Exact One-band Model Calculation Using the Tight-binding Method

D.A. MIRABELLA, C.M. ALDAO, Y R.R. DEZA

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

Año: 1998 vol. 68 p. 268 - 291

0020-7608

A one-dimensional one-band model is presented which enables a tight-binding calculation to be performed with full rigor.  All the multicenter integrals involved in the calculation of the Hamiltonian matrix elements can be analytically computed in terms of a single parameter: the ratio between the lattice spacing and the extension of the “atomic” wave function.  Moreover, the exact expression for the spectrum shows how the usual approximations of limiting the range of interactions and neglecting the nonorthogonality of the basis set degrade the results of the calculations.