Electron correlations in crystals and molecules

An expression for the Green’s function of a disordered crystal is obtained with allowance for the electron-electron interaction. The electron states of the system are described in the framework of a multiband tight-binding model. The possibility of using the proposed approach for describing the energy spectrum of molecules is demonstrated in the limit of an infinitely large primitive cell of the crystal. The energy spectrum and effective charges of atoms of a tricyanobutadienecarbazole molecule are calculated.     

Thermodynamic Potential of a System of Electrons and Phonons in a Disordered Alloy

We obtain a cluster expansion for the two-time retarded Green's functions and the thermodynamic potential of a disordered crystal taking the electron–phonon and electron–electron interactions into account. The electron states of the system are described in the framework of a multiband tight-binding model. The calculations are based on the diagram techniques for the temperature Green's functions. The coherent potential approximation is chosen as a zeroth-order one-site approximation in this cluster expansion method. We show that the contributions from the processes of scattering of elementary excitations on clusters decrease as the number of sites in the cluster increases in accordance with certain small parameters. Analytic estimates of the influence of the electron–phonon interaction on the energy spectrum of electrons of an alloy being ordered are obtained in a one-band model. The applicability of these results to describing the influence of strong electron correlations on the electron structure and properties of alloys of transition metals with narrow energy bands is illustrated with the example of the Fe–Ti alloy.