  An accurate numerical consideration is carried out of the ground state for
the simplified model which is traditionally used for the description of Verwey
transition and related phenomena. In the framework of 1D spinless fermion
model, the effects of next-nearest neighbour (NNN) interaction on the
metal-insulator transition are investigated for electron concentrations 1/2 and
2/3. It is shown that for large enough NNN transfer integrals the electronic
topological transition of metal-metal type is also possible. The corresponding
phase diagrams are presented.
