Amongst other things it contains a discussion of singlet and triplet states in terms of Young tableau, something I have never understood....
Aside: In the Appendix a value for U/t is estimated by comparison of the energy levels with experiment. But, this looks a little inconsistent because the expressions used look like they are only valid for small U/t....
This was a paper that I was thinking of writing in terms of second quantised notation. Maybe that would still be helpful....
A more detailed quantitative description of the potential energy surfaces for the valence states of ethylene based on high level quantum chemistry (but does not explicitly mention a Hubbard model but can be mapped onto one) is by Krawczyk et al.
I feel compelled to plug the work of my former colleagues, particularly a paper by my good friend Jay Quenneville:
ReplyDeleteJ. Quenneville and T. J. Martinez, Ab Initio Study of cis-trans Photoisomerization in Stilbene and Ethylene, J. Phys. Chem., 107A, 829 (2003)
Both molecules are prototypes of double bond photoisomerization. Stilbene is a model for viscotic environmental effects on the reaction, due to the bulky rings. Also, it is similar to azobenzene, which is what you get when you turn the central carbons become nitrogens. Azobenzene is an extremely stable and interesting photoswitchable molecule.
One of the points I really like about this paper is the comparison between ethylene and stilbene (1,2-diphenyl ethylene). Ethylene and stilbene are, in Hoffmann's words, "the same and not the same". Jay shows that the valence state that governs the photoisomerization is like "ethylene within stilbene", right down to the geometry of the low-lying intersections, which are actually superimposable...