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Nanoparticle
============
ASE provides a module, :mod:`ase.cluster`, to set up
metal nanoparticles with common crystal forms.
Please have a quick look at the documentation.
Build and optimise nanoparticle
-------------------------------
Consider :func:`ase.cluster.Octahedron`. Aside from generating
strictly octahedral nanoparticles, it also offers a ``cutoff``
keyword to cut the corners of the
octahedron. This produces "truncated octahedra", a well-known structural motif
in nanoparticles. Also, the lattice will be consistent with the bulk
FCC structure of silver.
.. admonition:: Exercise
Play around with :func:`ase.cluster.Octahedron` to produce truncated
octahedra. Set up a cuboctahedral
silver nanoparticle with 55 atoms. As always, verify with the ASE GUI that
it is beautiful.
ASE provides a forcefield code based on effective medium theory,
:class:`ase.calculators.emt.EMT`, which works for the FCC metals (Cu, Ag, Au,
Pt, and friends). This is much faster than DFT so let's use it to
optimise our cuboctahedron.
.. admonition:: Exercise
Optimise the structure of our :mol:`Ag_55` cuboctahedron
using the :class:`ase.calculators.emt.EMT`
calculator.
Ground state
------------
One of the most interesting questions of metal nanoparticles is how
their electronic structure and other properties depend on size.
A small nanoparticle is like a molecule with just a few discrete energy
levels. A large nanoparticle is like a bulk material with a continuous
density of states. Let's calculate the Kohn--Sham spectrum (and density
of states) of our
nanoparticle.
As usual, we set a few parameters to save time since this is not a
real production calculation.
We want a smaller basis set
and also a PAW dataset with fewer electrons than normal.
We also want to use Fermi smearing since there could be multiple electronic
states near the Fermi level::
from gpaw import GPAW, FermiDirac
calc = GPAW(mode='lcao', basis='sz(dzp)', setups={'Ag': '11'},
occupations=FermiDirac(0,1))
These are GPAW-specific keywords --- with another code, those variables
would have other names.
.. admonition:: Exercise
Run a single-point calculation of the optimised :mol:`Ag_55`
structure with GPAW.
After the calculation, dump the ground state to a file::
calc.write('groundstate.gpw')
Density of states
-----------------
Once we have saved the ``.gpw`` file, we can write a new script
which loads it and gets the DOS::
import matplotlib.pyplot as plt
from gpaw import GPAW
calc = GPAW('groundstate.gpw')
energies, dos = calc.get_dos(npts=500, width=0.1)
efermi = calc.get_fermi_level()
In this example, we sample the DOS using Gaussians of width 0.1 eV.
You will want to mark the Fermi level in the plot. A good way
is to draw a vertical line: ``plt.axvline(efermi)``.
.. admonition:: Exercise
Use matplotlib to plot the DOS as a function of energy, marking
also the Fermi level.
.. admonition:: Exercise
Looking at the plot, is this spectrum best understood as
continuous or discrete?
The graph should show us that already with 55 atoms, the plentiful d
electrons are well on their way to forming a continuous band (recall
we are using 0.1 eV Gaussian smearing). Meanwhile the energies of the
few s electrons split over a wider range, and we clearly see isolated
peaks: The s states are still clearly quantized and have significant
gaps. What characterises the noble metals Cu, Ag, and Au,
is that their d band is fully occupied so that the Fermi level lies
among these s states. Clusters with a
different number of electrons might have higher or lower Fermi level,
strongly affecting their reactivity. We can conjecture that at 55
atoms, the properties of free-standing Ag nanoparticles are probably
strongly size dependent.
The above analysis is speculative. To verify the analysis
we would want to calculate s, p, and d-projected DOS to see if our
assumptions were correct. In case we want to go on doing this,
the GPAW documentation will be of help, see: `GPAW DOS <https://gpaw.readthedocs.io/tutorialsexercises/electronic/pdos/pdos.html#module-gpaw.dos>`__.
Solutions
---------
Optimise cuboctahedron:
.. literalinclude:: solution/Ag_part1_optimise.py
Calculate ground state:
.. literalinclude:: solution/Ag_part2_groundstate.py
Plot DOS:
.. literalinclude:: solution/Ag_part3_dos.py
|
