# Effects of Electron Correlation inside Disordered Crystals
## 1 Introduction  
Breakthroughs in characterising the disordered systems are firmly connected with the evolution of the pseudopotential method [1]. The identical complication relates to apseudopotential method [1]. Due to a limited description of the pseudopotential, the difficulty of pseudopotential transferability remains. It is impossible to make use of the nuclear potentials set through the possessions of some systems in order to characterise another system. A fundamental breakthrough was accomplished during research of the electronic structure, as well as properties of the system due to the application of the ultra-soft pseudopotentials developed by [PERSON] [2, 3] as well as the projector augmented waves theory developed by [PERSON] [4, 5]. The previously mentioned theory was extended due to an application of the generalised gradient approximation (GGA) in the density functional theory (DFT) of the many-electron structures, refined in the papers [6, 7, 8, 9, 10]. Inthe augmented projector waves method, a wave function of valence states for the electron orbital (all-electron) is manifested due to the transformation via the pseudo orbital. The pseudo orbital expands into the pseudo fractional waves in the augment region. The all-electron orbital in the identical region is increased in size using the identical coefficients via partial waves, expressed by the Kohn-Sham equation. The term for the pseudo-Hamiltonian that we possess, in the equation with the pseudo wave function, is obtained by reducing the entire energy functional. From the previously mentioned equation, we can obtain the electron energetic spectrum wave functions as well as the value of the complete energy functional. The application of the method is very detailed, as described in [10] for the crystal electronic structure computed by means of the VASP computer codewell-known worldwide. By means of the cluster method's calculations, as well as the GAUSSIAN computer code, this method may be applied for the explanation of the electronic structure of molecules. It is worth noting that in [11; 12; 13; 14; 15; 16; 17; 18; 19], recently straightforward productive computation approaches of the electronic structure, as well as properties of large molecules, have been suggested. The proposed approach is to build on the tight-binding representation and functional density theory, which incorporates long-range Coulomb interplay of electrons at different crystal lattice sites. Introduced approaches [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19] are employed solely for the interpretation of pristine-ordered crystals and molecules. Effects related tothe electronic localised states, as well as lattice vibrations, happen at disordered crystals. These effects cannot be characterised using the model for a perfect crystal. On this subject, other methods are also developing. Crucial accomplishments in illustration of the effects of the disordered systems are connected with the implementation of the tight-binding model for multi-electron scattering, which includes an estimation of the coherent potential. Beginning out of [PERSON]'s and [PERSON]'s contributions [20; 21], the tight-binding model was widely used in electronic structure computations and in the explanation of the ideal crystal characteristics. Computations for the electronic structure of the alloy are based upon using the self-consistentmethod, namely the Korringa-Kohn-Rostoker coherent-potential approximations, which are made in [22; 23; 24]. Calculations of the energetic spectrum of disordered crystals in our contribution wererefined by the theory on the basis of the function of Green. Electronic correlations in the crystal are expressed by means of themulti-band, tight-binding representation. Electron-scattering actions on the nuclei potentialsof atoms of non-identical types, as well as on the oscillations of the crystal lattice, are included. Computations of two multiplications of Green's functionare derived from the temperature of Green's functions [25].