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A detailed analysis of the optical properties of filled tetrahedral semiconductors Li 3 AlN 2 and Li 3 GaN 2 has been performed, using the full potential linearized augmented plane wave method within the density functional theory. The real and imaginary parts of the dielectric function e(x), the optical absorption coefficient I(x), the reflectivity R(x), and the electron energy loss function are calculated within the random phase approximation. The interband transitions responsible for the structures in the spectra are specified. Looking at optical matrix element, we note that the major peaks are dominated by transition from metal s, N 2p states to N 2p, Ga 3d states. The theoretical calculated optical properties and electron energy loss spectrum yield a static dielectric constant of 5.34 and a plasmon energy of 19.47 eV for Li 3 GaN 2 . In the Li 3 AlN 2 compound, the static dielectric constant decreases to 4.75 and yields a plasmon energy of 18.5 eV. The effect of spin-orbit coupling on the optical properties is also investigated and found to be quite small, especially in the low-energy region. In order to check the reliability of our calculations, analogous results obtained for Be 3 N 2 in the same structure [space group Ia3(206)] are included in this work.

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A detailed analysis of the electronic and structural properties of the filled tetrahedral semiconductors Li 3 AlP 2 and Li 3 AlAs 2 has been performed, using the full potential linearized augmented plane wave method within the density functional theory. Experimental results about the structural properties, involves the positions of the elements Al and P(As). Since there were not any other efforts about the positions of the Li elements in these compounds, so to our knowledge there was no theoretical study about them till now. In the first step the interactional forces between atoms were minimized. The calculated internal coordinations of atoms agree well with the experimental results. Using these positions we obtained the equilibrium lattice constants, bulk modulus and their pressure derivative. In the second step the electronic properties of Li 3 AlP 2 and Li 3 AlAs 2 have been studied. The study of total and partial electronic DOS indicate the main contribution of DOS consists of P(As) 3p(4p) and P(As) 3s(4s) states. Our band structure calculation verifies that Li 3 AlP 2 is an indirect gap semiconductor with a value of about 2.36 eV between valance band maximum occuring at H point and conduction band minimum occuring at Г point; though the difference between the direct (2.38 eV) and indirect (2.36 eV) is very small. We also found that Li 3 AlAs 2 is a direct band gap (1.49 eV) in the center of BZ.