Nonanalytical term of force constant
LO and LA modes in semiconductor or insulator
may have long range interaction when
. On
contrary to these modes, TO and TA modes may have short range
interaction. Phonon calculation technique which fropho employs can
treat TO, LA and TA mode, but can not treat LO mode since the long
range the dipoledipole interaction of LO mode breaks the periodic
boundary condition. To correct this error, nonanalytical term is
added to dynamical
matrix [17,18,19]
as follows,

(3.17) 
where this is given in atomic unit.
is
the normal dynamical matrix, is the Born effective charge
tensor of the th atom in the unit cell, is the volume
of the unit cell, and
is the high
frequency dielectric contant tensor.
In fropho this is implemented as follows. The nonanalytical term is
multiplied with a function that is rapidly decreasing with getting
away from
. Then the dynamical matrix of the
general
is written in,

(3.18) 
where and are the adjustable damping factors. They should
be chosen as the damping function becomes close to zero at Brillouin
zone surface.
togo
20090212