A modified form of the polar model of crystals is proposed. A peculiarity of the model is the dependence of the hopping integral on the site occupation. In the cases of weak and strong interactions the effective model Hamiltonian, which generalises the known forms of the effective Hamiltonian, is derived. It is shown that the model has the electron-hole asymmetry, in contrast to the Hubbard model. The metal-insulator transition within the model is also studied. The obtained results are compared with experimental data for narrow-band materials. Some specific narrow-band effects are discussed.

PACS numbers: 71.10.Fd, 71.27.+a, 71.28.+d