The H slab
Up to now, a system with one peridic direction
has been considered. In this section, a hydrogen layer/slab
will be studied.
A cell with only a hydrogen atom
that is repeated by translation in two directions
is the way adopted to tackle this problem.
The cell is described by three
lattice parameters:
two lattice vectors,
a and b, and the angle between a and b,
;
in this case a=b
and =90º.
The infinite number of electronic states, that form a continuum in
energy, are grouped together in a band.
Each level in a band is labelled by a vector
k=(kx,ky).
The quantity k belongs to a space called,
the reciprocal space; in this space a twodimentional cell
can be also defined, the reciprocal cell, and it is
useful and convenient, as the system is also periodic in
the reciprocal space.
The reciprocal lattice parameters a* and b*
are related to the lattice parameters of the cell in direct space
according to the following formulas:
and
.
in addition, a* is perpendicular to b
and b* to a.
In this section you will calculate the wavefunction
and the band structure
for the hydrogen layer/slab.
Exercise 1: Start DLVisualize,
run a CRYSTAL calculation for the H slab:
H_slab.inp
Exercise 2: Run a CRYSTAL properties calculation
of the band structure for the H slab.
In the CRYSTAL Bands panel,
note that the coordinates are expressed in unit of a*
and b*.
Questions:
- How many atoms are there in the cell?
Look also the the output from the CRYSTAL
calculation (the LogFile).
- How many bands are visualised in the band structure?
- What are the differences between the band structure and the energy levels
diagrams obtained in the previous sections,
H100 and
H100 II?
- What are the differences between the current band structure
and the one
obtained for the H polymer?
- Where are the bonding and anti-bonding states?
Optional questions::
- Is there any non-bonding state?
Index
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