This directory contains examples, which are designed to cover most of the capabilities of the DFT-FE code. Please refer to the README file inside each example directory for more detailed information regarding the example, the associated accuracy studies, and any important notes for the user to setup similar or related calculations using DFT-FE.

General guidelines on Finite-element discretization input parameters

We refer to DFT-FE manual for full input parameters list, their associated description, and the precedure to setup the input file. The manual also provides more in-depth discussion on the usage of the key input parameters in DFT-FE. Below, we briefly discuss the Finite-element (FE) discretization related input parameters which will be repeatedly used in all the examples. Other input parameters specific to the example are discussed inside the associated example subfolder.

The three important FE discretization related parameters in DFT-FE, which the user needs to set are the POLYNOMIAL ORDER, MESH SIZE AROUND ATOM, and ATOM BALL RADIUS.

• First, the POLYNOMIAL ORDER sets the order of the piecewise continuous FE interpolating polynomial, with higher values affording faster convergence rates with respect to discretization. Default value is set to 6. Based on our numerical investigations, we recommend POLYNOMIAL ORDER=7 for soft pseudopotentials (<20 Ha plane-wave cutoff), POLYNOMIAL ORDER=6 for medium/hard pseudpotentials, and POLYNOMIAL ORDER=5 for all-electron calculations to be most computationally efficient choices on both CPUs and GPUs.

• Second, the MESH SIZE AROUND ATOM input parameter sets the size (in Bohr units) of the FE mesh element around the atoms, with the mesh sizes away from the atoms and the intervening mesh adaptivity heuristically set inside the code depending on the domain boundary conditions. The MESH SIZE AROUND ATOM is the most important parameter for the user to control in pseudopotential DFT calculations. This parameter is inversely related to the plane-wave cutoff in plane-wave based DFT codes. Smaller mesh sizes lead to lower discretization related errors, but at the cost of more degrees of freedom. Based on our numerical validation studies as will be demonstrated in many of the examples, we obtain chemical accuracy (~1e-4 Ha/atom in energy, ~1e-4 Ha/Bohr in ionic forces and ~5e-6 Ha/Bohr^3 in cell stresses) using following choice of discretization parameters: (POLYNOMIAL ORDER=7, MESH SIZE AROUND ATOM=1.5---2.5) for soft pseudopotentials, and (POLYNOMIAL ORDER=6, MESH SIZE AROUND ATOM=0.5---1.5) for medium/hard pseudopotentials. We advice the users to use the above recommendations as starting choices only and always check the convergence of their quantity of interest with respect MESH SIZE AROUND ATOM. For all-electron calculations, a value of around 0.5 is a good starting choice (see Benzamide example).

• Third, the ATOM BALL RADIUS input paramter denotes the radius of ball enclosing every atom (in a.u.), inside which the mesh size is set close to MESH SIZE AROUND ATOM and coarse-grained in the region outside the enclosing balls. For the default value of 0.0, a heuristically determined value is used, which is good enough for most cases but can be a bit conservative choice for fully non-periodic and semi-periodic problems as well as all-electron problems. To improve the computational efficiency user may experiment with values of ATOM BALL RADIUS ranging between 3.0 to 6.0 for pseudopotential problems, and ranging between 1.0 to 2.5 for all-electron problems.

• Finally, for all-electron calculations MESH SIZE AT ATOM is another additional input parameter, which sets the size of the FE mesh element in the immediate vicinity of the atom. By default for all-electron problems this is set to 0.1 times MESH SIZE AROUND ATOM. However, the user may need to manually tune this parameter to obtain efficient FE mesh for all-electron problems. See examples 3 and 4 for more discussion on usage of MESH SIZE AT ATOM for all-electron problems.

To conclude, for most cases and for pseudopotential problems, choosing POLYNOMIAL ORDER=(6 for medium/hard pseudopotentials and 7 for soft pseudopotentials) and tuning MESH SIZE AROUND ATOM would suffice to achieve a reasonably efficient FE mesh which provides chemical accuracy in the DFT calculations.

List and brief description of the examples

• BCCMo

This example demonstrates a ground-state calculation with fully periodic boundary conditions on BCC Mo supercell with a mono-vacancy. Norm-conserving pseudopotential and PBE exchange correlation are used.

• AlNP

This example demonstrates a ground-state calculation with non-periodic boundary conditions on Al nanoparticle. Norm-conserving pseudopotential and PBE exchange correlation are used.

• Benzamide

This example demonstrates an all-electron ground-state calculation with non-periodic boundary conditions and ionic relaxation on Benzamide. PBE exchange correlation is used.

• Al12Mg17

This example demonstrates a ground-state calculation with fully periodic boundary conditions and combined ionic-cell relaxation on Al12Mg17 intermetallic. Multiple k-points for sampling the Brillouin zone, norm-conserving pseudopotential, and PBE exchange correlation are used.

• WS2-bilayer

This example demonstrates a spin-polarized and spin-unpolarized ground-state calculations with non-periodic boundary conditions and ionic relaxation on a isolated system containing WS2 bi-layer. Norm conserving pseudopotential and PBE exchange correlation is used

• LLZO

This example demonstrates a spin-polarized and spin-unpolarized ground-state calculations with fully periodic boundary conditions along with combined ionic-cell and stress relaxation on LLZO (Lithium-Lanthanum-Zirconium-Oxide) unit-cell. Gamma point for sampling the Brillouin zone, norm-conserving pseudopotential, and PBE exchange correlation are used.

• NEB/Li2O

This example demonstrates a Nudged Elastic Band Lithium Oxide 2x2x2 supercell with 1 Li vacancy employing periodic boundary conditions in all directions

• FeCuPt2Postprocess

This example demonstrates the postprocessing tools, bandstructure, density of states (DOS) and projected density of states (PDOS) plots for FeCuPt2 unit cell with fully periodic boundary conditions.

• Pt3Ni

This example demonstrates a hubbard calculation when all the atoms in the simulation have Hubbard correction. This is a non-periodic calculation with spin polarization.

• TiAl

This example demonstrates a hubbard calculation when some of the atoms in the simulation have Hubbard correction. This is a periodic gamma-point calculation with spin unpolarization.