Asymmetric Top Views
The general convention is to define the axes such that the axis A has the smallest moment of inertia (and, hence, the highest rotational frequency) and other axes such that . Sometimes the axis A may be associated with the symmetric axis of the molecule, if any. If such is the case, then IA need not be the smallest moment of inertia. To avoid confusion, we will stick with the former convention for the rest of the article. The particular pattern of energy levels (and, hence, of transitions in the rotational spectrum) for a molecule is determined by its symmetry. A convenient way to look at the molecules is to divide them into four different classes (based on the symmetry of their structure). These are linear molecules (or linear rotors), symmetric tops (or symmetric rotors), spherical tops (or spherical rotors), and asymmetric tops
The body-fixed symmetry of the ideal asymmetric top is that of the double four (or quaternion) group. For integral spin this is equivalent to the ordinary four-group and the secular determinant breaks down diagonally into four distinct blocks, as in the standard theory. For half-odd-integral spin, however, one obtains two equivalent blocks, the levels being doubly degenerate. A generalization is then presented which entails making the top wavefunction a spinor-valued quantity. This is expanded in spinor hyperspherical harmonics which are generalizations of the ordinary hyperspherical harmonics, the DMNL. A systematic procedure is given for finding the elements of the secular determinant. The motivation for the generalization is that of spinor fields in a frozen Mixmaster universe.
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Asymmetric Top Images
