Data-driven methodologies are crucial for accelerating the identification of optimal conditions in eco-friendly chemical processes. Continuous-flow systems offer advantages like reproducibility, rapid heating/mixing, and ease of automation, making them ideal for computational and automated protocols. Gaussian process regression can predict reaction parameters efficiently. However, simultaneously optimizing multiple flow reaction variables (flow rate, pipe dimensions, micromixer type, and other reaction parameters) remains challenging. Bayesian Optimization (BO), a probabilistic method for finding the global maximum/minimum of a black-box function, is a powerful tool for multi-parameter screening in flow and batch systems. The authors' group previously applied BO to electrochemical reactions. Existing BO methods often require converting categorical variables (solvents, reagents) into numerical values using descriptors, which is complex and requires expertise. This study aims to develop a simpler, more practical BO-assisted method by directly optimizing categorical parameters using one-hot encoding without feature extraction or model construction. The focus is on the synthesis of functionalized biaryls, important motifs in natural products, pharmaceuticals, and chiral ligands, via a redox-neutral cross-coupling reaction of iminoquinone monoacetals (IQMAs) or quinone monoacetals (QMAs) with arenols. While metal-free organocatalytic processes using Brønsted acids exist, they often require high catalyst loading, long reaction times, and high temperatures. The authors hypothesized that a flow system could improve efficiency and sustainability.

Numerous studies highlight the benefits of data-driven approaches and continuous flow systems for reaction optimization. Computational and automated protocols are extensively investigated due to their reproducibility and efficiency. Gaussian process regression has shown promise in predicting reaction parameters. Bayesian optimization (BO) has emerged as a powerful tool for multi-parameter screening, particularly in handling both numerical and categorical variables. However, handling categorical variables often requires descriptor-based conversion, adding complexity. The authors cite previous work on BO-assisted screening for electrochemical reactions and other applications. Existing methods for metal-free synthesis of biaryls often involve Brønsted acid catalysis but suffer from drawbacks such as high catalyst loading, long reaction times, and high temperatures. The authors’ work builds upon previous studies on Brønsted acid-catalyzed cross-coupling of QMAs or IQMAs with arenols, aiming to improve efficiency and sustainability using flow chemistry and BO.

The study employed Bayesian Optimization (BO) with parallel lower confidence bounds (LCB) as the acquisition function to optimize the flow synthesis of biaryls. Six parameters were simultaneously optimized: the amount of arenol (1–3 equiv.), temperature (20–60 °C), concentration of IQMA in toluene (0.01–0.1 M), flow rate (0.05–0.2 mL/min), catalyst loading (0.5–2 mol%), and micromixer type (Comet X, β-type, and T-shaped). One-hot encoding was used to represent the categorical micromixer variable. The initial dataset consisted of six reactions to provide a broad initial search space. The reaction involved the cross-coupling of IQMA 1a and 2-naphthol 2a using TfOH as the catalyst in toluene. Parallel BO efficiently evaluated multiple conditions simultaneously. After the initial screening, additional experiments were conducted based on BO suggestions, iteratively refining the optimal conditions. The optimized conditions were then applied to a broader substrate scope, evaluating various IQMAs and arenols. A similar BO-assisted optimization was performed for the cross-coupling of QMAs with arenols, using 4a and 5-bromoresorcinol 2j as model substrates. Gram-scale synthesis was performed to demonstrate scalability, and post-synthetic transformations were carried out to showcase the utility of the synthesized biaryls. The flow system used syringe pumps to deliver reactants to the micromixer, and the product was collected after quenching with saturated aqueous NaHCO3 solution. Product purification was achieved using silica gel column chromatography.

Bayesian optimization successfully identified optimal reaction conditions for the flow synthesis of 2-amino-2'-hydroxy-biaryls, achieving a 96% NMR yield (93% isolated yield). The optimized conditions involved a Comet X micromixer, a flow rate of 0.08 mL/min, and a residence time of 15 min. A broad substrate scope was demonstrated for both IQMAs and QMAs, with various substituents on the aromatic rings tolerated, leading to good to excellent yields (71-97%). The optimized conditions for QMAs involved a β-type micromixer and different concentrations compared to IQMAs. Gram-scale synthesis of the target biaryl was successfully performed (85% yield). Post-synthetic transformations, including the removal of a methanesulfonyl group and a nickel-catalyzed reductive coupling, further demonstrated the utility of the synthesized biaryls. A plausible reaction mechanism involving mixed acetal formation followed by a [3,3]-sigmatropic rearrangement was proposed.

This study demonstrates a significant advancement in the efficient and sustainable synthesis of biaryl compounds. The combination of flow chemistry and Bayesian optimization offers a powerful approach for rapidly identifying optimal reaction conditions, overcoming the limitations of traditional methods. The use of one-hot encoding for categorical variables simplifies the optimization process, eliminating the need for complex descriptor-based conversion. The high yields, broad substrate scope, and gram-scale applicability highlight the practical potential of this methodology. The results emphasize the benefits of using flow chemistry for efficient and green synthesis, reducing waste and improving reaction control. The successful application of post-synthetic transformations further expands the synthetic utility of this method.

The authors successfully developed a highly efficient, rapid, and regioselective flow synthesis of functionalized biaryls using a redox-neutral cross-coupling reaction. Bayesian optimization with one-hot encoding efficiently determined optimal reaction conditions, including both numerical and categorical parameters. The methodology was successfully scaled up to the gram-scale. Future research could explore the application of this approach to other reactions and the development of highly enantioselective biaryl syntheses using immobilized chiral catalysts.

The study focused on a specific set of substrates and reaction conditions. The generalizability of the findings to other biaryl coupling reactions or different catalyst systems requires further investigation. While the one-hot encoding approach simplifies the handling of categorical variables, it may not be universally applicable to all types of categorical data. The substrate scope was explored, but it is possible that other substrates with significantly different steric or electronic properties might exhibit different reactivity.