DFT: Plane Wave

Introduction

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 next section describes the similarities and differences of the PlaneWaveCalculator and LCAOCalculator.

Background information

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.

Similarly to the DFT: LCAO calculator, the DFT: Plane Wave calculator allows for calculating basic physical quantities:

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.

In addition to norm-conserving Pseudopotentials, the DFT: Plane Wave calculator supports PAW potentials.

[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.