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Manuscript Title: PHON A program to calculate phonons using the small displacement method
Authors: Dario Alfè
Program title: PHON
Catalogue identifier: AEDP_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 180(2009)2622
Programming language: Fortran 90.
Computer: Any Unix, Linux.
Operating system: Unix.
RAM: Depends on super-cell size, but usually negligible
Keywords: phonons, vibrations, harmonic systems, thermodynamics of harmonic systems.
PACS: 63.20.-e, 63.20.dk.
Classification: 7.8.

External routines: subprograms ZHEEV and DSYEV (Lapack); needs BLAS. A tutorial is provided with the distribution which requires the installation of the quantum-espresso package (http://www.quantum-espresso.org)

Nature of problem:
Stable crystals at low temperature can be well described by expanding the potential energy around the atomic equilibrium positions. The movements of the atoms around their equilibrium positions can then be described using harmonic theory, and is characterised by global vibrations called phonons, which can be identified by vectors in the Brillouin zone of the crystal, and there are 3 phonon branches for each atom in the primitive cell. The problem is to calculate the frequencies of these phonons for any arbitrary choice of q-vector in the Brillouin zone.

Solution method:
The small displacement method: each atom in the primitive cell is displaced by a small amount, and the forces induced on all the other atoms in the crystal are calculated and used to construct the force constant matrix. Supercells of ~ 100 atoms are usually large enough to describe the force constant matrix up to the range where its elements have fallen to negligibly small values. The force constant matrix is then used to compute the dynamical matrix at any chosen q-vector in the Brillouin zone, and the diagonalisation of the dynamical matrix provides the squares of the phonon frequencies.
The PHON code needs external programs to calculate these forces, and it can be used with any program capable of calculating forces in crystals. The most useful applications are obtained with codes based on density functional theory, but there is no restriction on what can be used.

Running time:
Negligible, typically a few seconds (or at most a few minutes) on a PC. It can take longer if very dense meshes of q-points are needed, for example to compute very accurate phonon density of states.