Electronic properties of ordered and disordered linear clusters of atoms and molecules

The electronic properties of one-dimensional clusters of N atoms or molecules have been studied. The model used is similar to the Kronig-Penney model with the potential offered by each ion being approximated by an attractive δ-function. The energy eigenvalues, the eigenstates and the density of states are calculated exactly for a linear cluster of N atoms or molecules. The dependence of these quantities on the various parameters of the problem show interesting behavior. Effects of random distribution of the positions of the atoms and random distribution of the strengths of the potential have also been studied. The results obtained in this paper can have direct applications for linear chains of atoms produced on metal surfaces or for artificially created chains of atoms using scanning tunneling microscope or in studying molecular conduction of electrons across one-dimensional barriers.