  The hybrid halide perovskite CH$_3$NH$_3$PbI$_3$ is easy to manufacture and
inexpensive. Despite these, its efficiency as a solar cell is comparable to
today's efficient solar cells. For these reasons, it is attracting a lot of
attention today. However, the effects of the CH$_3$NH$_3^+$ (MA) molecule in
the perovskite structure on the electronic and structural properties are still
a matter of debate. Previous studies have generally focused on the rotation of
the MA molecule. In this study, from a different perspective, the effects of
the movement of the MA molecule along the C-N axis are investigated. With this
method, the effects of the MA molecule were examined in a more controlled way.
In this study, density functional theory (DFT) that accounts for van der Waals
(vdW) interactions was used in the calculations for the cases. According to the
data obtained, H-I ionic bonds are formed between the MA molecule and the
inorganic framework. Within the structure, the H-I bond length tends to be
preserved, although the position of the MA changes. In this mechanism, the I
ion plays an important role by moving away from its place in the Pb-I-Pb
alignment. The position of the I ion determines the nature of the band gap
transition. Another effect is on the value of the band gap. Depending on the
position of the I ion, the band gap may narrow by about 0.26 eV. The separation
of the I ion from the Pb-I-Pb alignment by the effect of the MA molecule breaks
the inverse symmetry. According to the data obtained from this study, this
mechanism in the band gap is due to the breaking of the inverse symmetry in the
crystal structure.
