The Wannier functions provide a real representation of electronic ground state in real space and are obtained from the Fourier transformation of the Bloch functions . The localized nature of Wannier functions can be exploited as convenient basis for describing the local phenomena such as orbital magnetization , electrical polarization , electronic traort , intersite charge transfer and the nature of chemical bonding . The Wannier functions are minimal basis for construction of model Hamiltonian and can be used for accurate and fast interpolation of the band structure onto very fine meshes . This is very useful for calculation of quantities like Seebeck coefficient , electrical conductivity , ordinary and anomalous hall coefficient , which are sensitive to the fine details of the band structure . In this dissertation , we investigate thermoelectric properties of AgSbTe 2 , as an interesting thermoelectric material , and the mechanism of charge transfer in double perovskites Ln Cu 3 Fe 4 O 12 ( Ln =lanthanides) by using theWannier functions. The Seebeck coefficients and electrical conductivity of AgSbTe 2 are computed within Boltzmann semi The conventional exchange-correlation functionals like GGA , underestimate the band gap . In this regard , the band gap problem is considered by hybrid functional . The computed Seebeck coefficients at different values of the band gap and carrier concentration are compared with the available experimental data to speculate a band gap of about 0.1–0.35 eV for AgSbTe 2 compound , in agreement with our calculated electronic structure within the hybrid HSE (Heyd-Scuseria-Ernzerhof) functional. The Fe-Cu intersite charge transfer and Fe charge disproportionation are interesting phenomena observed in some Ln Cu 3 Fe 4 O 12 compounds containing light and heavy Ln atoms , respectively . In Wannier representation , we find that the strength of the crystal-field splitting and the relative energy ordering between Cu 3dxy and Fe 3d states are the key parameters determining the intersite charge transfer (charge disproportionation) in light (heavy) Ln compounds . We show that a change in the spin state is responsible for the intersite charge transfer in the light $Ln$ compounds . At the high-spin state , such systems prefer an unusual Cu d 8 configuration , whereas at the low-spin state they retreat to the normal Cu d 9 configuration through a charge transfer from Fe to the Cu 3dxy .