ABINIT Discussion Forums

Dear ABINIT Developers and Users,

I have a question about the way ABINIT handles infinite quantities in a ground state calculation.

The calculation of the [Coulombian] total energy of a crystal includes:

- the Coulomb repulsion of the nuclei,
- the Coulomb repulsion of the electrons, and
- the Coulomb attraction of the electrons to the nuclei.

For an infinite crystal each of these Colomb energies is infinite;
nonetheless when all of them are added,
we get a finite result for the Coulomb interaction.

My question is:
- how is this actually implemented / handled in the ABINIT code?
- on which routines of the code can I see this procedure?

Thanks,
Témok

It is only necessary to treat the particles within the basic unit cell, and then take advantage of the Bloch theorem to construct system averages (so energies are reported per cell, and each component of the energy is reported per cell). In order to handle the long-range nature of the Coulomb interaction, Ewald sum methods are used. The general approach is outlined in Payne et al., Rev. Mod. Phys. 64, 1045 (1992).