Hopping energy(nearest-neighbour) and on-site energy

[sergio]

Hi,

I wonder how I can define or introduce nearest-neighbour hopping energy and on-site energies (defined in tight-binding Hamiltonian) for one dimensional chains.

Thanks for your answer(s)

[zh]

From the Hamiltonian and localized atomic orbitals ([tex]<\phi|[/tex]), you may define the nearest-neighbour hopping energy and on-site energies: [tex]<\phi_i|H|\phi_j> [/tex], where [tex]i \neq j[/tex] corresponds to the hopping energy and [tex]i=j[/tex] for the on-site energy. The atomic orbitals used in ATK  may be used to estimate these hopping and on-site energies, but not the best choice. The best choice is to use the  maximally-localized Wannier functions as the atomic orbitals to estimate the hopping and on-site energies.