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Phonon frequencies
The central quantity in the calculation of the phonon frequencies is
the forceconstant matrix
, since the
frequencies at wavevector are the eigenvalues of the
dynamical matrix
, defined as:

(1) 
where is a vector of the lattice connecting different
primitive cells and is the position of the atom in
the primitive cell. If we have the complete forceconstant matrix,
then
and hence the frequencies
can be obtained at any , so that
can be computed to any required precision. In principle, the elements
of
are nonzero for arbitrarily large
separations
, but in practice they decay rapidly with separation,
so that a key issue in achieving our target precision is the cutoff
distance beyond which the elements can be neglected.
Dario Alfe`
20120220