Far-Infrared Spectra of Ring Compounds. VIII. The Effect of a Finite Central Barrier on Pseudorotation in Five-Membered Rings

A two‐dimensional Schrödinger equation appropriate to pseudorotation in five‐membered rings with the potential function ${\mathrm{V=(z}}_1^2{\mathrm{+\; z}}_2^2{)}^2{\mathrm{+\; B\; (z}}_1^2{\mathrm{+\; z}}_2^2)$ , where z₁, z₂ are reduced coordinates of ring bending and twisting, has been solved numerically by several different approaches. The result of the two‐dimensional approach, as opposed to the method often used of solving an angular equation alone, is to show a negative curvature in the pseudorotation energy level separations and an increase in the ``pseudorotational constant,'' β, in the excited states of the radial mode. These effects are a direct result of the finite central barrier for $\text{B < 0}$ , given by B²/4. This increase in the pseudorotational constant in the excited state of the radial mode and the negative curvature of the transition frequencies had already been observed experimentally in the case of tetrahydrofuran and 1,3‐dioxolane.