The Asymmetric Rotor I. Calculation and Symmetry Classification of Energy Levels

Abstract

A table of energy level patterns for rigid asymmetric rotors is given, by means of which this approximation to the rotational energies of all molecules up to J = 10 may be readily evaluated. The symmetry classification of each level is determined and expressed in terms of the K values of the limiting prolate- and oblate-symmetric rotors. A simple method is developed for calculating the transformation which diagonalizes the energy matrix and is applied to the derivation of perturbation formulas.

PGOPHER: A program for simulating rotational, vibrational and electronic spectra

“…The complication of degenerate vibronic states is not possible for asymmetric tops so the l quantum number is not required, but the choice of the axis used to define K is now not obvious. Here we use the molecule-fixed z axis as the quantization axis for K, but this can be mapped to any of the three principal inertial axes, a, b or c. A choice must also be made for the x and y axes, giving six possible choices, normally referred to as the representation and specified using the notation devised by King et al [45] shown in Table 1. z a b c a b c x b c a c a b y c a b b c a Which of the six representations is used must be specified as part of the process of setting up the calculation.…”

Stark quantum beat spectroscopy of polyatomic molecules

“…The rotational constants A, B, C are connected to the quanti- (22) with A >-B-> C in the type F representation [26]. The eigenfunctions of Hro, are denoted JJK, K~) in the asymmetric rotor notation.…”

“…As an illustration we discuss in the following the emission tensor of molecules with Cs symmetry. The vibronic wavefunctions belong to the symmetry species a' or a" of the molecular point group C~ and the vibronic transition dipole moments are classified as A/B-or C-type where the principal axes of inertia a and b span the symmetry plane in F convention [26]. The components of the transition dipole tensor M~ (7) are given in Table 1 and the corresponding emission tensors are obtained by decomposing the sum ~ according to the symmetry species which results in ~f…”

Rotational Energy Levels of Asymmetric Top Molecules. Part 1: Discussion of the Theory

“…1,2,3,7,8,9,10) Since asymmetric top molecules do not have an axis of symmetry, there is no preferred direction which carries out__a simple rotation around the total angular momentum P. Although P is still quantized, and the quantum number J is defined, the quantum number K and the selection rule A K = 0 cease to have meaning. The approximate energy levels are derived using the symmetric top wave functions as a basis, but derivation of the exact levels is very difficult in the general case, since they cannot be represented by an explicit formula analogous to that for the symmetric top ( Refs.…”