Density Functional Theory and the Family of (L)APW-methods: a step-by-step introduction. Stefaan Cottenier. 1 Density Functional Theory as a way to solve the quantum many LAPW with Local Orbitals (LAPW+LO). Methodology. This chapter starts with a brief introduction to density functional theory (DFT) mented plane wave (LAPW) method that is used in the present work. This is followed .. This becomes a two step diagonalization process making the method .. [16] S. Cottenier, Density functional theory and the family of (L)APW-. Density Functional Theory and the family of (L)APW-methods: a step-by-step introduction. by: S. Cottenier. () Key: citeulike Posts Export Citation.

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Their densities of states curves bring out characteristic features in the valence band a core like peak, at environ Our results give a good agreement with other theoretical calculations and experimental data. Recently, it has become possible to compute with a great accuracy an important number of electronic structure materials from rst-principal calculations.

This development in computer simulations has opened up many interesting and existing possibilities in anv sciences. The most common example is the system: Tl 3 SbS 3 crystallize in rhombohedra structure of R3m space group where Sb presents an environment of six atoms of S three at shorter distances, 2. Faamily eI is an interesting compound for the antimony chalcogenide family. It’s present a semiconductor character with an indirect gap and monoclinic structure crystallization of P -1 space group.

Their calculated energy gaps are in ranging application of optoelectronics [ 4 – 9 ]. Study their properties was necessary to find a technique based on numerical simulation. Among these techniques we find the ab-initio, empirical and the semi empirical methods that became today a tool for the most complex electronic and structural property count.

All these methods are based on a minimization of the total energy system. We will use an ab-initio method because it plays an essential role in determination of the electronic structure. These methods do a rigorous resolution of the standard Schrodinger equation SE while calculating all integral of recovery the integral will be evaluated rigorously and all electrons are, in principle, taken in account [ 1011 ]. In the following section; we expose the method of calculations based on the theory of functional density, and in sec.

B we present the main results of this calculation and we discuss it. In the last section, some concluding remarks were described. The functional theory of density DFT is step-by-atep very widely used approach in microscopic studies of physical systems.

## Density of State Calculations for Tl3SbS3 and SbTeI

Even in situations where the two-body elementary interactions are well-known such as in atoms or molecules, or atomic clusters, it is not possible to solve exactly the many body Hamiltonian and it is necessary to use sophisticated many-body techniques to nd approximate solutions.

This is reason why DFT is quite often employed with great success to describing electronic systems [ 11 ]. Papw-methods calculations are based mainly on the use of many approximations such as the local density approximation LDAthe approximation of generalized conjugate gradient GGA [ 6 ].

Referring to the theorems of Hohenberg-Kohn HK [ 6 ], which present the most elementary theorems for this system of particles.

The quantum state of the system is no only described by the lapw-mthods function but by the electronic density. Where, is the kinetic energypresent the potential energy between ions and is repulsive energy from other electrons.

### Density of State Calculations for Tl3SbS3 and SbTeI

By writing the hamiltonian of Eq. To transform the study of this system with N particles in interaction at the study of a one particle in mean potential created by the N-1 other particles we use the variational principle. In this context, we have used the Wien2k package [ 12 – 14 ] based on the local density approximation LDA.

In attempting to understand the electronic properties of these compounds, one start with Tl3SbS3 and we wish this discussion by SbT eI. The calculation is based on the local density approximation LDA for exchange correlation potential which permitted us to obtain good densities of state for Tl3SbS3 and SbT eI.

So the applied data are the atomic positions and the group of space [ 15 ] that constitutes the start point that we took in account in this numeric simulation. For each step we have compared, judged and verified the consistency of results found and the validity of our calculations by basing over all applied and theoretical works done by other methods [ 16 ]. A Tl3SbS3 compound has an indirect gap 1. Several electronic structure calculations of the SbT eI are available in the literature [ 17 – 20 ].

In the present work, we find for SbT eI also an indirect gap [ 17 – 20 ] 1. The Table 1 give the value of predicted and calculated energy gap compared with experimental ones in eV [ 17 – 19 ]. The valence density of states VDOS curves exhibit three bands, with a characteristic three peak structure for the upper portion and core-like level for the lower band. The lowest band D, with a bandwidth of 0. Partial and total density of states of T l 3 SbS 3.

For summary the Table 2 gives positions in eV of di erent peaks deducted by calculation of the density of states of and SbT eI. We have calculated the band structure and the total density of states by using the DFT theory; we remark the following main results:.

Its width is around 9. J Material Sci Eng 7: This is oc open-access article distributed q the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Select your language of interest to view the total content in your interested language. Guidelines Upcoming Special Issues. In this work the atomic positions, the space group and the radii of Mu n are taken into account. Then starting from our Hamiltonian which is written as: To transform the study of this law-methods with N wnd in interaction at the study of a one particle in mean afmily created by the N-1 other particles we use the variational principle 3 Finally, we obtain the following equation: E i is the eigenstate.

Partial and total density of states of SbT eI. We have calculated the band structure and the total density of states by using the DFT theory; we remark the following main results: Goodman CHL New semiconductors with new combinations of properties.

Mater Res Bull Qnd State Commun Theoretical calculations and Sb Mossbauer spectroscopy. Phy Rev B J Solid State Chem A Andriesh AM Properties of chalcogenide glasses for optical waveguides. J Non-Cryst Solids J Alloys Compd Andersen OK Linear methods in band theory. Phys Rev B Phys Rev Lett Condens Matter Phys Ozbay ME Ferroelectrics