Studying Perturbation Theory with Explorer EyeChem

Guillermo A. Suñer(a) and Omer Casher(b)

(a) Departament de Química, Universitat de les Illes Balears, E-07071, Palma de Mallorca, SPAIN

(b) Department of Chemistry, Imperial College of Science, Technology and Medicine, London, GB-SW7 2AY

Abstract: In recent years, Computational Quantum Chemistry has emerged as a powerful tool for the study of many chemical reactions. Through the combined use of increasingly faster computers and sophisticated programs, chemists are now able to study many chemical properties, such as molecular structure and chemical reactivity.

The corresponding emergence of visualization programs is allowing chemists to better treat the quantum results, and consequently leads to a better understanding of the molecular properties. Moreover, visualization allows chemists to present their results in a highly comprehensible manner.

Some difficulties can arise, however, since all the theoretical calculations imply the use of the "supermolecule approach" technique, that is, the treatment of the two (or n) chemical moieties as a supermolecule by the program. For instance, the calculation of the Diels-Alder reaction path requires that the the diene and the dienophile be included in the same input file. This means that all the calculated molecular properties belong to the "supermolecule" and not to the individual moieties.

How, then, can the properties of one moiety being perturbed by the other be studied in the Diels-Alder reaction? One approach would be the calculation of the Molecular Orbitals (MO) for each moiety (dieno and dienophile) instead of the MO of the supermolecule (dieno plus dienophile). To achieve this, we first performed a normal reaction coordinate calculation in order to obtain the minium energy reaction pathway (MERP). We used the AM1 semi-empirical SCF-MO method, as implemented in the MOPAC 93 package. At every reaction coordinate, we then created two new MOPAC input files, one for each moiety. The coordinates of the other moiety was replaced by dummy atoms. Here, custom built Explorer EyeChem visualization modules automated what would otherwise have been a very tedious process. We finally ran MOPAC on each input file and generated graph files for both the HOMO and LUMO MOs. Again EyeChem was used to visualize the overlap of the HOMO/LUMO MO of each moiety and to create animations of the compleate Diels-Alder reaction pathway.

We use, as an example, the well-known Diels-Alder reaction between methoxybutadiene and acrolein, which experimentally gives the ortho adduct rather than the meta adduct. A preliminary study of the two reactions that would lead to both adducts shows that the energies of both maximum points near the transition state (TS) are very close. The visualization of the MO of both supermolecules shows only the bonding MO at the HOMO and anti-bonding MO at LUMO, but no conclusion about the regioselectivity of such reactions can be made.

When visualizing the HOMO of the diene and the LUMO of the dienophile at the TS with Explorer EyeChem the ortho shows the only suitable overlap, thereby confirming the experimental reaction. The other cases show a non-overlapping interaction. It should be noted that for the meta adduct, an overlap can be seen between the LUMO of diene and the HOMO of dienophile. This weak overlap has a large E(LUMO)-E(HOMO): 10 eV as compared to 8 eV for the suitable orto adduct. We conclude that this tool can be useful for the evaluation of the regioselectivity of organic reactions at the TS rather than at the products or reactants.

This perturbation theory approach - the effect of the interaction of the MO of the two components as a perturbation on each other - was applied to a wide range of well known Diels-Alder reactions (with C, Z and X-side groups) in order to better study the regioselectivity of such reactions.