The goal of the present work is to obtain accurate potential energy surfaces (PESs) for high-dimensional molecular systems with a small number of ab initio calculations in a system-agnostic way. We use probabilistic modeling based on Gaussian processes (GPs). We illustrate that it is possible to build an accurate GP model of a 51-dimensional PES based on 5000 randomly distributed ab initio calculations with a global accuracy of <0.2 kcal/mol. Our approach uses GP models with composite kernels designed to enhance the Bayesian information content and represents the global PES as a sum of a full-dimensional GP and several GP models for molecular fragments of lower dimensionality. We demonstrate the potency of these algorithms by constructing the global PES for the protonated imidazole dimer, a molecular system with 19 atoms. We illustrate that GP models thus constructed can extrapolate the PES from low energies (<10 000 cm−1), yielding a PES at high energies (>20 000 cm−1). This opens the prospect for new applications of GPs, such as mapping out phase transitions by extrapolation or accelerating Bayesian optimization, for high-dimensional physics and chemistry problems with a restricted number of inputs, i.e., for high-dimensional problems where obtaining training data is very difficult.
Bayesian optimization (BO) is regarded as an efficient approach that can identify optimal conditions using a restricted number of experiments. Despite demonstrated potential of BO, applications of BO‐based approaches in synthetic organic chemistry remain limited. Herein, we achieved the first rapid and mild (5.1 s, 20 °C) one‐flow synthesis of unsymmetrical sulfamides from inexpensive sulfuryl chloride. Undesired reactions were successfully suppressed and the risk in handling sulfuryl chloride was minimized by the use of micro‐flow technology. The reaction conditions producing ≥75 % yield were identified by a machine learning approach based on BO. It was demonstrated that BO produced the desired reaction conditions with a small number of experiments (19 and 10 experiments) in the entire search space (10,500 combinations of reaction conditions). Gaussian process (GP) models produced by BO provided the relationships between combinations of reaction parameters and outputs (RCRPO).
We demonstrate a sequential nucleophilic substitution of highly electrophilic and inexpensive phosphorus trichloride with three different alcohols in a continuous‐flow reactor. A variety of alcohols including ones that contained acid‐ and/or basic‐labile functionalities were rapidly reacted. A over nucleophilic substitution that occurred during reaction of the second alcohol was suppressed by the addition of imidazole. Density functional theory calculations of the sequential nucleophilic substitutions of alcohols were performed both with and without imidazole, and Berry pseudorotation was suggested as a rate‐limiting step in both cases. Herein, we discuss the reasons for the decreased selectivity in the absence of imidazole as well as those for improved selectivity in the presence of imidazole during the second nucleophilic substitution.
Sequential nucleophilic substitution of phosphorus trichloride with alcohols has been achieved. Over‐reaction was suppressed by rapid mixing through micro‐flow technology, and asymmetric phosphotriesters containing acid‐ and/or base‐labile functional groups were synthesized in good to high yields. Moreover, a mechanistic study by using DFT calculations suggested interesting reaction pathways. More information can be found in the Research Article by S. Fuse and co‐workers (DOI: 10.1002/chem.202200932).
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