Figure 4: (Color online) Valence charge density for Na-hp4 in (110) plane at 320 GPa. Contour lines are drawn from 0.0 to 1.0 with interval of 0.05 eÅ − $^{3}$. Figure 3: (Color online) Calculated total density of states, site-projected and angular momentum decomposed density of states of Na-hp4 at 320 GPa. The zero of the energy scale shows the position of the Fermi level. Table I: Calculated charge and volumes according to Bader partitioning as well as Na1-Na2 distances at different pres- sures. (about 0.6 electrons per Na atom) from Na1 to Na2. Be- sides, the valence of charge transfer increases with in- creasing pressure, which implies that the ionicity become stronger under compression. The main reason lies in that the energy level for Na2 is lower than that for Na1. With increasing pressure, the energy level difference becomes larger. exists between them. In the valence band, the s state covers larger energy range than the p and d states. From Fig. 3(d)-3(f), the $_{s}$, p and d states decrease to zero at 7.4, 5.8 and 3.1 eV below $_{E$_{f}$}$, while begin to emerge at 2.3, 1.8 and 2.2 eV above $_{E$_{f}$}$, respectively. The contribu- tions from$_{p}$ and$_{d}$ states imply$_{pd}$ and$_{pd}$ 2 hybridizations for Na1 and Na2, respectively. The 3 d contribution rises basically with increasing binding energy in conduction band, while the s state contribution begins to decrease with energy at about 3 eV above $_{E$_{f}$}$. In order to clarify the cause of the insulating phase, we present in Fig. 4 the valence charge density in the (110) plane of Na-hp4. Density isocontours are drawn at intervals of 0.05 $_{e}$Å − 3 color-coded from 0 (blue) to 1 $_{e}$Å − 3 (red). It shows that the charge concentration is very strong in interstitial regions, while minimal near and between the ions, which is resulted by the exclusion- ary effect mentioned above. The transition to the insu- lating phase (Na-hp4) is eventually culminated. From this figure, charge transfer from Na1 to Na2 can also be concluded consistently. To describe the ionic character quantitatively and more clearly, we perform the Bader analysis of Na-hp4 at different pressures. Bader analysis is a well established analysis tool for studying the topol- ogy of the electron density and suitable for discussing the ionicity of a material 19,20 . The charge Q$_{B}$ enclosed within the Bader volume ($_{V}$$_{B}$) is a good approximation to the total electronic charge of an atom. In present study 128 × 128 × 192 charge density grids are used, which give excellent precision of the effective charge ( < 0 . $_{01%)}$. The calculated results are listed in Table I. From Table I, the ionic character is obviously shown through a charge flux The interband optical functions of Na-hp4 at 320 GPa calculated using expressions (1) and (2) are shown in Fig. 5(a) and 5(b), in which x , y and z correspond to the three principle directions E || x , E || y , and E || z , regard- ing to the electric field vector polarized along the crys- tallographic axes x , y and z respectively. It is evident that Na-hp4 is optically anisotropic: E || x and E || y spec- tra are the same, while E || z spectrum is different. The macroscopic dielectric constants ε ∞ are calculated using different methods and approximations, as shown in Table II. A $_{Γ}$-centered grid with 18 × 18 × 12 k points yields 4 B. Optical properties of Na-hp4 Pressure Q$_{B}$ ( Na1 ) Q$_{B}$ ( Na2 ) V$_{B}$ ( Na2 ) V$_{B}$ ( Na2 ) Na1-Na2 (GPa) ( e ) ( e ) ( Å 3 ) ( Å 3 ) ( $^{Å}$) 260 8.4024 9.5976 5.0458 9.1543 0.9222 280 8.3950 9.6050 4.8979 8.8720 0.9191 300 8.3875 9.6125 4.4607 8.6191 0.9067 320 8.3828 9.6172 4.6468 8.3879 0.8991 340 8.3783 9.6217 4.5404 8.1746 0.8920 GLYPH<s78>GLYPH<s97>GLYPH<s49> GLYPH<s78>GLYPH<s97>GLYPH<s49> GLYPH<s78>GLYPH<s97>GLYPH<s50> GLYPH<s48>GLYPH<s46> GLYPH<s48>GLYPH<s48>GLYPH<s48> GLYPH<s48>GLYPH<s46> GLYPH<s53>GLYPH<s48>GLYPH<s48>GLYPH<s48> GLYPH<s49>GLYPH<s46> GLYPH<s48>GLYPH<s48>GLYPH<s48> GLYPH<s78>GLYPH<s97>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s54> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s56> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s54> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s56> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s54> GLYPH<s45>GLYPH<s56> GLYPH<s45>GLYPH<s52> GLYPH<s48> GLYPH<s52> GLYPH<s56> GLYPH<s49>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s56> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s54> GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s53> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s53> GLYPH<s45>GLYPH<s56> GLYPH<s45>GLYPH<s54> GLYPH<s45>GLYPH<s52> GLYPH<s45>GLYPH<s50> GLYPH<s48> GLYPH<s50> GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s32> GLYPH<s32> GLYPH<s32>GLYPH<s116>GLYPH<s111>GLYPH<s116>GLYPH<s97>GLYPH<s108> GLYPH<s32> GLYPH<s32>GLYPH<s115> GLYPH<s32>GLYPH<s112> GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s32> GLYPH<s32>GLYPH<s100> GLYPH<s40>GLYPH<s97>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s78> GLYPH<s97>GLYPH<s49>GLYPH<s95>GLYPH<s100> GLYPH<s32>GLYPH<s78> GLYPH<s97>GLYPH<s50>GLYPH<s95>GLYPH<s100> GLYPH<s32> GLYPH<s78> GLYPH<s97>GLYPH<s49>GLYPH<s95>GLYPH<s112> GLYPH<s32>GLYPH<s78> GLYPH<s97>GLYPH<s50>GLYPH<s95>GLYPH<s112> GLYPH<s32> GLYPH<s78> GLYPH<s97>GLYPH<s49>GLYPH<s95>GLYPH<s115> GLYPH<s32>GLYPH<s78> GLYPH<s97>GLYPH<s50>GLYPH<s95>GLYPH<s115> GLYPH<s40>GLYPH<s98>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s40>GLYPH<s99>GLYPH<s41> 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<s40>GLYPH<s101>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s40>GLYPH<s100>GLYPH<s41> GLYPH<s40>GLYPH<s102> GLYPH<s41> GLYPH<s78> GLYPH<s97>GLYPH<s49>GLYPH<s95>GLYPH<s116>GLYPH<s111>GLYPH<s116>GLYPH<s97>GLYPH<s108> GLYPH<s32> GLYPH<s78> GLYPH<s97>GLYPH<s50>GLYPH<s95>GLYPH<s116>GLYPH<s111>GLYPH<s116>GLYPH<s97>GLYPH<s108> GLYPH<s32> GLYPH<s68>GLYPH<s79>GLYPH<s83>GLYPH<s32>GLYPH<s40>GLYPH<s101>GLYPH<s86> GLYPH<s45> GLYPH<s49> GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s112> GLYPH<s120> GLYPH<s43>GLYPH<s112> GLYPH<s121> GLYPH<s32> GLYPH<s112> GLYPH<s122> GLYPH<s32> GLYPH<s32> GLYPH<s32>