rXXXX American Chemical Society 246 dx.doi.org/10.1021/cs100129u | ACS Catal. 2011, 1, 246–253 RESEARCH ARTICLE pubs.acs.org/acscatalysis What Makes for a Bad Catalytic Cycle? A Theoretical Study on the Suzuki-Miyaura Reaction within the Energetic Span Model Sebastian Kozuch* ,† and Jan M. L. Martin ‡ † Department of Organic Chemistry, Weizmann Institute of Science, IL-76100 Rechovot, Israel ‡ Department of Chemistry and the Center for Advanced Scientific Computing and Modeling (CASCAM), University of North Texas, Denton, Texas 76203-5017, United States b S Supporting Information ABSTRACT: The Suzuki-Miyaura cross-coupling reaction using PMe 3 , PPh 3 , and PtBu 3 as ligands was studied theoretically with accurate density functional theory (DFT) methods and the Ener- getic Span Model. The energetic span model is a tool to compute catalytic turnover frequencies (TOF) from computationally ob- tained energy states. In this work the model is expanded to include turnover numbers (TON) and off-cycle intermediates. The results show that although the monophosphine route is the fastest pathway, the diphosphine cis route (accessible for small ligands) may also be reactive. The death sentence of the PMe 3 catalyst is the possibility to reach the low energy trans diphosphine species, which substantially reduces the TON. In the PPh 3 case, the formation of Pd 0 L 3 was found to be the major drawback for efficient catalysis. The PtBu 3 system is the most efficient of the three, as only the monophosphine mechanism is accessible. KEYWORDS: energetic span, cross-coupling, Suzuki-Miyaura, theoretical, density functional theory ’ INTRODUCTION: SUZUKI-MIYAURA REACTION The cross-coupling reaction of Suzuki-Miyaura has proven to be a practical way to generate C-C bonds by coupling an organic halide with an organoboron molecule, in the presence of a palladium catalyst (see Figure 1). 1-7 The reaction proceeds in a basic medium, thus a boronate is the substrate involved in the substitution of the halide from the Pd II complex. 8,9 It is known that bulky phosphines with big cone angles 10 like Pt Bu 3 11,12 are more effective than small phosphines for cross-coupling reactions. 1-3,13-17 The size of the ligand is even more important than its electronic effects, 18,19 since while the electron donating/with- drawing power of the ligand can “fine-tune” the oxidative addition and reductive elimination steps, 1-3 a bulky ligand will qualitatively change the mechanism of the reaction by forcing the dissociation of a phosphine. The monophosphine pathway produced by bulky ligands is a constant factor in highly efficient cross-coupling reactions. On the basis of previous theoretical studies of the Suzuki- Miyaura reaction, 8,13,19-28 herein we will study the mono and diphosphine routes for the coupling of PhBr and PhB(OH) 3 - using Pd(PMe 3 ) 2 , Pd(PPh 3 ) 2 , and Pd(Pt Bu 3 ) 2 as catalysts. The analysis of this systems can provide information on the reason for the ineffi- ciency of small ligand Pd complexes. Is the diphosphine mechanism actually worse than the mono- phosphine one? Which factors enhance or degrade the rate of reac- tion? To answer these questions we will employ the energetic span model. 29-32 With this tool we can estimate the turnover frequency (TOF) of a reaction and the determining states that shape the kinetics of the cycle. However, to understand the reasons for the deactivation of a catalyst, we must expand the model to include more complex systems, and consider the possibility to theoretically deter- mine the turnover number (TON) of a catalyst. ’ TOF IN THE ENERGETIC SPAN MODEL The TOF is the rate of reaction of a catalytic cycle, and is measured as the number of cycles (N Δt ) per time span (Δt) and total catalyst concentration ([C t ]): 1-3 TOF ¼ N Δt ½C t  3 Δt ð1Þ The higher the TOF, the better the catalyst. In a recent series of papers, 29-34 a way was proposed to calculate the TOF from the energetic profile of a serial catalytic cycle: the energetic span model. This method works from the energy representation of the reaction (the E-representation), as opposed to the equivalent rate-constant representation (k-representation) 31 more typical of experimentalists (see Figure 2). It is possible to move from one representation to the other by means of Eyring’s transition state theory, but the E-representation was found to be mathematically simpler and more manageable for theoreticians. Hence, in a serial catalytic cycle with I j being the Gibbs energy of the j th intermediate, T i the energy of the i-th transition state, Received: December 8, 2010 Revised: January 6, 2011