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^*.

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. Where are the bonding and anti-bonding states? Is there any non-bonding state?

Index