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Table of Contents

Table of ContentsPBE and HSE06 band structures of GaAs

IntroductionPBE band structureHSE06 band structureBasis sets and integration gridsGermanium band structureReferences

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PBE and HSE06 band structures of GaAs

Version: 2016.4

In this tutorial you will learn the basics of how to use the FHI-aims calculator in ATK. FHI-aims is anall-electron electronic structure simulations package, so it does not employ any pseudopotentials.Moreover, it provides access to a wide range of beyond-GGA methods, including hybrid densityfunctionals, the random-phase approximation for total energies, and the GW approximation forexcited states. See the FHI-aims website for more details.

Attention

Due to the Synopsys acquisition of QuantumWise in the fall of 2017, see the Synopsys pressrelease, it is no longer possible to obtain a VNL-ATK license that includes access to the FHI-aimscalculator.

Introduction

We shall consider the band structure of GaAs using the PBE and HSE06 density functionals, the latterof which employs a screened variant of exact exchange. The HSE06 can be computationally intense,but is often more accurate than standard GGA methods. See also Refs. [HSE03], [PMH+06], and[KVIS06].

Tip

The video below considers silicon as an example semiconductor, while the written below it gives

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instructions using GaAs instead. Do not let this confuse you; the difference in workflow is verysmall.

ATK 2017: The video was made before the default ATK datafile format was changed to HDF5.Therefore, ATK 2017 users should just use the ”.hdf5” extension wherever the tutorial text says”.nc”.

Many more video tutorials are available on the QuantumWise YouTube channel.

Note

Your ATK license file must include the ATKFHIaims feature in order to use FHI-aims with ATK.Please contact us for any inquiries.

Important

This tutorial uses rather low accuracy settings in order to keep the computational time to aminimum, for instructional purposes. Please remember that settings related to k-point grids,basis sets, and integration grids should always be carefully checked for convergence inpublication-quality scientific work.

PBE band structure

Open the Builder and set up the GaAs crystal (zincblende structure).Send the structure to the Scripter and add the New Calculator and Analysis ‣Bandstructure script blocks.Open the New Calculator block and select the FHI-aims calculator.Select the PBE density functional and set up a 12x12x12 k-point grid.In Control Parameters, use the system default settings for “Insulator”.

Save the script as pbe.py (but do not close the Script Generator window) and run the script usingthe Job Manager. Alternatively, you can run the FHI-aims calculation from the command line:

atkpython pbe.py > pbe.log

The calculation should take only a few minutes, and the GaAs band structure will pop up on the VNLLabFloor. You can visualize it using the Bandstructure Analyzer and zoom in around the Fermilevel:

HSE06 band structure

You will now compute the same band structure using HSE06 and compare it to the PBE results.HSE06 can be computationally heavy for periodic systems, so we will here use a coarser 6x6x6 k-point grid.

Note

In the following, the PBE and HSE06 calculations are conveniently done after each other in asingle Python script. This illustrates one of the advantages of running FHI-aims calculationsthrough ATK Python scripts: Composite workflows are easily created using the flexibility ofPython scripting, see more at Python in ATK.

PBE calculation:Go back to the Script Generator window used above. Set the k-point grid to 6x6x6, andchange the band structure route to L, G, X.

HSE calculation:Add one more pair of New Calculator and Bandstructure blocks.Adjust the settings to make them identical to those for PBE, but chooce HSE06 as xcfunctional.

Finally, change the default output file name to hse.nc , and save the script as hse.py .

Run the calculations, preferably in parallel using e.g. 4 MPI processes:

You can of course obtain the same in a terminal:

QWDIR/libexec/mpiexec.hydra -n 4 atkpython hse.py > hse.log

where QWDIR is the VNL-ATK installation directory.

The calculations should take roughly 30 minutes in total if parallelized over 4 CPU cores on amodern laptop.

When finished, you can mark both band structure objects on the LabFloor and use the CompareData plugin to visualize both band structures in one plot:

The two band structures are clearly different; the HSE06 conduction bands (green, object ID gID003)are pushed up relative to the PBE ones, leading to a predicted band gap of 1.36 eV, not too far fromthe experimental value of 1.52 eV.

Note

Please be aware that the results above were obtained using Medium accuracy (“Light” integrationgrids and “Tier 1” basis sets) and a somewhat coarse k-point grid. Calculations with Tight settings,more basis functions, and more k-points may give different results. See more below.

Also note that band structure calculations should usually be preceeded by a first principlesgeometry optimization of the structure.

Basis sets and integration grids

Fig. 105 GaAs band gap calculated with different FHI-aims settings.

As seen in the figure above, FHI-aims results do in general depend on the computational settings, forexample basis sets and integration grids. “Tight” means more refined integrations grids than “Light”,while “Tier 2” has more basis functions than “Tier 1”. Note that increased computational qualityrequires in general also more computing resources (CPU hours and/or memory).

The calculations were performed using the script GaAs.py, which is reproduced below. The first 18script lines (highlighted) set up a Python loop over different combinations of basis sets and levels ofintegration accuracy. SCF and band structure calculations for all 6 combinations are hereby executedin a single ATK job.

