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Abstract (English):
Ion-molecular metal azides are well known because of their high reactivity, and nowadays they are widely used as energetic materials. Despite the large amount of experimental data exists on such kind compounds, the number of theoretical studies is still not so large. The aim of the present work is to study of the electronic structure of Me(N3)2 compounds, where Me=Sr, Ca, Cd, Hg. All the calculations have been carried out within the framework of the density functional theory with the use of the numerical pseudo-atomic orbitals basis. The results of the band structure calculations are presented in the work together with a maps of total and partial electronic density; the data on Cd(N3)2 and α-Hg(N3)2 are presented for the rst time. The values of band gaps calculated are in good agreement with those obtained by other authors or estimated in the experiments. The all the crystals under consideration, except of α-Hg(N3)2, are predominantly ionic compounds with a relatively small fraction of the covalent bonding. The overall structure of the valence band spectra, as well as the character of conduction band bottom, is similar to other heavy metal azides. The comparative analysis of the data on band gaps led to the conclusion about lesser stability of the heavy metal azides than that of the second group metal azides, what is also conrmed by the experimental data

Divalent azides, density functional theory, pseudo-atomic orbitals basis, band gap
INTRODUCTIONThe ion-molecular metal azides (general rational formula Men+(N3)2) are well known because of their high reactivity which manifests as their instability in respect of external impact. At the same time, the reaction rate of the decomposition process may vary signicantly for different types of metal azides what denes a scope of their practical applications including both initiating explosives (e.g. lead and silver azides), as well as sources of chemically pure nitrogen (alkali metal azides) [1].The present work was intended to study the electronic structure for a group of azides of divalent metals, which belongs to the second group of the periodic table (Sr(N3)2, Ca(N3)2) and a group of transition elements (Cd(N3)2, Hg(N3)2). While the strontium and mercuric azides have already been studied using the rst-principle methods [2, 3], the similar data on calcium and cadmium azides did not appear in the literature so far. Therefore, the study of such compounds is still the actual task nowadays.MATERIALS AND METHODS1. The method and computational parametersThe electronic structure calculations for the crystals under study have been performed within the framework of the density functional theory (DFT) and with the use of the pseudo-atomic orbitals basis (PAO, [4]). For the latter, the one-particle function is written as:) ,,()()( rkkCrkn∑Φ=µ αµ αµ αψwhere ),( rkµ αΦ are Bloch functions built as lattice sums of pseudo-functions localized at the atomic positions:) .(1),()(αµ αµ αϕαtarerkataki--Ω=Φ∑+The main advantage of that basis is its small dimension what makes possible the calculations for a complex compounds with the strongly localized electronic states to be performed in a quite effective way.The radial parts of the pseudo-atomic orbitals used in this work are presented in the numerical form on radial grid; those are nodeless solutions of the atomic problem with all-electron Coulomb potential replaced by the corresponding non-local pseudopotential.The calculations have been carried out within the both local density approximation (LDA) as parameterized by Perdew and Zunger [5] as well as generalized gradient one (GGA) with modied Becke-Johnson exchange potential [6]. The basis of pseudo-atomic orbitals has been generated for HGH pseudopotentials [7, 8]. In all cases the electronic density was calculated with the use of the special points method [9] for the 2x2x2 k-point grid and the linear tetrahedron method was applied to obtain the density of states. The following scheme has been adopted to perform the calculations: rst, the optimal number of plane waves involved in the basis functions Science Evolution, 2017, vol. 2, no. 18(а) (b) (c) (d)Fig. 9. Sr(N3)2 electronic density: (a), (b) - total valence; (c) - partial from 1πu4σg3σu states; (d) - partial from 1πg states.(а) (b) (c) (d)Fig. 10. Ca(N3)2 electronic density: (a), (b) - total valence; (c) - partial from 1πu4σg3σu states; (d) - partial from 1πg states.(а) (b) (c)Fig. 11. Cd(N3)2 electronic density: (a) - total valence; (b) - partial from 1πu4σg3σu + 4d-Cd states; (c) - partial from 1πg states. Science Evolution, 2017, vol. 2, no. 19(а) (b) (c)Fig. 12. α-Hg(N3)2 electronic density: (a) - total valence; (b) - partial from 1πu4σg3σu + 5d-Hg states; (c) - partial from 1πg states.Moreover, in the case of the α-Hg(N3)2 crystal, one can already speak about the predominant covalent nature of the chemical bonding, which agrees with the result of the work [2].CONCLUSIONSIn summary, the electronic structure of 4 divalent metal azides has been investigated; the band spectra, maps of the total and partial electronic density have been provided, wherein the data for Cd(N3)2 and Ca(N3)2 crystals have been presented for the rst time. The obtained values of the band gap are in good agreement with that calculated by other authors; the agreement with the available experimental data appears to be quite acceptable as well. It is shown that all the considered crystals, except of α-Hg(N3)2, are mostly ionic compounds with a small covalent constituent of the chemical bonding, which becomes to be more pronounced in the case of the mercuric azide. Based on the band gap comparison, the conclusion has been drawn about lesser stability of Cd(N3)2 and α-Hg(N3)2, as opposed to the second group metal azides, which is also conrmed by the experimental data [14].ACKNOWLEDGMENTSThe work has been completed with a support from the governmental assignment № 3.235.2014К

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