Phonons from finite differences

First of all to run a phonon calculation a sufficiently large super cell is needed.

The phonon calculations are simply carried out by setting IBRION=5 or IBRION=6 in the INCAR file. IBRION=5, is available as of VASP.4.5, IBRION=6 starting from VASP.5.1. Both flags allow to determine the Hessian matrix (matrix of the second derivatives of the energy with respect to the atomic positions) and the vibrational frequencies of a system.

Important: Only zone centered (Γ-point) frequencies are calculated.

To calculate the Hessian matrix, finite differences are used, i.e. each ion is displaced in the direction of each Cartesian coordinate, and from the forces the Hessian matrix is determined. The two modes differ in the way symmetry is considered. For IBRION=5, all atoms are displaced in all three Cartesian directions, resulting in a significant computational effort even for moderately sized high symmetry systems. For IBRION=6, only symmetry inequivalent displacements are considered, and the remainder of the Hessian matrix is filled using symmetry considerations.

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