  Ewald-parameter dependence of Coulomb interaction in ionic crystals was
studied using a point-charge model. In the presence of the long-range
interaction, the ion configuration breaks spherical symmetry of local potential
and charge at each ion site, and gives non-scalar contributions to them. This
non-scalar potential has similar effects to Heisenberg interaction, while is
intrinsically distinct from conventional multipole expansions of the scalar
potential. Symmetry and magnitude of the scalar and non-scalar potentials are
similar for most materials despite the different definitions, but one exception
can be seen in parent materials of hole-doped high-$T_{\mathrm{c}}$ cuprates.
