Electronic Structure, Pressure Dependence and Optical Properties of FeS 2
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LMTO method provide a simple and efficient way to predict quantitatively the electronic structure, equation of state, optical properties and bonding character in the pyrite-type materials. TB-LMTO COMPUTATIONAL THEORY In the present study the electronic structure was calculated self-consistently using the TB-LMTO technique the details of which have been described in [4]. We use the scalarrelativistic version in the atomic-sphere-approximation including the combined correction (ASA+CC). Exchange and correlation contributions to both atomic and crystal potentials were included through the local-density-functional description using the von Barth-Hedin formula [5]. We also performed the total-energy calculation with the gradient exchange correlation potential using a Langreth-Mehl-Hu non-local correction to the LDA [5]. In the
ASA+CC, the one electron potential entering the Schrddinger equation is a superposition of overlapping spherical potential wells with position R and radii SR, plus a kinetic-energy error proportional to the 4th power of the relative sphere overlap [6]: 8 SR SR' + (1) ]RRI=IR-
R'l
In the pyrite structure and with only atom-centered spheres, the ASA would cause substantial errors, either due to large overlap and misrepresentation of the potential, or due to neglect of charge in the van der Waals gap. Therefore, it is necessary to pack the van der Waals gap with interstitial spheres. In general, the requirements for choosing sphere positions and radii are that the superposition of the spherical potentials approximate the full three-dimentional potential as accurately as possible, so that the overlap error for the kinetic energy be acceptable. Here, as a model for the full potential we use the superposition of neutral-atom potentials and for simplicity, take only the Hatree part. The atomic-centered spheres are then determined by tracing the potential along the lines connecting nearest-neighbour atoms and finding the saddle-points. For a given atom with position R, the distance to the closest saddle-point is taken as the radius of a sphere and usually touch the sphere constructed in the same way for other atoms. The ASA radii are then obtained by inflating these atom-centered non-overlapping spheres until they either fill space or until their overlap w•RR reaches a maximum of 16%. In the latter case, the potential between the atomic potentials must be represented by additional interstitial spheres, which are usually repulsive. The positions of these interstitial spheres are first chosen among the non- occupied symmetry positions of the space group. Then their radii are chosen in such way that the maximum overlap between an atomic and an interstitial sphere is 18% and maximun overlap between two interstitial spheres is 20%. This precedure has been made automatic in computer program of ref. [4]. FeS 2 crystallizes in the cubic primitive structure with space group Pa3. The experimental value of lattice parameter is a=5.4179 A and the positions of the atoms are generated by Fe: (4a) (0,0,0) and S: (8
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