Intramolecular distributions. III. N coupled modes

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Abstract
A previous theory of intramolecular distributions (ID) is extended to N (Duschinsky) mixed vibrational modes. For this case a multidimensional ID is derived which provides a comprehensive, complete, and unified description of vibronically assisted electronic transitions in polyatomic molecules. The multidimensional ID is introduced with the aid of a multivariable generating function. The latter quantity incorporates both the transformation of normal mode coordinates between the initial and final electronic states and its frequency changes. This normal coordinate transformation leads to the generation of additional sets of geometrical displacements which cannot be uniquely assigned to normal mode displacements as in the parallel mode approximation. It is shown that normal coordinate rotation causes the final state vibrational distribution or the spectral line shape to deviate considerably from that observed at parallel modes. A further derivable property of the multidimensional ID is its selectivity which at certain values of the rotation angles leads to specific mode selections. Similarly, the nonradiative decay probability is subject also to variations and exhibits considerable increase under certain circumstances.