Rotational Constants of Torsionally Excited Molecules

Abstract

Molecular torsion is described by a model which has only one internal degree of freedom but allows for distortions depending on the torsional angle $\tau$ . Evidence for such distortions is found by comparing observed and calculated rotational constants associated with ground and excited states of skeletal torsion in symmetric conformers of ethyl formate, propionyl fluoride, and fluoroacetyl fluoride. For these cases, possible torsional modes involving only skeletal angular distortions are discussed. Effective rotational constants are calculated from exact energy levels for $\text{J\hspace{0.17em}=\hspace{0.17em}0}$ and $\text{J\hspace{0.17em}=\hspace{0.17em}1}$ . A convenient numerical method, based on discretization of the torsional angle and trigonometric interpolation, is applied and tested with respect to over‐all numerical convergence. An internal axis method is found to converge faster than the principal axis method and shows that the effective rotational constants are approximated to considerable accuracy by the expectation values of instantaneous rotational constants if the respective torsional wavefunctions are localized. In such cases it is easy to evaluate corrected instantaneous rotational constants which may be related in the usual way to a τ‐dependent molecular structure, i.e., to the torsional mode.