Connecting Gas-Phase Computational Chemistry to Condensed Phase Kinetic Modeling: The State-of-the-Art

Accurately Predicting Barrier Heights for Radical Reactions in Solution Using Deep Graph Networks

Quantitative estimates of reaction barriers and solvent effects are essential for developing kinetic mechanisms and predicting reaction outcomes. Here, we create a new data set of 5,600 unique elementary radical reactions calculated using the M06-2X/def2-QZVP//B3LYP-D3(BJ)/def2-TZVP level of theory. A conformer search is done for each species using TPSS/def2-TZVP. Gibbs free energies of activation and of reaction for these radical reactions in 40 common solvents are obtained using COSMO-RS for solvation effects. These balanced reactions involve the elements H, C, N, O, and S, contain up to 19 heavy atoms, and have atom-mapped SMILES. All transition states are verified by an intrinsic reaction coordinate calculation. We next train a deep graph network to directly estimate the Gibbs free energy of activation and of reaction in both gas and solution phases using only the atom-mapped SMILES of the reactant and product and the SMILES of the solvent. This simple input representation avoids computationally expensive optimizations for the reactant, transition state, and product structures during inference, making our model well-suited for high-throughput predictive chemistry and quickly providing information for (retro-)synthesis planning tools. To properly measure model performance, we report results on both interpolative and extrapolative data splits and also compare to several baseline models. During training and testing, the data set is augmented by including the reverse direction of each reaction and variants with different resonance structures. After data augmentation, we have around 2 million entries to train the model, which achieves a testing set mean absolute error of 1.16 kcal mol-1 for the Gibbs free energy of activation in solution. We anticipate this model will accelerate predictions for high-throughput screening to quickly identify relevant reactions in solution, and our data set will serve as a benchmark for future studies.

Efficient Generation of Torsional Energy Profiles by Multifidelity Gaussian Processes for Hindered Rotor Corrections

Accurate thermochemistry computations often require proper treatment of torsional modes. The one-dimensional hindered rotor model has proven to be a computationally efficient solution, given a sufficiently accurate potential energy surface. Methods that provide potential energies at various compromises of uncertainty and computational time demand can be optimally combined within a multifidelity treatment. In this study, we demonstrate how multifidelity modeling leads to (1) smooth interpolation along low-fidelity scan points with uncertainty estimates, (2) inclusion of high-fidelity data that change the energetic order of conformations, and (3) predicting best next-point calculations to extend an initial coarse grid. Our diverse application set comprises molecules, clusters, and transition states of alcohols, ethers, and rings. We discuss limitations for cases in which the low-fidelity computation is highly unreliable. Different features of the potential energy curve affect different quantities. To obtain "optimal" fits, we apply strategies ranging from simple minimization of deviations to developing an acquisition function tailored for statistical thermodynamics. Bayesian prediction of best next calculations can save a substantial amount of computation time for one- and multidimensional hindered rotors.

Fixed-node diffusion Monte Carlo shows promise for modeling reaction thermochemistry of hydrocarbon-based radicals

Reliable thermodynamic and kinetic properties of free radical polymerization reactions are essential for synthesizing both primary polymeric materials and specialty polymers. The computational generation of these data from quantum chemistry requires a time-efficient method capable of capturing the essential physics. One such method, fixed-node diffusion Monte Carlo (FN-DMC) (using single Slater-Jastrow trial wavefunctions), has demonstrated the capability to recover 90%-95% of missing dynamic correlation energy for typical systems. In this study, methyl radical addition to ethylene serves as a simple model to test FN-DMC's ability to calculate enthalpies of reaction and activation energies with different time steps, antisymmetric trial wavefunctions, basis set sizes, and effective core potentials. The FN-DMC computational protocol thus defined for methyl radical addition to ethylene is subsequently benchmarked against Weizmann-1 and experimental reaction enthalpies from Lin et al.'s test set of 21 radical addition and 28 hydrogen abstraction enthalpies. Our findings reveal that FN-DMC consistently generates reaction enthalpies with chemical accuracy, exhibiting mean absolute deviation of 3.5(7) and 1.4(8) kJ/mol from the Weizmann-1 reference for radical addition and hydrogen abstraction reactions, respectively. Given its favorable computational scaling and high degree of parallelizability, we, therefore, recommend more comprehensive testing of FN-DMC with effective core potentials to address more extensive and intricate polymerization reactions and reactions with other radicals.

Improved Approach for ab Initio Calculations of Rate Coefficients for Secondary Reactions in Acrylate Free-Radical Polymerization

Secondary reactions in radical polymerization pose a challenge when creating kinetic models for predicting polymer structures. Despite the high impact of these reactions in the polymer structure, their effects are difficult to isolate and measure to produce kinetic data. To this end, we used solvation-corrected M06-2X/6-311+G(d,p) ab initio calculations to predict a complete and consistent data set of intrinsic rate coefficients of the secondary reactions in acrylate radical polymerization, including backbiting, β-scission, radical migration, macromonomer propagation, mid-chain radical propagation, chain transfer to monomer and chain transfer to polymer. Two new approaches towards computationally predicting rate coefficients for secondary reactions are proposed: (i) explicit accounting for all possible enantiomers for reactions involving optically active centers; (ii) imposing reduced flexibility if the reaction center is in the middle of the polymer chain. The accuracy and reliability of the ab initio predictions were benchmarked against experimental data via kinetic Monte Carlo simulations under three sufficiently different experimental conditions: a high-frequency modulated polymerization process in the transient regime, a low-frequency modulated process in the sliding regime at both low and high temperatures and a degradation process in the absence of free monomers. The complete and consistent ab initio data set compiled in this work predicts a good agreement when benchmarked via kMC simulations against experimental data, which is a technique never used before for computational chemistry. The simulation results show that these two newly proposed approaches are promising for bridging the gap between experimental and computational chemistry methods in polymer reaction engineering.

