Modelling a gallium arsenide surface
This example shows how to use the atomistic simulation environment or ASE for short, to set up and run a particular calculation of a gallium arsenide surface. ASE is a Python package to simplify the process of setting up, running and analysing results from atomistic simulations across different simulation codes. For more details on the integration DFTK provides with ASE, see Atomistic simulation environment.
In this example we will consider modelling the (1, 1, 0) GaAs surface separated by vacuum.
Parameters of the calculation. Since this surface is far from easy to converge, we made the problem simpler by choosing a smaller Ecut and smaller values for n_GaAs and n_vacuum. More interesting settings are Ecut = 15 and n_GaAs = n_vacuum = 20.
miller = (1, 1, 0) # Surface Miller indices
n_GaAs = 2 # Number of GaAs layers
n_vacuum = 4 # Number of vacuum layers
Ecut = 5 # Hartree
kgrid = (4, 4, 1); # Monkhorst-Pack meshUse ASE to build the structure:
using ASEconvert
a = 5.6537 # GaAs lattice parameter in Ångström (because ASE uses Å as length unit)
gaas = ase.build.bulk("GaAs", "zincblende"; a)
surface = ase.build.surface(gaas, miller, n_GaAs, 0, periodic=true);Get the amount of vacuum in Ångström we need to add
d_vacuum = maximum(maximum, surface.cell) / n_GaAs * n_vacuum
surface = ase.build.surface(gaas, miller, n_GaAs, d_vacuum, periodic=true);Write an image of the surface and embed it as a nice illustration:
ase.io.write("surface.png", surface * pytuple((3, 3, 1)), rotation="-90x, 30y, -75z")Python: None
Use the pyconvert function from PythonCall to convert to an AtomsBase-compatible system. These two functions not only support importing ASE atoms into DFTK, but a few more third-party data structures as well. Typically the imported atoms use a bare Coulomb potential, such that appropriate pseudopotentials need to be attached in a post-step:
using DFTK
system = attach_psp(pyconvert(AbstractSystem, surface);
Ga="hgh/pbe/ga-q3.hgh",
As="hgh/pbe/as-q5.hgh")FlexibleSystem(As₂Ga₂, periodic = TTT):
bounding_box : [ 3.99777 0 0;
0 3.99777 0;
0 0 21.2014]u"Å"
Atom(Ga, [ 0, 0, 8.48055]u"Å")
Atom(As, [ 3.99777, 1.99888, 9.89397]u"Å")
Atom(Ga, [ 1.99888, 1.99888, 11.3074]u"Å")
Atom(As, [ 1.99888, 6.96512e-16, 12.7208]u"Å")
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Ga| |
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We model this surface with (quite large a) temperature of 0.01 Hartree to ease convergence. Try lowering the SCF convergence tolerance (tol) or the temperature or try mixing=KerkerMixing() to see the full challenge of this system.
model = model_DFT(system;
functionals=PBE(),
temperature=0.001, smearing=DFTK.Smearing.Gaussian())
basis = PlaneWaveBasis(model; Ecut, kgrid)
scfres = self_consistent_field(basis; tol=1e-4, mixing=LdosMixing());n Energy log10(ΔE) log10(Δρ) Diag Δtime
--- --------------- --------- --------- ---- ------
1 -16.58924001682 -0.58 5.4 556ms
2 -16.72539114260 -0.87 -1.01 1.0 281ms
3 -16.73065810185 -2.28 -1.57 2.4 355ms
4 -16.73125330517 -3.23 -2.16 1.0 272ms
5 -16.73132769707 -4.13 -2.59 1.9 1.04s
6 -16.73133623713 -5.07 -2.88 1.8 295ms
7 -16.73112007047 + -3.67 -2.64 1.9 310ms
8 -16.73111379114 + -5.20 -2.60 2.2 329ms
9 -16.73122791625 -3.94 -2.76 1.8 291ms
10 -16.73132397210 -4.02 -3.16 1.0 256ms
11 -16.73133771741 -4.86 -3.52 1.1 260ms
12 -16.73133981530 -5.68 -3.92 1.7 317ms
13 -16.73133976855 + -7.33 -3.94 2.1 319ms
14 -16.73134019333 -6.37 -4.60 1.0 248msscfres.energiesEnergy breakdown (in Ha):
Kinetic 5.8594014
AtomicLocal -105.6101557
AtomicNonlocal 2.3494788
Ewald 35.5044300
PspCorrection 0.2016043
Hartree 49.5615689
Xc -4.5976644
Entropy -0.0000035
total -16.731340193329