  The present work performs full bandstructure calculations to investigate the
structural effect and the transition mechanisms of the second harmonic
generation (SHG) susceptibility of the $\alpha-LiIO_{3}$ crystal. The anomalous
inconsistency of associated experimental data of the SHG susceptibility tensor
is elucidated to be dominated by the structural effect especially on the
topology of $O$-atoms. On the manipulation of the structural effect, the
modification of SHG susceptibility using an external pressure is simulated. The
calculations of SHG susceptibility tensor are completed at finite frequencies
and the static limit. The comparison with the experiments is also incorporated.
On the analysis of the transition mechanisms, the inter-band transition is
determined to entirely dominate the whole SHG susceptibility at the static
limit; however, the effect of the intra-band motion is revealed to be as
important as that of the inter-band transition at finite frequencies.
