  Based on ab initio density-functional-theory using generalized gradient
approximation, we systematically study the optical and electronic properties of
the insulating dense sodium phase (Na-hp4) reported recently [Ma \textit{et
al.}, Nature \textbf{458}, 182 (2009)]. The structure is found optically
anisotropic and transparent to visible light, which can be well interpreted
using its electronic band structure and angular moment decomposed density of
states. Through the bader analysis of Na-hp4 at different pressures, we
conclude that ionicity exists in the structure and becomes stronger with
increasing pressure. In addition, the absorption spectra in the energy range
from 1.4 to 2.4 eV are compared with recent experimental results and found good
agreement. It is found that the deep-lying valence electrons participate in the
interband transition.
