ent insulating phase Na-hp4 using the first-principles method. The insulating mechanism that exclusionary ef- fect induces the valence electrons being excluded from the core region is clearly demonstrated from the calculated band structure, angular moment decomposed density of states and valence charge density. The dielectric func- tions and all main optical spectra indicate that Na-hp4 is optically anisotropic. The macroscopic dielectric con- stants ε ∞ have been obtained and are expected to be useful for future reference. Especially, our calculated ab- sorption spectrum in the energy range from 1.4 to 2.4 eV agrees well with the experimental observation. Fi- nally, we have shown that during the interband transi- tion, deep-lying valence electrons of Na-hp4 also partici- pate. large optical anisotropy in Na-hp4. Since the optical properties of Na-hp4 are anisotropic, it is particularly interesting to calculate the effective number of valence electrons per Na atom n$_{eff}$ contribut- ing to the optical properties in each direction. This can be accomplished by means of the sum rule 22 : where E$_{m}$ denotes the upper limit of integration, m is the electron mass, and N stands for the electron density. The effective number of valence electrons per Na atom participating in the interband transitions along the crys- tallographic directions at 320 GPa is shown in Fig. 7 as a function of$_{E}$$_{m}$. One can see that$_{n}$$_{eff}$ remains lager be- fore 13 eV and smaller after 13 eV in E || z direction than in E || x ( y ) direction. This is connected with the larger reflectivity feature observed in E || z direction at low en- ergy range than in E || x ( y ) direction. In addition, the n$_{eff}$ doesn’t reach a saturation value up to 30 eV. This shows that deep-lying valence orbitals do participate in the interband transition. We thank Yanming Ma for dicussions. This work was supported by NSFC under Grant No. 60776063, No. 10734140 and No. 10674021, the National Basic Re- search Program of China (973 Program) under Grant No. 2009CB929103 and No. 2005CB724500. In summary, we have performed systematic study of the electronic and optical properties of the transpar- Acknowledgments IV. CONCLUSIONS 6 n$_{eff}$ = 2 m Ne $^{2}$h2 ∫ E$_{m}$ 0 E $_{(}$Im$_{(}$$_{ε}$$_{))}$$_{dE,}$ (9) Figure 7: (Color online) Calculated effective number of elec- trons n eff participating in the interband optical transitions along the principle axes at 320 GPa. Figure 6: (Color online) (a) Calculated optical conductivity spectrum σ ( ω ) , (b) reflectivity spectrum R ( ω ) , (c) energy- loss spectrum L ( ω ) , (d) refractive index n ( ω ) , and (e) ex- tinction coefficient k ( ω ) along the principal axes at 320 GPa. GLYPH<s48> GLYPH<s54> GLYPH<s49>GLYPH<s50> GLYPH<s49>GLYPH<s56> GLYPH<s50>GLYPH<s52> GLYPH<s51>GLYPH<s48> GLYPH<s32> GLYPH<s69>GLYPH<s124> GLYPH<s124> GLYPH<s120>GLYPH<s32> GLYPH<s32> GLYPH<s40> GLYPH<s69>GLYPH<s124> GLYPH<s124> GLYPH<s121> GLYPH<s41> GLYPH<s32> GLYPH<s69>GLYPH<s124> GLYPH<s124> GLYPH<s122> GLYPH<s110> GLYPH<s101>GLYPH<s102>GLYPH<s102> GLYPH<s32> GLYPH<s69>GLYPH<s110>GLYPH<s101>GLYPH<s114>GLYPH<s103>GLYPH<s121>GLYPH<s32>GLYPH<s40>GLYPH<s101>GLYPH<s86>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s48>GLYPH<s46>GLYPH<s56> GLYPH<s49>GLYPH<s46>GLYPH<s54> GLYPH<s50> GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s51> GLYPH<s48>GLYPH<s46>GLYPH<s54> GLYPH<s50> GLYPH<s52> GLYPH<s48> GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s49>GLYPH<s53> GLYPH<s50>GLYPH<s48> GLYPH<s50>GLYPH<s53> GLYPH<s51>GLYPH<s48> GLYPH<s50> GLYPH<s52> GLYPH<s32> GLYPH<s32> GLYPH<s32>GLYPH<s40> GLYPH<s99>GLYPH<s109>GLYPH<s41> GLYPH<s45> GLYPH<s49> GLYPH<s32>GLYPH<s69>GLYPH<s124>GLYPH<s124>GLYPH<s120> GLYPH<s32>GLYPH<s32>GLYPH<s40>GLYPH<s69>GLYPH<s124>GLYPH<s124>GLYPH<s121> GLYPH<s41> GLYPH<s32>GLYPH<s69>GLYPH<s124>GLYPH<s124>GLYPH<s122> GLYPH<s40> GLYPH<s97>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s76> GLYPH<s32>GLYPH<s40> GLYPH<s41> GLYPH<s40> GLYPH<s98>GLYPH<s41> GLYPH<s40> GLYPH<s99> GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s82>GLYPH<s32>GLYPH<s40> GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s110>GLYPH<s32>GLYPH<s40> GLYPH<s41> GLYPH<s40> GLYPH<s100>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s75>GLYPH<s32>GLYPH<s40> GLYPH<s41> GLYPH<s112>GLYPH<s104>GLYPH<s111>GLYPH<s116>GLYPH<s111>GLYPH<s110>GLYPH<s32>GLYPH<s101>GLYPH<s110>GLYPH<s101>GLYPH<s114>GLYPH<s103>GLYPH<s121> GLYPH<s32>GLYPH<s40>GLYPH<s101>GLYPH<s86> GLYPH<s41> GLYPH<s40> GLYPH<s101>GLYPH<s41> GLYPH<s32>