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 mesh
Use ASE to build the structure:
using ASEconvert
using PythonCall
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);
CondaPkg Found dependencies: /home/runner/.julia/packages/ASEconvert/kvmT8/CondaPkg.toml
CondaPkg Found dependencies: /home/runner/.julia/packages/PythonCall/WMWY0/CondaPkg.toml
CondaPkg Resolving changes
+ ase
+ libstdcxx-ng
+ openssl
+ python
CondaPkg Initialising pixi
│ /home/runner/.julia/artifacts/cefba4912c2b400756d043a2563ef77a0088866b/bin/pixi
│ init
│ --format pixi
└ /home/runner/work/DFTK.jl/DFTK.jl/docs/.CondaPkg
✔ Created /home/runner/work/DFTK.jl/DFTK.jl/docs/.CondaPkg/pixi.toml
CondaPkg Wrote /home/runner/work/DFTK.jl/DFTK.jl/docs/.CondaPkg/pixi.toml
│ [dependencies]
│ openssl = ">=3, <3.1"
│ libstdcxx-ng = ">=3.4,<13.0"
│ ase = ">=3.23,<3.24"
│
│ [dependencies.python]
│ channel = "conda-forge"
│ build = "*cpython*"
│ version = ">=3.8,<4"
│
│ [project]
│ name = ".CondaPkg"
│ platforms = ["linux-64"]
│ channels = ["conda-forge"]
│ channel-priority = "strict"
└ description = "automatically generated by CondaPkg.jl"
CondaPkg Installing packages
│ /home/runner/.julia/artifacts/cefba4912c2b400756d043a2563ef77a0088866b/bin/pixi
│ install
└ --manifest-path /home/runner/work/DFTK.jl/DFTK.jl/docs/.CondaPkg/pixi.toml
✔ The default environment has been installed.
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 the ASE atoms
to an AtomsBase-compatible system.
This can then be used in the same way as other AtomsBase systems
(see AtomsBase integration for details) to construct a DFTK model:
using DFTK
using PseudoPotentialData
pseudopotentials = PseudoFamily("cp2k.nc.sr.pbe.v0_1.largecore.gth")
model = model_DFT(pyconvert(AbstractSystem, surface);
functionals=PBE(),
temperature=1e-3,
smearing=DFTK.Smearing.Gaussian(),
pseudopotentials)
Model(gga_x_pbe+gga_c_pbe, 3D):
lattice (in Bohr) : [7.55469 , 0 , 0 ]
[0 , 7.55469 , 0 ]
[0 , 0 , 40.0648 ]
unit cell volume : 2286.6 Bohr³
atoms : As₂Ga₂
atom potentials : ElementPsp(Ga, "/home/runner/.julia/artifacts/9a2a5dc89d1b33bff2ad61eaf2d000191050d15c/Ga.gth")
ElementPsp(As, "/home/runner/.julia/artifacts/9a2a5dc89d1b33bff2ad61eaf2d000191050d15c/As.gth")
ElementPsp(Ga, "/home/runner/.julia/artifacts/9a2a5dc89d1b33bff2ad61eaf2d000191050d15c/Ga.gth")
ElementPsp(As, "/home/runner/.julia/artifacts/9a2a5dc89d1b33bff2ad61eaf2d000191050d15c/As.gth")
num. electrons : 16
spin polarization : none
temperature : 0.001 Ha
smearing : DFTK.Smearing.Gaussian()
terms : Kinetic()
AtomicLocal()
AtomicNonlocal()
Ewald(nothing)
PspCorrection()
Hartree()
Xc(gga_x_pbe, gga_c_pbe)
Entropy()
In the above we use the pseudopotential keyword argument to
assign the respective pseudopotentials to the imported model.atoms.
Try lowering the SCF convergence tolerance (tol)
or try mixing=KerkerMixing() to see the full challenge of this system.
basis = PlaneWaveBasis(model; Ecut, kgrid)
scfres = self_consistent_field(basis; tol=1e-6, mixing=LdosMixing());
n Energy log10(ΔE) log10(Δρ) Diag Δtime --- --------------- --------- --------- ---- ------ 1 -16.58731169617 -0.58 5.3 1.06s 2 -16.72499645787 -0.86 -1.01 1.0 591ms 3 -16.73052609602 -2.26 -1.57 2.1 278ms 4 -16.73121597015 -3.16 -2.16 1.0 224ms 5 -16.73132220762 -3.97 -2.58 2.1 264ms 6 -16.73133188404 -5.01 -2.83 2.0 258ms 7 -16.73078007811 + -3.26 -2.44 2.2 284ms 8 -16.73126715740 -3.31 -2.77 2.4 265ms 9 -16.73114223005 + -3.90 -2.65 2.0 264ms 10 -16.73133977758 -3.70 -3.65 1.2 215ms 11 -16.73133595709 + -5.42 -3.45 3.2 309ms 12 -16.73134011151 -5.38 -3.99 1.2 217ms 13 -16.73133944032 + -6.17 -3.83 1.8 569ms 14 -16.73134017301 -6.14 -4.53 1.4 222ms 15 -16.73134019963 -7.57 -5.04 1.9 244ms 16 -16.73134019502 + -8.34 -4.86 2.1 283ms 17 -16.73134019980 -8.32 -5.27 1.1 208ms 18 -16.73134019997 -9.78 -5.44 1.0 207ms 19 -16.73134020043 -9.34 -6.05 1.9 238ms
scfres.energies
Energy breakdown (in Ha):
Kinetic 5.8593983
AtomicLocal -105.6100293
AtomicNonlocal 2.3494815
Ewald 35.5044300
PspCorrection 0.2016043
Hartree 49.5614425
Xc -4.5976641
Entropy -0.0000035
total -16.731340200428