Rondan-Houk theory

The Rondan-Houk theory rationalizes many experimental results and leads to several predictions which have since been confirmed. Exceptions have been explained by Houk and co-workers, using numerical calculations. In a sense, the problem of electrocyclic reaction torquoselectivity may be considered solved. 

However, some anomalies are not easily anticipated. We have discussed the 3-carboxylate-3-methylcyclobutene case. It would be useful to be able to predict these exceptions. The problem amounts to determining the limitations of the Rondan-Houk theory which requires an analysis of the approximations made. Clearly one important approximation is the assimilation of the cyclobutene FOs to the o34 and o 34 orbitals, because the frontier coefficients at C4 and C2 are far from negligible.15 Dropping this approximation but representing R by a carbon 2p orbital, we can then model the molecule by a pentadiene (numbered as in Figure 6.1) ... 

With this model, we need only apply the method already used to derive the selection rules for electrocyclic reactions (p. 53). From the Coulson equations, we can deduce that in the in conrotatory cyclization of pentadiene, the MO generates a destabilizing C5-C4 secondary interaction, a stabilizing and Fg a destabilizing interaction. The absolute values of these contributions rise steadily because the terminal coefficients increase from Fg to Fg. Therefore, the sign of their sum is given by the HOMO contribution. If R is an attractor, the HOMO is Fg and rotation inwards is favored. If R is a donor, the HOMO is 4T and rotation inwards is disfavored. As the Coulson equations are valid only for polyenes, these conclusions are correct insofar as R can be modeled by a carbon 2p orbital. It follows that the Rondan-Houk theory works better for conjugative than for saturated substituents. 

Houk KN, Paddon-Row MN, Rondan NG, Wu Y-D, Brown FK, Spelfrneyer DC, Metz JT, Li Y, Loncharich RJ (1986) Theory and modeling of stereoselective organic reactions. Science 231 1108-1117... 

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