Origin of the ring-puckering potential energy function for four-membered rings and spiro compounds: a possibility for pseudorotation
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The origin and form of the ring-puckering potential energy function for a four-membered ring are derived, assuming that harmonic angle strain is the restoring force for the puckering motion. The resulting function is of the form V = aangx4 + bangx2, where x is the puckering coordinate and where the coefficients aang and bang depend on the angle bending force constants and where bang, in addition, depends on initial angle strain. Torsional interactions give rise to additional contributions to the quartic and quadratic coefficients. This derivation is extended to spiro compounds such as spiro[3.3]heptane, and the applicable ring-puckering potential has the form V = a(x14 + x24) + b(x12 + x22) + cx12x22, where x1 and x2 represent the puckering coordinates of the two four-membered rings. The coefficients a and b have relationships to the angle strain similar to that in the single four-membered ring. The expected magnitude of c, the coefficient for the cross term, is examined on the basis of the interaction between the ring angles of the central atom connecting both rings. It is found that the ratio of coefficients c/a can become as large as 4/3 on the basis of angle strain effects alone if the interaction between ring angles is large. This value can further be increased by torsional effects. This estimation of this ratio is significant since a value of 2 would represent pure pseudorotation. Values approaching that magnitude would represent perturbed pseudorotors. © 1991 American Chemical Society.
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