## The H crystal

A cell with only a hydrogen atom
repeated by translation in three directions
will be considered.
The cell is described by six lattice parameters:
three lattice vectors,
**a**, **b** and **c**, and three angles
(between **b** and **c**),
(between **a** and **c**) and
(between **a** and **b**);
in this case **a**=**b**=**c**
and all the angles are
==
=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},k_{z}).
The quantity **k** belongs to a space called,
the **reciprocal space**; in this space a three dimentional 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**^{*}, **b**^{*}
and **c**^{*}
are related to the lattice parameters of the cell in direct space
according to the following formula:

.
In this section you will calculate the wavefunction
and the band structure
for the hydrogen crystal.

**Exercise 1**: Start DLVisualize,
run a CRYSTAL calculation for the H crystal:
H_crystal.inp

**Exercise 2**: Run a CRYSTAL properties calculation
of the band structure for the H crystal.

In the **CRYSTAL Bands** panel,
note that the coordinates are expressed in unit of **a**^{*},
**b**^{*} and **c**^{*}.

**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?
- Where are the bonding and anti-bonding states?

**Optional questions:**:
- Is there any non-bonding state?

Index