A point charge is spreaded as
:
while the self term ( of equation(15)) for atom
is obtained by setting
and
in the above expression.
In calculating the term given by formula (16) we are actually doing an error : as we
sum over the whole lattice we are considering also a spurious affect coming from the interaction of the charge
with itself. In a case of rigid ions the self term
simply subtracts to
and the spurious
terms in
and in
would delete each other. However in the case of polarizable shells, as can be seen
in equation (15),
and
have a life on their own, being multiplied sometimes by
and some other time by
. The spurious term has thus to be removed from
and
. That can be obtained
removing to the diagonal blocks of
and
, for each atom
the following quantity :
The following subsection explains how the difference between a point charge and a gaussian one is recovered