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The TSs 22-24 of the oxygen exchanges (Scheme 3) have only one imaginary mode in which the oxygen atom is transferred between the two equivalent parts ofthe molecules. The reaction between IO4- and IO3- has about the same AQt value as the oxidation of Me2S with IO4- (Table 2, entries 1 and 11). On the other hand, the oxygen exchanges between Me2S and Me2SO, as well as between Me2SO and Me2SO2, would need a much higher free energy of activation (Table 2, Entries 9 and 10).
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