Coulomb long-range makes the real-space summation of forces very slow because of the
behaviour. On the other hand in reciprocal spaces Colomb interaction
behaves as
for a point charge. Convergence at high
can be accelerated
by gaussian-spreading the point charges, and introducing thus a gaussian factor in the Coulomb interaction.
This spreading changes the dynamical matrix, by a little amount if the spreading is small, and
the correct result can be recovered by subtracting the difference between the field of a gaussian charge
and the field of a point charge. This difference tends to zero very rapidly for distances bigger than
the charge spreading and thus the real-space summation converges vary fast.
The Coulomb contribution to the dynamical matric is thus made of two contribution :
a reciprocal space summation for spreaded charges, and a real space summation for the difference between
a point charges and the spreaded charges.