Adequacy of the Molecular Orbital Approximation for Predicting Rotation and Inversion Barriers

Abstract

We demonstrate by numerical analysis that quantitatively useful barrier magnitudes may be obtained within the framework of the molecular orbital method. Use is made of a theorem by K. F. Freed that the first derivative at a midpoint between adjacent extrema in a sinusoidal potential energy curve can be determined to second order for Hartree‐Fock wavefunctions and the fact that potential energy functions of the form $$\begin{array}{c}{\mathrm{E(x)\; =\; ax}}^2{\mathrm{+\; bx}}^4\mathrm{+\; c\hspace{0.17em}}\exp {\mathrm{(-gx}}^2\mathrm{),}\\ {\mathrm{E(x)\; =\; ax}}^2{\mathrm{+\; bx}}^4{\mathrm{+\; fx}}^3,\\ \text{E(x) = (1/2 )}{\displaystyle \sum _j}{\mathrm{\hspace{0.17em}V}}_j\text{(1−}\cos \mathrm{jx),}\end{array}$$ are known to represent all existing rotation and inversion barriers within experimental error. We then show by illustrative computations that the stated potential functions usually have first derivatives (at midpoints between adjacent extrema) equal, within $\text{± 5 \%}$ , to first derivatives of the sine curve arcs required by Freed's theorem. Thus, barriers may be predicted adequately by ab initio and, in principle, by semiempirical molecular orbital methods. This suggests that quantitative prediction of conformations of large organic molecules may be possible.