  Currently, self-induced InAlN core-shell nanorods enjoy an advanced stage of
accumulation of experimental data from their growth and characterization as
well as a comprehensive understanding of their formation mechanism by the ab
initio modeling based on Synthetic Growth Concept. However, their electronic
and optical properties, on which most of their foreseen applications are
expected to depend, have not been investigated comprehensively. $G_0W_0$ is
currently regarded as a gold-standard methodology with quasi-particle
corrections to calculate electronic properties of materials in general. It is
also the starting point for higher-order methods that study excitonic effects,
such as those based on the Bethe-Salpeter equation. One major drawback of
$G_0W_0$, however, is its computational cost, much higher than
density-functional theory (DFT). Therefore, in many applications, it is highly
desirable to answer the question of how well approaches based on DFT, such as
e. g. LDA, LDA-1/2, and mBJ, can approximately reproduce $G_0W_0$ results with
respect to the electronic and optical properties. Thus, the purpose of the
present paper is to investigate how the DFT-based methodologies LDA, LDA-1/2,
and mBJ can be used as tools to approximate $G_0W_0$ in studies of the
electronic and optical properties of scaled down models of core-shell InAlN
nanorods. For these systems, we observed that band gaps, density of states,
dielectric functions, refractive indexes, absorption and reflectance
coefficients are reasonably well described by LDA-1/2 and mBJ when compared to
$G_0W_0$, however, at a much more favorable computational cost.
