A reactivity model for oxidative addition to palladium enables quantitative predictions for catalytic cross-coupling reactions

Abstract

Making accurate, quantitative predictions of chemical reactivity based on molecular structure is an unsolved problem in chemical synthesis, particularly for complex molecules. We report an approach to reactivity prediction for catalytic reactions based on quantitative structure-reactivity models for a key step common to many catalytic mechanisms. We demonstrate this approach with a mechanistically based model for the oxidative addition of (hetero)aryl electrophiles to palladium(0), which is a key step in myriad catalytic processes. This model links simple molecular descriptors to relative rates of oxidative addition for 79 substrates, including chloride, bromide and triflate leaving groups. Because oxidative addition often controls the rate and/or selectivity of palladium-catalyzed reactions, this model can be used to make quantitative predictions about catalytic reaction outcomes. Demonstrated applications include a multivariate linear model for the initial rate of Sonogashira coupling reactions, and successful site-selectivity predictions for Suzuki, Buchwald-Hartwig, and Stille reactions of multihalogenated substrates relevant to the synthesis of pharmaceuticals and natural products.

Fig. 1. (A) Simplified cross-coupling mechanism, highlighting oxidative addition as the rate and/or selectivity determining step. (B) Competition experiment approach to determining relative rates of oxidative addition by quantifying ratios of Pd(ii) products via³¹P NMR spectroscopy. (C) Relative reactivity scale for oxidative addition to Pd(PCy₃)₂ for selected substrates; observed ΔG^‡_OA for 2-bromo-5-nitropyridine set to 0 kJ mol⁻¹. (D) Utility of reactivity model in predictions for cross-coupling in synthesis.

Fig. 2. Design and performance of a quantitative reactivity model for oxidative addition to Pd(0). (A) General mechanism for oxidative addition to L_nPd(0), with π-complex intermediate preceding either Pd insertion into C–X bond, or an S_NAr-like displacement of X. (B) Molecular descriptors used to model oxidative addition reactivity as a function of substrate structure. (C) Multivariate linear regression model of ΔG^‡_OA for 70 Ar–Cl and Ar–Br substrates in THF, including all data points in regression analysis. (D) Representative multivariate linear regression model generated using a 60/40 training/test split. (E) Univariate plot of IBSI_C–Xversus ΔG^‡_OA for Ar–Cl, Ar–Br, and Ar–OTf, revealing that bond strength is poorly correlated to ΔG^‡_OA within each leaving group set. (F) Unified linear regression model of ΔG^‡_OA for Ar–Cl, Ar–Br, and Ar–OTf substrates in THF, including all data points in regression analysis. MAE = mean absolute error. Colour-coding on R², Q², and MAE values corresponds to the matching data subset, values in black are for all data.

Fig. 3. Electronic and steric features of oxidative addition. (A) ESP_Pd for calculated π-complex intermediate structures correlates with oxidative addition rates; structures for 7 of 11 examples shown; electrostatic potential maps for each intermediate are overlaid onto the line structures. (B) Calculated structures of π-complex intermediates reveal how steric strain induced by R¹ and R² (here, –CF₃ groups) in 2-halopyridines affect oxidative addition reactivity in equal proportions.

Fig. 4. Translating oxidative addition predictions to quantitative models of catalytic reactivity. (A) General reaction scheme and chemical space explored for 410 Sonogashira reactions, with two distinct substrate sets; initial rates determined previously. (B) Univariate linear correlations between predicted ΔG^‡_OA for oxidative addition to Pd(PCy₃)₂ and ln k for Sonogashira coupling with three phosphines; out-of-model substrates are Ar–Br molecules not included in ΔG^‡_OA training set. (C) Unified three-descriptor model for predicting ln k for the entire set of 410 reactions (29 substrates, 17 ligands), with data partitioned into training (60% of set #1), test (40% of set #1), and external validation (set #2); two external outlier points (red) are not included in the external validation statistics. (D) Subset of the model with 13 “small” phosphines (% V_bur <75). (E) Subset of the model with 4 “large” phosphines (% V_bur >75); two external outlier points (red) are not included in the external validation statistics. MAE = mean absolute error. Colour-coding on R², Q², and MAE values corresponds to the matching data subset.

Fig. 5. Predicted and reported selectivities for multihalogenated heterocycles in Suzuki–Miyaura and Buchwald–Hartwig cross-coupling reactions (examples of Buchwald–Hartwig substrates denoted with “BH”). Coloured labels on the heterocycles correspond to predicted major site (blue), predicted minor site (red, along with percentage of exceptions as reported in ref. 60), and observed site (purple sphere). The magnitude of ΔΔG^‡_OA between the two sites is given in green.

Fig. 6. (A) Quantitative selectivity predictions for dihalogenated heterocycles with small-to-medium ΔΔG^‡_OA between two sites, and observed product ratios. (B) Predictions for substrates with observed tunable selectivity, demonstrating that “simple” catalysts are quantitatively consistent with predicted selectivities; overriding predicted reactivity requires targeted screening and/or catalyst design. Coloured labels on the heterocycles correspond to predicted major site (blue), predicted minor site (red, along with percentage of exceptions as reported in ref. 60), and observed site (purple sphere). The magnitude of ΔΔG^‡_OA between the two sites is given in green.

Fig. 7. Retrospective analysis of applying ΔG^‡_OA predictions to synthesis design: dragmacidin D. (A) Retrosynthesis of core structure, involving selective fragment coupling to a dihalogenated pyrazine. (B) Approach involving differential halogenation, tosylate protecting group on indole 1, and switch from 5-chloro to 5-bromopyrazine intermediates for selective coupling. (C) Approach involving regioselective coupling to dibromopyrazine, TBS protecting group on indole 1, and regioselective Stille coupling.