Relaxation()

Background

In this lesson we discuss two different methods to find the equilibrium structure of a system. In the first method, we use the GS part of Abinit to calculate the total energy of silicon for different volumes and then we fit the energy vs the volume with a model for the equation of state (EOS). The fit provides the optimal volume (i.e. the volume for which the total energy is minimal), as well as the bulk modulus (the 'compressibility' of the system). Note that this approach is only applicable to isotropic materials without any degree of freedom for the atomic positions. Indeed, the equation of state is obtained by performing a homogeneous compressions/dilatation of the initial Bravais lattice while keeping the atoms fixed in the initial high-symmetry positions.

In the second example, we find the equilibrium configuration of GaN. In this case, the approach used for computing the EOS of silicon is not applicable because, one should optimize both the lattice parameters as well the distance between Ga and N. For this reason, we employ the relaxation algorithms implemented in Abinit (ionmov and optcell) in which the forces and the stresses obtained at the end of the SCF cycle are used to find the minimum energy configuration.

The related abinit variables

    •   ionmov

    •   optcell

    •   dilatmx

    •   ecutsm

    •   ntime

    •   tolmxf

    •   tolrff

The full description of the variables, directly from the abinit documentation is available via the shell command:

        abidoc.py man inputvariable

that prints the official description of inputvariable.

As in the previous lessons, executing the python script creates the folder structure with the input files for this lesson.

For the flow_si_relax folder, look in particular to the changes in the unit cell (rprim) in the input files and the corresponding change in the unit cell volume (ucvol), total energy (etotal) and stresses (strten) in the output file. For the flow_gan_relax, observe in the output files how the automatic relaxation takes place. At each step of the relaxation, a full SCF-cycle is performed and forces and the stress are computed. The ions are then moved according to the forces and a new SCF-cycle is started. The procedure is interated until convergence is achieved. This is the reason why there are two stopping criteria for structural relaxation: tolrff or tolvrs are used for the SCF cycle whereas tolmxf govers the relaxation algorithm.

Exercises

Edit the input files to run the same jobs with different values of ecut.

You can also try to change the stopping criterion to see if this affects the final results.

Finally, try to generate the input file for silicon, and try to guess why setting the stopping criterion on the forces won't work in this case!