S1 Supporting Information Mechanism of the Palladium-Catalyzed Homocoupling of Aryl-Boronic Acids: Key Involvement of a Palladium Peroxo Complex Carlo Adamo, a Christian Amatore,* b Ilaria Ciofini, a Anny Jutand,* b Hakim Lakmini b a Ecole Nationale Supérieure de Chimie, Laboratoire d’Electrochimie et Chimie Analytique, UMR CNRS 7575, 11 Rue Pierre et Marie Curie. F-75231 Paris Cedex 5, France b Ecole Normale Supérieure, Département de Chimie, UMR CNRS-ENS-UPMC 8640 24 Rue Lhomond. F-75231 Paris Cedex 5, France General kinetic laws. An experimental reaction-order of +1 and +2 has been found for 4 and 1 respectively (in excess of 1). The following mechanism has been examined to ascertain the experimental results. 1 k 1 OOB(OH) 2 K 1 = k 1 /k -1 + ArB(OH) 2 6 Pd(PPh 3 ) 2 + ArB(OH) 2 O O Ar _ Pd _ PPh 3 PPh 3 4 1 k -1 k 2 cis-7 O O B OH OH Ar 6 PPh 3 PPh 3 Pd (1) (2) The experimental rate for the peroxo complex 4 consumption is expressed by the following equation with α = 1 and β = 2: rate = k [4] α [1] β . An analytical expression of the rate can be obtained by solving the following coupled differential equations: d[4] dt - k 1 [4] [1] + k -1 [6] = d[6] dt k 1 [4] [1] - (k -1 + k 2 [1]) [6] = d[cis-7] dt k 2 [6] [1] = This general case (excess of 1) will be noted na (no approximation). However, some approximations could be made to simplify the kinetic problem and to derive analytical solutions of the rate law. If the reaction rate of complex 6 in reaction (2) is sufficiently slow so that the first reaction may be considered as being at equilibrium, the relation between rates becomes: k -1 [6] >> k 2 [6][1]. This approximation corresponds to the pre-equilibrium approximation (noted pe). The second step (Eq 2) is thus the rate determining step. The rate of peroxo complex consumption then becomes: v = k 1 k 2 [4] [1] 2 k -1 In the opposite case, where k -1 [6] << k 2 [6][1], the concentration of 6 is small, and remains constant. This approximation corresponds to the steady state hypothesis (noted ss). The forward reaction in Eq (1) is thus the rate determining step. The rate of peroxo complex consumption becomes: v = k 1 [4][1]. However, these three cases may a priori be in competition. Competition parameters, p i , may be introduced, such as the ratio of the average concentration of the key species obtained when each case is considered alone. 29 = p 1 [6] ss [6] pe = p 2 [6] pe [6] na = p 3 [6] ss [6] na , , = p 2 p 1 The average concentration may be expressed as: , = [6] ss k 1 C° k 2 = [6] pe k 1 C°[1] k -1 = [6] na C° , where C° is the limit concentration of 4. Thus, one has: