The performance of pharmaceutical processes depends on the flowsheet structure, the design of the equipment and the operating conditions, to a large extent, on the choice of solvents. The performance of the reaction steps is strongly affected by solvent choice: the rate of a given reaction in two different solvents can vary over several orders of magnitude as the solvent affects the solubility of the reactants and the rate constant – itself a function of the reaction’s free energy surface. In practice, solvents are often selected in the early stages of process development, and considered as fixed for the purpose of reactor design. The search for optimal solvents is often limited to a restricted set of options, potentially leading to sub-optimal designs. This is partly due to the complexity of predicting solvent effects on reactions.
In this work, we propose a systematic methodology for solvent design for reactions based on quantum mechanical calculations and optimization-based computer-aided molecular design (CAMD). The first step of the design methodology involves the computation of the reaction rate constants for the reaction(s) of interest in 7 different solvents. This is done using conventional transition-state theory. The free energy barrier in each solvent is obtained through quantum mechanical calculations on the reactants and transition states, in which the solvent is captured via a continuum solvation model. Specifically, we use the M06-2X functional with the SMD solvation model, as implemented in Gaussian 09. In the second step of the design methodology, we use the quantum mechanical data to build a predictive model of solvent effects on the rate of reaction. For this purpose, we use the solvatochromic equation and group contribution approaches. This yields a “surrogate” simplified model which can be used to predict the reaction rate constant in thousands of solvents at very low computational cost. In a third step, we embed this model in a mixed-integer CAMD formulation, in which we specify the size of the solvent design space and any additional design constraints (e.g., limits on the solvent melting point). By solving this optimization problem, we obtain a prediction of the solvent which maximizes the reaction rate constant. We verify the rate constant obtained for the best solvent with the surrogate model by comparing to a quantum mechanical calculation. If there is a mismatch, we return to the second step and improve the surrogate model by including the newest rate constant obtained by quantum mechanics. We iterate until convergence is achieved and verify the performance of the final predicted solvent experimentally.
The proposed approach is applied to a Menschutkin reaction, a classical SN2 reaction often studied in the context of solvent effects, where a solvent that maximizes the reaction rate constant is sought. The results of the quantum mechanical calculations are compared to experimental measurements of the kinetics by H1 NMR, for a range of solvents. Good quantitative agreement is obtained. The application of the design methodology leads to the identification of an improved solvent for the reaction, a finding which is verified experimentally. Such an approach is readily applicable to the selection of solvents in systems with competing reactions, and is particularly promising where selectivity is an issue.