In this project, we performed a first principle study of some half metals which are of importance in spintronics. All of the calculations are in density functional theory (DFT) frame work; depending on the requirements of the problem in different arts of the project, we applied one of two computational code, PWscf or WIEN2k. WIEN2kis an all electron-LAPW computational code while calculation i PWscf is based on pseudo potential method and using plane waves as basis set for wave functions. Initially we have performed an overview on DFT. In this part we did especial focus on LDA+U (to improve on site correction) have been applied in some part of this project. The first part of the project is assigned to the study of bulk properties of Co2FeSi alloy and its interface with GaAs(001) substrate. Co2FeSi belongs to heusler alloys for which half metallic character is expected. At first a overview on bulk properties was performed. In thi study it was found that in the case of this alloy, improving the onsite correlation using LDA+U is relevant so that half-metallic character that is lost in GGA, within GGA+U is seen for this alloy. Hence for remaining of computations on different surface and interface properties of the alloy, this correction is applied. Structural properties at (001) surface of the alloy and its interface with GaAs(001) substrate were studied. Relative stability of different terminations were investigated and more stable terminations at surface and interface were determined. The results show that both the standard terminations of the alloy beside Fe rich termination allocate in the stable region of the phase diagram. On the other hand, at interface of the alloy with GaAs, only CoCo/As standard termination is formable, while the modified termination FeFe/As and the FeGa/As complex termination occupy some part of the allowable region of the phase diagram. Comparison between cohesive energy of the bulk compounds, corresponding to the surface (or interface) showed that this quantity could be used as a criteria for relative favor of atoms to be at surface or interface terminations. The surface (or interfacial) effects on magnetic and electronic properties were studied. It was seen that due to changes in electronic structures of surface and interface atoms, half metallic character is not held across surface and interface terminations. In the second part, we studied a group of 3d transition element arsenides, in the met stable phase of zinc blende. These studies were performed from point of view of the topology of the electronic charge density at different volumes (hydrostatic pressures). At first we introduced the applied method for calculation of the topology of the charge density as an scalar field, then this method was applied for studying XAs (X=V, Cr, Mn, Fe, Co) compounds. Topological calculations were performed using CRITIC or TECD programs that use charge densities prepared by WIEN2k and PWscf codes respectively. After determining topology of critical points of charge density in this zin blende structures, we did more detailed investigations on the behavior of topological parameters during volume changes and also varying the atomic number of 3d transition element. As a result of these studies, we found that bulk modulus has near correlation with the value of charge at bond critical points, so that the more charge at bond points, the less compressibility of the bonds and so the higher bulk modulus. On the other hand, near correlation between directionality of the bonds and cohesive energy of under study structures was observed. in addition, by comparison between topology of the charge in two spin channels, it was seen that spin splitting in topological parameters is related to inter-atomic exchange interaction and so have similar behavior to the Curie temperatures of materials. keywords : Density Functional Theory, Spintronics, Topology Of Charge Density.