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
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,kz). 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*.