# ====================================================basis_sets = [Light, Tight]tiers = [0, 1, 2]# ====================================================

for basis in basis_sets: for tier in tiers: out = 'GaAs_pbe_%s_tier-%i.nc' % (basis.speciesDefaultAsString(), tier)

#---------------------------------------- # Basis Set #---------------------------------------- basis_set = FHIaimsBasisSet() species_bases = [ FHIaimsBasisSetSpecies(Arsenic, basis, tier), FHIaimsBasisSetSpecies(Gallium, basis, tier), ] basis_set.setAndCheckSpeciesBasis(species_bases)

# ------------------------------------------------------------- # Bulk Configuration # ------------------------------------------------------------- # Set up lattice lattice = FaceCenteredCubic(5.6537*Angstrom) # Define elements elements = [Gallium, Arsenic] # Define coordinates fractional_coordinates = [[ 0. , 0. , 0. ], [ 0.25, 0.25, 0.25]] # Set up configuration bulk_configuration = BulkConfiguration( bravais_lattice=lattice, elements=elements, fractional_coordinates=fractional_coordinates

fractional_coordinates=fractional_coordinates )

# ------------------------------------------------------------- # Calculator # ------------------------------------------------------------- k_point_sampling = MonkhorstPackGrid(9,9,9) numerical_accuracy_parameters = NumericalAccuracyParameters( k_point_sampling=k_point_sampling, ) iteration_control_parameters = IterationControlParameters( damping_factor=0.6, algorithm=PulayMixer(), )

#---------------------------------------- # FHI-aims Parameters #---------------------------------------- fhiaims_parameters = FHIaimsParameters() fhiaims_parameters.addControlKeywordValuePair("sc_accuracy_eev","0.001") fhiaims_parameters.addControlKeywordValuePair("charge","0") fhiaims_parameters.addControlKeywordValuePair("sc_accuracy_etot","1e-06") fhiaims_parameters.addControlKeywordValuePair("sc_accuracy_rho","1e-05") fhiaims_parameters.addControlKeywordValuePair("occupation_type","gaussian 0.000001")

#---------------------------------------- # Working Directory #---------------------------------------- working_directory = '.'

#---------------------------------------- # FHI-aims calculator #---------------------------------------- calculator = FHIaimsCalculator( basis_set=basis_set, exchange_correlation=FHIaims_GGA_PBE, numerical_accuracy_parameters=numerical_accuracy_parameters, iteration_control_parameters=iteration_control_parameters, fhiaims_parameters=fhiaims_parameters, working_directory=working_directory, )

bulk_configuration.setCalculator(calculator) nlprint(bulk_configuration) bulk_configuration.update()

# ------------------------------------------------------------- # Bandstructure # ------------------------------------------------------------- bandstructure = Bandstructure( configuration=bulk_configuration, route=['G','L'], points_per_segment=5, ) nlsave(out, bandstructure)

The script plot.py may then be used to read the band structures, extract the band gap, plot theresults, and save the plot as a PNG file:

# READING DATAbasis_sets = [Light, Tight]tiers = [0, 1, 2]gaps = []labels = []for tier in tiers: for basis in basis_sets: out = 'GaAs_pbe_%s_tier-%i.nc' % (basis.speciesDefaultAsString(), tier) bandstructure = nlread(out, Bandstructure)[0] gap = bandstructure._directBandGap().inUnitsOf(eV) gaps.append(gap) label = "%s\n" % basis.speciesDefaultAsString().capitalize() label += "Tier %i" % tier labels.append(label)

# PLOTTING DATAimport pylabx = range(len(labels))pylab.figure(figsize=(7,4))pylab.plot(x, gaps, 'bo-')pylab.xlim((-0.2,5.2))pylab.ylabel('GaAs direct band gap (eV)')pylab.title('XC=PBE using 9x9x9 k-points')ax = pylab.gca()ax.set_xticks(x)ax.set_xticklabels(labels)pylab.tight_layout()pylab.savefig('GaAs.png')pylab.show()

You can try to run the scripts yourself – the calculations should take ca. 30 mins in total if run inserial on a modern laptop.

Germanium band structure

For completeness, you can also calculate the band structure of Ge using HSE06: Download the script germanium.py and run the calculation. It takes roughly 25 minutes when parallelized on 16 cores,but can of course be run on fewer cores. The result is illustrated below.

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References

[HSE03] Jochen Heyd, Gustavo E. Scuseria, and Matthias Ernzerhof. Hybrid functionals based on a screenedcoulomb potential. J. Chem. Phys., 118(18):8207–8215, 2003. doi:10.1063/1.1564060.

[KVIS06] Aliaksandr V. Krukau, Oleg A. Vydrov, Artur F. Izmaylov, and Gustavo E. Scuseria. Influence of theexchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys.,2006. doi:10.1063/1.2404663.

[PMH+06] J. Paier, M. Marsman, K. Hummer, G. Kresse, I. C. Gerber, and J. G. Angyan. Screened hybrid densityfunctionals applied to solids. J. Chem. Phys., 2006. doi:10.1063/1.2187006.

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