It is shown that vibrational displacements satisfying the Eckart-Sayvetz conditions can be constructed by projection of unconstrained displacements. This result has a number of interesting direct and indirect ramifications: (i) The normal coordinates corresponding to an electronic state or an isotopologue of a molecule are transformed to those of another state or isotopologue by a linear and, in general, non-orthogonal transformation. (ii) Novel interpretation of axis switching. (iii) One may enhance the separation of rotational-large- amplitude internal motions and the vibrational motions beyond that offered by the standard use of the Eckart-Sayvetz conditions. (iv) The rotational- vibrational Hamiltonian given in terms of curvilinear internal coordinates may be derived with elementary mathematical tools while taking into account the Eckart conditions with or without enhancement.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry