Determination of quantum labels based on projections of the total angular momentum on the molecule-fixed axis

Abstract

Molecular line lists, particularly those computed for high temperature applications, often have very few states assigned local quantum numbers, i.e rotational and vibrational quantum labels. These are often important components for accurately determining line shape parameters required for radiative transfer simulations. Through variational calculations, the projection of the total angular momentum onto the molecule fixed axis (k) is investigated in the Radau internal coordinate system to determine when it can be considered a good quantum number. In the Radau coordinate system, when the square of the th component of the wavefunction is greater than one half, then we can classify k as a good quantum number in accordance with the theorem of Hose and Taylor, a quantum analogue of the Kolmogorov–Arnold–Moser theorem. When the theorem is satisfied, it is shown that k can reliably be used to determine oblate and prolate quantum labels Ka and Kc. This approach is tested on the states of the water and ozone molecules.