A new class of chemical bonds II

Yesterday in Paris I had some really nice discussions with Philippe Hiberty about valence bond theory. Philippe helped me understand better his work on charge-shift bonding, described in this recent Nature Chemistry paper.

Some signatures of charge-shift bonding are illustrated in the figure above (left click to see a legible version) include:

there is a smaller charge density in between the bonded atoms and there are large fluctuations in this density

the laplacian of the electron density has the opposite sign to that for covalent bonds (compare the C-C bond and the F-F bond).

I also came across this paper by Barbosa and Barcelos. They discuss bonding in halogen molecules in terms of GVB wave functions and suggest that among halogen molecules charge-shift bonding is only responsible for bonding in F2 (flourine). [Note that at the Hartree-Fock level the F-F molecule does not even bond, i.e., there is a meta-stable minimun in the ground state energy vs. internuclear separation, but the binding energy is negative.

I would really like to understand this qualitative difference between the different types of bonding in terms of a simple model Hamiltonian (a two site Hubbard model?) with just a few orthogonal orbitals. Could it just be that the key difference between covalent and charge shift is just the sign of the "hopping integral" between the two relevant orbitals? This will make the anti-symmetric orbital, L - R, more stable than the symmetric orbital, L+R. [L and R denote the frontier orbitals on the left and right atoms respectively].
i.e., the ordering of the sigma and sigma* orbitals below will be reversed.

The anti-symmetric orbital will have the desired properties of a negative laplacian and more density away from the region between the bonds.