Abstract
In this chapter, the limits of traditional theories of molecular rotation are discussed. First, the basic ideas of angular momentum theory are introduced and in particular the technique of equivalent rotations is discussed, which is used to map the molecular symmetry group, i.e. the identical nuclear permutation/inversion operations, onto a subgroup of the rotation group, SO(3). This procedure is shown to fail for permutation groups of more than four particles, which is demonstrated for a particular example and is explained by a rigouros mathematical statement.
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Notes
- 1.
See Chap. 2 for some general discussion of angular momentum and Part III for a semi-classical treatment.
- 2.
See Sect. 4.1 for a description of the subduced representations in the case of finite groups. The generalization to continuous “parental” groups with finite subgroups is straightforward.
- 3.
Notice the synonymous use of separable “molecular coordinates”, “degrees of freedom” and “molecular wave function”. The degrees of freedom are usually used as an umbrella term for the molecular coordinates, whereas the molecular wave function shows a functional dependence on them. Therefore separating the molecular coordinates is equivalent to separating the degrees of freedom and to write the molecular wave function as a product.
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Schmiedt, H. (2017). Symmetry Beyond Perturbation Theory. In: Molecular Symmetry, Super-Rotation, and Semiclassical Motion. Springer Series on Atomic, Optical, and Plasma Physics, vol 97. Springer, Cham. https://doi.org/10.1007/978-3-319-66071-4_6
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DOI: https://doi.org/10.1007/978-3-319-66071-4_6
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