Theoretical Study of Solvent-Exchange Reactions on Hexasolvated Divalent Cations in the First Transition Series: Model Calculation of a Hydrogen Cyanide Exchange

The stability of divalent cations (M(II)) of the first transition series, penta-, hexa-, and heptasolvated by hydrogen cyanide was studied in order to clarify the reaction mechanisms of nitrile-exchange reactions. The structural stabilities of the [M(NCH)7]^2+s depend on the d-electron configurations, though all of the [M(NCH)5]^2+s and [M(NCH)6]2+s are located at the local minima. The [M(NCH)7]^2+s are structurally more stable than the heptahydrated analogues. Successive binding energies show that it is difficult for an incoming ligand to penetrate the first solvation shells of cations in the later members. Thus, the associative mechanism of solvent-exchange reactions is favorable for cations in the earlier members resulting from energetics as well as structural stability. The symmetry of the imaginary vibrational mode along the reaction path corresponds to that of the transition density induced by one-electron excitation from the antibonding orbital occupied in the d^3 ion to the 4s orbital. The stable [M(NCH)7]^2+s arise from the large excitation energies sufficient to reduce the second term (see Eq. 4 in the text) of Bader-Pearson’s second-order perturbation expansion.