A DFT and TD-DFT approach to the understanding of statistical kinetics in substitution reactions of M3Q4 (M = Mo, W; Q = S, Se) cuboidal clusters

For many years it has been known that the nine water molecules in M(3)Q(4)(H(2)O)(9)](4+) cuboidal clusters (M = Mo, W; Q = S, Se) can be replaced by entering ligands, such as chloride or thiocyanate, and kinetic studies carried out mainly on the substitution of the first water molecule at each metal centre reveal that the reaction at the three metal centres occurs with statistical kinetics; that is, a single exponential with a rate constant corresponding to the reaction at the third centre is observed instead of the expected three-exponential kinetic trace. Such simplification of the kinetic equations requires the simultaneous fulfilment of two conditions: first that the three consecutive rate constants are in statistical ratio, and second that the metal centres behave as independent chromophores. The validity of those simplifications has been checked for the case of the reaction of Mo(3)S(4)(H(2)O)(9)](4+) with Cl(-) by using DFT and TD-DFT theoretical calculations. The results of those calculations are in agreement with the available experimental information, which indicates that the H(2)O ligands trans to the μ-S undergo substitution much faster than those trans to the μ(3)-S. Moreover, the energy barriers for the substitution of the first water molecule at the three metal centres are close to each other, the differences being compatible with the small changes in the numerical values of the rate constants required for observation of statistical kinetics. TD-DFT calculations lead to calculated electronic spectra, which are in reasonable agreement with those experimentally measured, but the calculations do not indicate that the three metal centres behave as independent chromophores, although the mathematical conditions required for simplification of the kinetic traces to a single exponential are reasonably well fulfilled at certain wavelengths. A re-examination of the kinetics of the reaction by using global fitting procedures yields results, which are compatible with statistical kinetics, although an alternative interpretation in which substitution only occurs at a single metal centre under reversible conditions is also possible.