Direct method
PHONON
An ab initio program optimizes the
structure of the crystalline supercell
within constraints imposed by a
crystallographic space group.
In optimized configuration the forces
acting on all atoms of the supercell vanish.
Displacing one atom from its equilibium position,
one generates non-zero Hellmann-Feynman
forces acting on all atoms of the supercell.
The lattice dynamics requires to know the force constants,
which are the second derivatives of the potential energy.
In the direct method one calculates the
force constants from the Hellmann-Feynman forces,
and from the used atomic displacements.
In this way all force constants of the supercell
can be found.
To obtain the reliable phonon dispersion relations the supercell
diameter should be about 8 - 10 angsterms.
The magnitude of the force constants
beyond that distnce is usually negligible,
and in such a case
the phonon dispersion curve can be exactly calculated.
But even if the supercell size is small, exact phonon
frequencies can be obtained for the wave vectors
commensurate with the supercell size.
Then, the phonon dispersion curves are the
symmetry controlled interpolations between the exact points.
For high-symmetry supercells treated by an ab initio program,
Phonon calculates the phonon dispersion curves
within minutes.
Within the direct method approach and according to the
symmetry imposed by the crystal space group
Phonon calculates the following items:
- Required atomic displacements for generating the Hellmann-Feynman forces
- Wave vectors at which exact phonon frequencies can be calculated
- Neighbor list of atoms in the supercell
- Symmetry of force constant's matrices
- Number of independent parameters for each force constant matrix
- Modification of the force constants due to
translational-rotational invariances
- Plot the force constants as a functin of distance
between involved atoms
- Phonon dispersion relations along any line of reciprocal space
- Frequency of the soft mode if it appears
- LO/TO splitting from known effective charges and dielectric constant
- Polarization vectors for any mode
- Atomic displacements related to a phonon mode
- Irreducible representations of all phonon modes at the
Brillouin zone center
- Total density of phonon states
- Partial density of phonon states for each
degree of freedom and each atom
See: