  We perform first-principles calculations of optical properties for
ferroelectric phase of $LiNbO_3$ crystal using density functional theory for
wide range of wavelengths, from far-infrared to ultraviolet. We study frequency
dependence of complex dielectric tensor and related quantities, such as
refractive and reflection indices, absorption coefficients, etc. Our
calculation incorporate advantages of numerical approaches based on
atomic-orbital all-electron Gaussian-type basis sets, as it is realized in
CRYSTAL14 program. We compared predictions obtained in general-gradient
approach with PBESOL exchange-correlation functional and in hybrid approach
with PBESOL0 functional, and we have found that hybrid PBESOL0 functional is
more applicable to describe the wide set of the experimental data.
