4.11. Germanium solid

This example calculates a Germanium solid, utilizing the periodic boundary conditions of the code.

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import numpy as np

from eminus import Atoms, SCF
from eminus.units import ang2bohr, ev2ha

Create a germanium crystal with an FCC crystal structure

Here, a is not only the unit cell size but the lattice constant as well, defining the periodicity

As a reminder, the center option should not be used when explicitly using periodicity

Since electronvolt and Angstrom are common in solid-state physics convert the units here to atomic units

atom = "Ge8"
a = ang2bohr(5.658)
ecut = ev2ha(500)
pos = a * np.array(
    [
        [0, 0, 0],
        [0, 0.5, 0.5],
        [0.25, 0.25, 0.25],
        [0.25, 0.75, 0.75],
        [0.5, 0, 0.5],
        [0.5, 0.5, 0],
        [0.75, 0.25, 0.25],
        [0.75, 0.75, 0.25],
    ]
)
atoms = Atoms(atom=atom, pos=pos, a=a, ecut=ecut)

Use the pseudopotential from Tomas Arias (only local and only for germanium)

The GTH pseudopotential will work as well and would include non-local effects

Reduce the convergence tolerance for this example

scf = SCF(atoms, pot="Ge", etol=1e-4)
scf.run()

Save the density as a CUBE file

atoms.write("Ge_solid_density.cube", scf.n)

If you have the viewer extra installed, the following line will plot the unit cell and 20 isosurfaces of the density, such that 50% of the density is contained

# scf.view(plot_n=True, surfaces=20, percent=50)

Download 11_germanium_solid.py