ORIGIN OF ELECTRONIC PROPERTIES OF α-Hg 3 S 2 Cl 2 POLYMORPH

To investigate the energy bands structure of α-Hg3S2Cl2, first-principles calculations were performed within the density functional theory (DFT) formalism using the SIESTA software package. Using the local density approximation the atomic positions are relaxed so as to minimize the forces acting on the atoms. The analysis of band energy dispersion shows that the VBM and CBM are located at Г symmetry point, resulting in a direct energy band gap of 3.198 eV. It is established that the nature of interatomic interactions has complex character and includes covalent and ionic parts. The inclusion of spin-orbit coupling does not strongly modifies the structure of energy bands.


Introduction
Hg3X2Y2 (X = S, Se, Te; Y = F, Cl, Br, I) compounds present a class of perspective materials for nonlinear optics.Physical and chemical properties of these crystals are very useful for the creation of functional elements for optical devices.][6][7][8][9][10] The main structural feature of mentioned crystals is the tendency to formation of various polymorphic modifications.At the same time due to the wide transparency in the visible and IR-range (from 0.3 to 40 m) their optoelectronic features are very useful for possible applications.
Regarding α-Hg3S2Cl2, no reports concerning electronic structure can be found in literature.Therefore, we thought it would be worthwhile to perform the band structure calculations of α-Hg3S2Cl2.In this paper, the band structure and optical transitions of α-Hg3S2Cl2 have been investigated using DFT.The study on the origin of electronic properties provides an important information and prediction of physical properties of title crystal.

Structure of α-Hg3S2Cl2
The α-Hg3S2Cl2 is cubic (a= 0.89 nm) and belongs to the space symmetry group T 5 -I213.Figure 1 displays the crystal structure of the title compound.Observe that the basic structural unit in α-Hg3S2Cl2 is a [SHg3] pyramid.2][13][14][15][16][17][18][19] A characteristic structural feature is the presence of two sets of octahedral spirals with different radii and twisting directions.They are located side by side, oriented in the same direction and consistently alternated. 4ere are three crystalline phases of Hg3S2Cl2.These are corderoite minerals α-Hg3S2Cl2 (I213), β-Hg3S2Cl2 (Pm3n) and γ-Hg3S2Cl2 (Pbmm), 20,21 which have variable structure depending on number of halogens entered into their structure.The first crystalline polymorph is metastable at normal conditions.The structure of the α-Hg3S2Cl2 type is realized in the cases, when the chalcogen anion size is more than the halogen anion size: S 2-(0.182nm), Se 2-(0.193nm), Te 2-(0.211nm) > Cl -(0.181 nm); Te 2-(0.211nm) > Br -(0.196 nm).The main feature of this structural type is existence of (Hg3X2)2n 2+ infinite chains from [XHg3] trigonal pyramids connected by the mercury atoms which are joined for two pyramids.These chains unite in three-dimensional framework in which octahedral emptiness the halogen ions are localized. 3The mercury atoms are two-coordinated with a linear geometry.The chalcogen atoms are threecoordinated, [SHg3], forming trigonal pyramids.In title crystal, the interior bond angles Hg-S-Hg are 92 and the interior bond distances Hg-S and Hg-Cl are 0.245 and 0.292 nm.In this compound the lead atoms located at the 12b and 8a Wyckoff positions in the body-cantered unit cell.Due to specific atomic structure of corderoite-type compounds one can expect a possible applications of them as a non-linear optical materials.

Calculation procedure
To calculate the energy bands structure of α-Hg3S2Cl2, the DFT 22,23 with the local density approximation is used.The total and partial densities of electron states were determined by the tetrahedral method.We used the experimental lattice constants and atomic structure for these calculations.The DFT calculations are carried out on the minimized structure of α-Hg3S2Cl2.Integration over the irreducible part of the Brillouin zone was conducted using the method of special kpoints. 24,25We determined that 4x4x4 k-point grid and a cutoff energy of 1200 Ry are sufficiently converged.We first relaxed the crystal structure with respect to the lattice constants and internal parameters.A Hubbard correction was used to obtain a better band gap value [26][27][28] that is mostly underestimated by LDA.

