A first principle calculation is performed to investigate the electronic and the thermodynamic properties of a dimer in a potential characterized by the random site energy and the random screening length. The exact Hamiltonian from which the extended Hubbard model Hamiltonian is derived is formulated. All the coupling constants are calculated systematically using the analytical eigenfunctions. The breaking of the electron-hole symmetry leads to a temperature dependent chemical potential and so affects the thermoelectric power. In terms of the strengths of the coupling constants, the model Hamiltonian does not well approximate the exact Hamiltonian; and in terms of the properties of the eigensolutions, the model Hamiltonian does not yield a strong enough “band-narrowing” and therefore does not predict the correct low-temperature thermodynamical properties. The key conclusion also holds for bulk systems. Theoretical results can be applied to strongly dimerized charge-transfer salts such as BIP(TCNQ)2.
