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note
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Strictly speaking, stable complexes appear between reactants or intermediates and TSs. In fact, we obtained the optimized structures and the thermodynamic energies of these complexes and found that the free energies of several stable complexes were less than those of the corresponding precursors, that is, the reactants or intermediates. However, these stabilization energies were less than that due to the association of two acetic acids: the same is possible for the peroxyacetic acids or trifluoroacetic acids. This means that the stable complexes appearing between reactants or intermediates and TS correspond simply to the intermediate states in the overall reaction process and these will not affect the overall rate constant. Taking these facts into consideration, the free-energy diagrams in Figures 3 and 6 will be appropriate to provide essential information, even though the strict free-energy diagrams, possibly involving many molecules, may differ slightly from our diagrams, e.g., in a more strict sense, two acetic acid molecules associate with each other in the initial stage of reaction, but their influence on the relative size of the involved free-energy barriers would be negligible.
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