## 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:

1. How many atoms are there in the cell? Look also the the output from the CRYSTAL calculation (the LogFile).
2. How many bands are visualised in the band structure?
3. What are the differences between the band structure and the energy levels diagrams obtained in the previous sections, H100 and H100 II?
4. What are the differences between the current band structure and the one obtained for the H polymer?
5. Where are the bonding and anti-bonding states?

Optional questions::

1. Is there any non-bonding state?

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