Knowledge Bank

The assignment of high-J rotation-torsion or vibration-rotation-torsion transitions in acetaldehyde is complicated by labeling problems for numerical eigenvectors obtained by diagonalizing the Hamiltonian matrix. These labeling problems arise because of strong mixing of the basis functions used in the TAM (PAM-IAM hybrid) basis set, which in turn is caused by a competition between the a-principal-axis, the c-principal-axis and the methyl-top-axis for dominance in determining the axis of quantization of the projection quantum number of the total angular momentum J. Harter and $Patterson1$ introduced the concept of rotational energy surfaces, and illustrated their use both classically and semi-classically for obtaining simple descriptions of high-J three-dimensional semi-rigid-body rotations in terms of J-projection quantizations along various axes in the molecule. In the present work we are trying to extend their ideas to find approximate quantization directions (and therefore approximately good projection quantum number labels) for rotational motion in acetaldehyde, which can be thought of classically as a three-dimensional rotor containing a hindered gyroscope. The details of the approach will differ for states well below the top of the barrier, near the top of the barrier, and well above the top of the barrier, since the torsional motion changes from nearly harmonic small-amplitude oscillations to nearly free internal rotation in this energy range. Since the concept of rotational energy surfaces is based on the adiabatic freezing of rotations with respect to other degrees of freedom in the molecule, we expect application of this approach to be most difficult near the top of the barrier, where the degree of change of wave functions from those of a harmonic oscillator to those of a free rotor may be quite sensitive to the J value.