## 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**=(k_{x},k_{y}).
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,
H
_{100} and
H_{100} 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?

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