Disproportionation of Bromous Acid HOBrO by Direct O-Transfer and via Anhydrides O(BrO)2and BrO–BrO2. An Ab Initio Study of the Mechanism of a Key Step of the Belousov–Zhabotinsky Oscillating Reaction

Abstract

The results are reported of an ab initio study of the thermochemistry and of the kinetics of the HOBrO disproportionation reaction 2HOBrO (2) ⇄ HOBr (1) + HBrO(3) (3), reaction ( R4' ), in gas phase (MP2(full)/6-311G*) and aqueous solution (SMD(MP2(full)/6-311G*)). The reaction energy of bromous acid disproportionation is discussed in the context of the coupled reaction system R2-R4 of the FKN mechanism of the Belousov-Zhabotinsky reaction and considering the acidities of HBr and HOBrO(2). The structures were determined of ten dimeric aggregates 4 of bromous acid, (HOBrO)(2), of eight mixed aggregates 5 formed between the products of disproportionation, (HOBr)(HOBrO(2)), and of four transition states structures 6 for disproportionation by direct O-transfer. It was found that the condensation of two HOBrO molecules provides facile access to bromous acid anhydride 7, O(BrO)(2). A discussion of the potential energy surface of Br(2)O(3) shows that O(BrO)(2) is prone to isomerization to the mixed anhydride 8, BrO-BrO(2), and to dissociation to 9, BrO, and 10, BrO(2), and their radical pair 11. Hence, three possible paths from O(BrO)(2) to the products of disproportionation, HOBr and HOBrO(2), are discussed: (1) hydrolysis of O(BrO)(2) along a path that differs from its formation, (2) isomerization of O(BrO)(2) to BrO-BrO(2) followed by hydrolysis, and (3) O(BrO)(2) dissociation to BrO and BrO(2) and their reactions with water. The results of the potential energy surface analysis show that the rate-limiting step in the disproportionation of HOBrO consists of the formation of the hydrate 12a of bromous acid anhydride 7 via transition state structure 14a. The computed activation free enthalpy ΔG(act)(SMD) = 13.6 kcal/mol for the process 2·2a → [14a](‡) → 12a corresponds to the reaction rate constant k(4) = 667.5 M(-1) s(-1) and is in very good agreement with experimental measurements. The potential energy surface analysis further shows that anhydride 7 is kinetically and thermodynamically unstable with regard to hydrolysis to HOBr and HOBrO(2) via transition state structure 14b. The transition state structure 14b is much more stable than 14a, and, hence, the formation of the "symmetrical anhydride" from bromous acid becomes an irreversible reaction for all practical purposes because 7 will instead be hydrolyzed as a "mixed anhydride" to afford HOBr and HOBrO(2). The mixed anhydride 8, BrO-BrO(2), does not play a significant role in bromous acid disproportionation.