  The bandstructure was calculated by the full-potential linearized augmented
plane wave method. The result reveals two important insights to the novel
second harmonic generation (SHG) of alpha-phase lithium iodate
($\alpha-LiIO_{3}$) crystal: the existence of finite intra-band momentum matrix
elements due to the non-inversion symmetry of the crystal illuminating the
potential of the intra-band transition, and the strong covalent bonding between
the $I$-atoms and the ligand $O$-atoms resulting the condition of the
double-resonance. An inter-band transition scenario in SHG as $\alpha-LiIO_{3}$
in nano-structure is proposed. The optical properties were calculated within
the theoretical framework of the time-dependent perturbation of the
independent-particle model. The dielectric tensors and the refractive index
were evaluated. Comparisons between the predictions and the results were made:
the x-ray near edge absorption spectra; the refractive index at the static
limit, and at finite frequencies. Possible factors attributing the calculation
errors is discussed.
