On relationships among effective potential functions: 2,5-dihydrofuran, s-tetrazine, 1,4-dioxadiene, cyclopentene, and carbon suboxide

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Abstract
Using Van Vleck perturbation theory, a relationship between two-dimensional potential functions in ring-puckering and ring-twisting coordinates and effective one-dimensional ring-puckering coordinates is demonstrated. It is shown that effective one-dimensional potential functions can be derived for 2,5-dihydrofuran and s-tetrazine which have essentially the same eigenvalue separations as the two-dimensional potential functions previously derived. More useful is the fact that this procedure may be reversed and two-dimensional potential surfaces have been derived for 1,4-dioxadiene and cyclopentene. In mass weighted coordinates the potential function for dioxadiene is V (Q1,Q2) =28.49 Q14+24.00 Q12 +2555.2 Q22+294.6 Q12Q22, where V is in cm−1, Q in U1/2 Å. Q1 is a mass weighted ring-puckering coordinate and Q2 is a mass weighted ring-twisting coordinate. The potential function for cyclopentene is V (Q1,Q2) =51.50 Q14−217.4 Q12+2262.4 Q22 −9.10 Q12Q22 yielding a barrier to planarity of 229 cm−1 essentially unchanged from the barrier of 232 cm−1 reported earlier from the one-dimensional potential function. This same formalism has been used to correlate the potential functions for the large amplitude bending mode, ν7, of carbon suboxide in the ground state and several excited states of other modes.

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