A first principle derivation is presented of a Hubbard-like Hamiltonian describing the motion of electron on a lattice of soft, non-orthogonal orbitals with a polarizable core. Non-orthogonality of the on-site orbitals is explicitly accounted for by expanding the Hamiltonian at different orders in the nearest neighbor overlap. The resulting Hamiltonian contains terms not included in the Hubbard Hamiltonian, such as non-site-diagonal e—e interactions and occupations-dependent hoping terms. The first principle approach we develop yields reliable a priori estimates of microscopic parameters and leads to the unambiguous definition of the reliability range of the proposed model. The properties of the Hamiltonian are investigated through numerical calculations on finite rings.