Kinetic, Computational and Mechanistic Investigation of Rh(κ2-dppe)2-Catalyzed Transfer Hydroformylation of Alkenes with Formaldehyde Assisted by Bayesian Parameter Estimation

Transfer hydroformylation of alkenes with formaldehyde constitutes a green and sustainable route to aldehydes. In this work, the transfer hydroformylation of styrene with formaldehyde was efficiently catalyzed by Rh(κ2-dppe)2+ (A), where dppe stands for 1,2-bis(diphenylphosphino)ethane. The reaction was found to be first order with respect to both Rh and substrate concentrations and fractional order with respect to formaldehyde concentration, in line with the behavior previously reported for 1-hexene. DFT was used to investigate the reaction mechanism by using ethene and Rh(κ2-dpe)2+ (A), where dpe stands for 1,2-bis(phosphine)ethane, as simplified models of the substrate and catalyst, respectively, and by considering several functionals. The DFT calculations indicate that M06-L provides the most suitable description of the thermodynamic and activation parameters associated with the elementary steps. The combined analysis of kinetic results and the DFT calculations allowed us to propose a detailed catalytic cycle for this reaction, initiated by the reversible oxidative addition of formaldehyde to complex A to afford Rh(H)(CHO)(κ2-dppe)2+ (B, K1). Coordination of ethene occurs through partial dissociation of one phosphorus atom of the diphosphine ligand, generating Rh(H)(alkene)(CHO)(κ2-dppe)(κ1-dppe)+ (IB, K2), followed by the transfer of the hydride to the alkene to give Rh(alkyl)(CHO)(κ2-dppe)2+ (C, k3), which is considered the rate-determining step of the process. The cycle is completed by reductive elimination of propanal, thereby regenerating A. The overall activation energy calculated by DFT (Ea = 20.0 kcal mol−1) is in good agreement with the experimental values determined for 1-hexene and styrene (20.1 and 22.9 kcal mol−1, respectively). On the basis of these experimental and DFT results, a mathematical kinetic model with the canonical form r0=K1K2k3RhoalkeneCH2O/(1+K1CH2O) was developed and fitted using a tandem LMFit/Bayesian approach, allowing the values of K1 and K2k3 to be estimated, with comparatively low uncertainty. Overall, this integrated kinetic, computational, and statistical study provides a consistent mechanistic and quantitative framework for understanding the transfer hydroformylation of alkenes with formaldehyde.