensed Matter, 32(1):015901, Oct 2019. URL: https://doi.org/10.1088/1361-648X/ab4007, doi:10.1088/1361-648x/ab4007.|