Machine learning from quantum chemistry to predict experimental solvent effects on reaction rates

Fast and accurate prediction of solvent effects on reaction rates are crucial for kinetic modeling, chemical process design, and high-throughput solvent screening. Despite the recent advance in machine learning, a scarcity of reliable data has hindered the development of predictive models that are generalizable for diverse reactions and solvents. In this work, we generate a large set of data with the COSMO-RS method for over 28 000 neutral reactions and 295 solvents and train a machine learning model to predict the solvation free energy and solvation enthalpy of activation (ΔΔG‡solv, ΔΔH‡solv) for a solution phase reaction. On unseen reactions, the model achieves mean absolute errors of 0.71 and 1.03 kcal mol-1 for ΔΔG‡solv and ΔΔH‡solv, respectively, relative to the COSMO-RS calculations. The model also provides reliable predictions of relative rate constants within a factor of 4 when tested on experimental data. The presented model can provide nearly instantaneous predictions of kinetic solvent effects or relative rate constants for a broad range of neutral closed-shell or free radical reactions and solvents only based on atom-mapped reaction SMILES and solvent SMILES strings.

Free-Radical Propagation Rate Coefficients of Diethyl Itaconate and Di-n-Propyl Itaconate Obtained via PLP–SEC

The propagation step is one of the key reactions in radical polymerization and knowledge about its kinetics is often vital for understanding and designing polymerization processes leading to new materials or optimizing technical processes. Arrhenius expressions for the propagation step in free-radical polymerization of diethyl itaconate (DEI) as well as di-n-propyl itaconate (DnPI) in bulk, for which propagation kinetics was yet unexplored, were thus determined via pulsed-laser polymerization in conjunction with size-exclusion chromatography (PLP-SEC) experiments in the temperature range of 20 to 70 °C. For DEI, the experimental data was complemented by quantum chemical calculation. The obtained Arrhenius parameters are A = 1.1 L·mol–1·s–1 and Ea = 17.5 kJ·mol−1 for DEI and A = 1.0 L·mol–1·s–1 and Ea = 17.5 kJ·mol−1 for DnPI.

Molecular Pathways for Polymer Degradation during Conventional Processing, Additive Manufacturing, and Mechanical Recycling

The assessment of the extent of degradation of polymer molecules during processing via conventional (e.g., extrusion and injection molding) and emerging (e.g., additive manufacturing; AM) techniques is important for both the final polymer material performance with respect to technical specifications and the material circularity. In this contribution, the most relevant (thermal, thermo-mechanical, thermal-oxidative, hydrolysis) degradation mechanisms of polymer materials during processing are discussed, addressing conventional extrusion-based manufacturing, including mechanical recycling, and AM. An overview is given of the most important experimental characterization techniques, and it is explained how these can be connected with modeling tools. Case studies are incorporated, dealing with polyesters, styrene-based materials, and polyolefins, as well as the typical AM polymers. Guidelines are formulated in view of a better molecular scale driven degradation control.

Verification for Temperature Dependence of Tacticity in Polystyrene Radical Polymerization with the Combination of Reaction Pathway Analysis and Red Moon Methodology

Radical polymerization is an economic and practical polymerization method over ionic and coordination polymerizations and is widely used for polymer production. Although many efforts have been made to improve the convenience and controllability of radical polymerization, it is still a challenge to directly observe the microbehaviors of propagation, which may provide inspiration for the development of polymerization processes. In this study, we focused on the tacticity of polystyrene produced by bulk radical polymerization since there is a debate over the temperature dependence. The propagation process is simulated via Red Moon methodology, which is a cost-effective method for handling complex chemical reaction systems. By the multiple pathway analysis for the propagation reaction model composed of the dimer radical and the monomer using density functional theory, we obtained the relative energies in multiple transition states, whose energy differences are partly explained by the π-π stacking interactions. Via performing Red Moon simulations from 30 to 190 °C, we confirmed that meso contents moderately increase as the temperature increases, which is explained by the influence of temperature on the probability density of the reaction conformations of each pathway. The successful prediction and explanation for tacticity demonstrate the potential of Red Moon methodology in unveiling the microbehaviors of propagation.

A general model for the ideal chain length distributions of polymers made with reversible deactivation

A general model is developed for the distribution of polymers made with reversible deactivation. The model is applied to a range of experimental systems including RAFT, cationic and ATRP.

Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression

This paper proposes a new method for calculating the monomer reactivity ratios for binary copolymerization based on the terminal model. The original optimization method involves a numerical integration algorithm and an optimization algorithm based on k-nearest neighbour non-parametric regression. The calculation method has been tested on simulated and experimental data sets, at low (<10%), medium (10–35%) and high conversions (>40%), yielding reactivity ratios in a good agreement with the usual methods such as intersection, Fineman–Ross, reverse Fineman–Ross, Kelen–Tüdös, extended Kelen–Tüdös and the error in variable method. The experimental data sets used in this comparative analysis are copolymerization of 2-(N-phthalimido) ethyl acrylate with 1-vinyl-2-pyrolidone for low conversion, copolymerization of isoprene with glycidyl methacrylate for medium conversion and copolymerization of N-isopropylacrylamide with N,N-dimethylacrylamide for high conversion. Also, the possibility to estimate experimental errors from a single experimental data set formed by n experimental data is shown.