  We have computed the cross sections of the mutual neutralization reaction
between I$^{+}$ and I$^{-}$ for a collision energy varying from 0.001 eV to 50
eV. These cross sections were obtained using the adiabatic potential energy
curves of the I$_{2}$ system computed with a direct relativistic
Multi-Reference Configuration Interaction method and a semi-classical approach
(i.e. Landau Zener Surface Hopping). We report the cross sections towards the
following neutral states: $\text{I}(^{2}P_{3/2})+\text{I}(^{2}P_{3/2})$,
$\text{I}(^{2}P_{3/2})+\text{I}(^{2}P_{1/2})$,
$\text{I}(^{2}P_{1/2})+\text{I}(^{2}P_{1/2})$ and
$\text{I}(5p^{4}6s)+\text{I}(^{2}P_{3/2})$. We also discuss the cross sections
towards the two following excited ionic states :
$\text{I}^{-}(^{1}S_{0})+\text{I}^{+}(^{3}P_{0})$ and
$\text{I}^{-}(^{1}S_{0})+\text{I}^{+}(^{3}D_{2})$. The results of these
calculations are in accordance with recent experimental measurements conducted
in the double ion ring DESIREE in Stockholm. These results can be used to model
iodine plasma kinetics and thus to improve our understanding of the latter.
