Body-fixed frame, molecular internal space

For a secure account to be given in terms of the separation (O Eq. 2.43), which is what is really required if one is to use the clamped nuclei electronic Hamiltonian, it would be necessary to consider more than one coordinate space. On the manifold at least two coordinate spaces are required to span the whole manifold. The internal coordinates within any coordinate space are such that it is possible to construct two distinct molecular geometries at the same internal coordinate specification, so that a potential expressed in the internal coordinates cannot be analytic everywhere (CoUins and Parsons 1993). It would therefore seem to be a very tricky job. But even if it were to be accomplished it seems very unlikely that a multiple minima argument could be constructed to account for point group symmetry in this context It is possible to show (see Section IV of Sutcliffe (2000)) that in the usual Eckart form of the Hamiltonian for nudear motion, permutations can be such as to cause the body-fixed frame definition to fail completely. 

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