Which set of parameters defines the configuration for vibrational modes in a molecule?

The correct answer is the set of character tables and symmetry properties, as these are key tools used in group theory to analyze the vibrational modes of a molecule.

In vibrational spectroscopy, molecules can be associated with certain symmetry operations, which can be systematically classified using character tables. These tables provide information about how various vibrational modes transform under the symmetry operations corresponding to the molecular point group. The vibrational modes of a molecule can be categorized as symmetric or antisymmetric, and the character table helps to determine how these modes behave when the symmetry operations are applied.

Furthermore, symmetry properties help to identify the allowed and forbidden vibrational transitions based on the selection rules, which are derived from group theory. By analyzing the symmetry of the molecule and its vibrational modes using character tables, one can effectively predict the spectroscopic behavior of the molecule.

The other options do not fully encapsulate this relationship. While degrees of freedom and bond angles reflect some structural features of molecular vibrations, they do not incorporate the symmetry aspects necessary for a complete vibrational analysis. Similarly, character tables provide information, but without an explicit understanding of symmetry properties, one would lack insight into how these vibrational modes interact under the influence of external perturbations, like those encountered in spectroscopy.