Electronic eigenvalues and eigenfunctions in crystals by a pseudopotential method

The electronic band structure of a face-centred monatomic crystal is calculated by a plane wave method. A model pseudopotential is used depending on two adjustable parameters. The object of this work is mainly to investigate how the change of the potential affects the band structure, for the case of a potential similar in some respect to pseudo-potentials which have been Used for real metals. A detailed calculation is made for the points of symmetry and along the axis of symmetry within the Brillouin Zone. Five different sets of parameters for the pseudopotential are considered and the corresponding Energy v. Wave vector graphs are plotted. Also the coefficients of the Fourier expansion of the wove function, the so-called momentum eigen functions, are plotted against the wave vector k in an extended zone scheme. The features of the band structure which are independent of the potential and those which are sensitive to any change of it are found. Finally the results given by this model are compared with the band structure of actual elements having a face-centred cubic lattice.