Tight Binding Theory

For H we take to be the 1s wavefunctions of H sited at the positions of the nuclei. Then the Hamiltonian and overlap matrices become

The eigenvalues are then and the wavefunctions are . Since V < 0, then the + sign gives the lower energy orbital occupied by 2 electrons. The - state is called an anti-bonding one and its wavefunction contains a node midway between the atoms. This node depleted the electron density in the middle of the bond and thus the proton-proton repulsion is imperfectly screened and the energy for the anti-bonding state is higher than that of the bonding state. On the other hand, the wavefunction of the bonding state has a peak between the ions and thus the electrons are shared between the ions. This is described as covalent bonding.

As a problem, show that if the two atoms had very different energy levels, then there would be a transfer of electrons from one to the other.