Results and Discussion
The calculated band structure of α-Hg3S2Cl2 using LDA+U is presented in Figure 2. The energy structure of crystal under investigation defines by short-range order in the location of atoms (pyramids [SHg3] and octahedras [HgS2Cl4]).Moreover, the indirect band gap indicated in the LDA calculation is changed to a direct band gap of 3.198 eV between the valence band maximum and conductive band minimum at Г in the LDA+U calculation.It is in satisfactory agreement with experimental data from studies of diffuse reflectance spectra. 17α-Hg3S2Cl2 is a direct band gap semiconductor.

Figure 2. Band structure of α-Hg3S2Cl2 polymorph
The partial DOS helps to identify the origin of electronic properties of α-Hg3S2Cl2.The calculated partial density of states is illustrated in figure 3. The Fermi level is taken to be 0.0 eV.We have found that the conductive band is formed prevailingly from S-p/d states and Hg-s states.The valence band maximum consists of the S-p/Cl-p orbitals and a relatively small contribution of the Hg-s orbitals.Considering the DOS/PDOS, one can conclude that in α-Hg3S2Cl2 the sulphur and chlorine atoms play more prominent role in the valence band than the mercury atoms, which is attributed to the higher electron negativity of sulphur and chlorine atoms than the mercury.The bonding wave functions are localized around of chalcogen and halogen atoms.
The calculated DOS/PDOS of α-Hg3S2Cl2 are compared with our previous DFT calculations for Hg3Se2Cl2 and Hg3Te2Cl2. 7,8In general, the whole region of valence states has a complex hybrid character caused by the interaction of all atoms species inherent to the crystals of the Hg3X2Y2 type.The analysis of rotation dispersion 16 of α-Hg3S2Cl2 and our DFT calculations indicates that the rotation of polarization plane in this crystal is connected with direct optical transitions.Atomic transitions of [Hg3S2Cl4] octahedra in excited electronic states makes contributions to gyrotropy caused by C1 local symmetry group. 4It should be noted that the direct optical transitions in the α-Hg3S2Cl2 are localized on [Hg3S2Cl4] octahedras.
The investigation of the band structure of solids including rather heavy atoms requires including the effect of spin-orbit coupling.The spin-orbit splitting in mercury orbitals are slight at the conductive band minimum.Thus, it not significantly affects the band gap size.In addition, the results from the calculation using spin-orbit coupling shows that the band topology near the conductive band minimum is insignificantly changed due to a larger spin-orbit splitting in the S-p orbitals at the Г point.
To understand the bond nature of Hg-S and Hg-Cl in α-Hg3S2Cl2, the two-dimensional charge distribution in (100) plane is plotted in figure 4. Furthermore, by consideration of the electronic charge distribution plot, one can claim the covalence origin for the Hg-S bonds and ionic nature for the Hg-Cl bonds.The presence of covalent bonding between mercury and strongly polarized sulphur atoms leads to the high magnitude of refractive index in the title compound. 3he covalent bond arises due to the significant degree of the hybridization and the electro-negativity differences between atoms.

Conclusions
The band structure of gyrotropic α-Hg3S2Cl2 is investigated by means of the first-principles calculations in the framework of the DFT.Using local density approximation within Hubbard correction, the atomic positions are relaxed so as minimize the forces acting on each atom.The analysis of DOS/PDOS indicates the origin of electronic properties in α-Hg3S2Cl2 that connected with rare space symmetry group of mentioned crystal.The calculated electronic charge density distribution confirms the covalence and ionic nature for the Hg-S and Hg-Cl bonds respectively.The title compound combine important features needed for good X-ray and γ-ray detection applications, namely high atomic numbers and specific densities, wide band gap of 3.198 eV.It is in good agreement with experimental results.This may open a new area in applications of corderoite family compounds as multifunctional materials.