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Presented By:
Z. Y. Mijbil1 and M. G. Merdan2
1 Babylon University, College of Veterinary.
2 Babylon University, College of Science, Department of Physics.

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Summary
Lattice constant, cohesive energy, direct band gap and valence band width had been calculated for grey tin by using ( CNDO-LUC ) method, then we had been making a comparison with experimental and other workers results for ( C, Si, Ge and Sn ) with zinc-blende structure in order to study the efficiency of this method. The results had showed that this method is good for lattice constant and bad for other properties all at the same time



I. Introduction
The semiempirical methods gave us a privilege of no long time for getting results, because it had been adopted many approximations, according to that it is used in many fields ( Harker and Larkins 1979, Freund and Hohlneicher 1979, Schmid and Brodbek 1985, Vogl et al. 1983) and for along time even in the last years (Marshed 2006, Mijbil 2006, Hassan 2001), as well as papers about had been published (Thiel 2002). Nevertheless these approximations led to inaccurate data in some aspects which became a disadvantage ( Dorestt and White 2000), for this reason we made this research in order to measure the efficiency of CNDO (Complete Neglect of Differential Overlap) as one among the primary semiempirical methods, that presented by ( Pople et al. 1965) in which he neglected many electron-electron interactions and focused on both valence electrons and nuclei as a core of the atom ( with the other electrons) ( Pople and Beveridge 1970). Here LUC approximation ( Large Unit Cell) or ( Supercell ) ( Bredow 2000) is used in order to minimize the size of BZ (Brillion Zone) and so to diminish the number of the special points in which the aspects of the crystal such as band structure could be calculated ( Rogan and Lagos 2001, Chadi and Cohen 1973).
We have firstly studied how CNDO method practically and mathematically work, and see how its parameter the orbital exponent ( ξ ), bonding parameter ( β ), s-shell electronegativity ( EES ) and p-shell elecronegativity ( EEP ) could be changed and how this change may effect on the results, and secondly we have calculated the lattice constant, cohesive energy valence band width and the direct band gap for the semimetal grey tin ( α-Sn) ( Myles et al. 2001, Cuenya et al. 2002) which has 50 electrons, exist at atmospheric pressure (Akdim et al. 2002, Mujica et al. 2003) and under 13oC with diamond structure ( Khan et al.1996, Cuenya et al. 2001), and compared our results with the experimental and other workers used the same method for the substance and other materials which are (C, Si and Ge) with the same diamond structure.