Eigen states of graphene nanoribbon

[GJK]

Hi,

Eigen states have been given for a water molecule.
1. Can we apply the same principle to calculate the eigen states between any two atoms in functionalized graphene???
2.The change in eigen states from localized s wave function to p wave wave function at the Fermi energy  between will be proportional to the reactivity. Am I correct??

This question came in picture as we have only Bloch wave function analysis for graphene nanoribbon.

[Jess Wellendorff]

I assume you refer to this tutorial: http://quantumwise.com/publications/tutorials/item/108-visualize-the-lumo-state-of-a-water-molecule

1) How do you define eigenstates between specific atoms in functionalized graphene? I guess you would need a valid Hamiltonian for those two atoms only.
2) My feeling is that you are correct. Stronger hybridization should indicate increased chemical reactivity, but I cannot come up with a scientifically more elaborate answer.

[zh]

The two atoms in the functiontionalized graphene are already bonded with the graphene.  That is to say, the atomic orbitals (or the molecular orbitals formed by these two atoms in isolated case) of these two atoms may be hybridized with the the carbon atoms of graphene. Most probably, there is no eigenstates involved only with these two atoms. To find out the contribution of these two atoms to some eigenstates, you may first analyze the projected DOS of these two atoms. From the projected DOS, you can get energy position for most largest weight of these tow atoms, and then analyze the local DOS.

For the chemical activity, you may look at the change (increase or decrease) of density of states (DOS) near the Fermi level.  More precisely, you may use the methology introduced by the conceptual DFT to analyze the chemical activity.