Knowledge Bank

In the quadratic approximation, the molecular relaxation to a minimum energy configuration following a specific nuclear distortion is given by the minimum energy coordinates, $R1$, which are directly related to compliance constants. In the case of a fixed distortion of a bond stretching coordinate, the corresponding minimum energy coordinate provides a first order approximation to the minimum energy path for unimolecular dissociation. In effect, the general quadratic potential function obtained from a detailed vibrational spectroscopic study can be used to estimate the reaction coordinate for unimolecular dissociation. Minimum energy coordinates also provide an approximation of the MEP for intramolecular rearrangement in fluxional molecules such as $PF5$. The symmetry constraints imposed on the reaction pathway via the minimum energy coordinate approximation can be treated using the second order Jahn-Teller theorem. Essentially, the symmetry species for $Ri$ and the lowest unoccupied MO must be the same. Minimum energy coordinates also help clarify the physical significance of primary force and compliance constants. Unique general quadratic compliance functions and $\{Ri\}$ have been determined for a number of systems ($ML_{6}, ML_{4}, AB_{3}, CH_{3}X, $etc) in order to evaluate the utility of $Ri$ as an approximation to the reaction pathways for unimolecular dissociation. In several cases, $R1$ correctly models the known structural changes in the molecular fragments accompanying bond cleavage.