Theories tight-binding 1-electron 1-dimensional

Tight-binding band theory is described first for the case of distinct molecules uniformly stacked with equivalent separation, a, between each site, Fig. 1. The potential in which the electron moves, K(r), is periodic, V r + a) — V(r). Here r is the vector coordinate for electrons and a is the vector length between equivalent sites in the chain. Vector notation is used because of the three-dimensional extent of the individual molecules. Assuming the chain axis is parallel to the z-axis, a — az (z is a unit vector along the z-axis). 

The tight-binding band theory and the accompanying Peierls instability discussion assumed that all electrons move independently of each other in a perfect uniform lattice. Electron-electron Coulomb repulsion, disorder, and interruptions in the strands alter the band theory results. These effects are important for the understanding of one-dimensional metals and are now introduced. 

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