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
two lattice vectors,
a and b, and the angle between a and b,
in this case a=b
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:
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*.