Incorporation of finite temperature effects into reaction simulation methods for accurate prediction of kinetic and thermodynamic rate parameters is a long-standing challenge in computational chemistry. Routine methods for adding finite temperature effects such as the rigid-rotor harmonic-oscillator approximation (RRHO) begin to break down as systems increase in complexity. In this work, we revisit Blue Moon thermodynamic integration (BMTI) based on constrained ab-initio molecular dynamics simulations along the intrinsic reaction coordinate. By sampling configurations orthogonal to the defined reaction coordinate, we can directly calculate of free energies of activation and kinetic rate constants at the simulation temperature. We assess the efficiency and convergence accuracy of the BMTI approach using semi-empirical density functional theory (SE-DFT) across a diverse test set of chemical reactions including bond breaking, formation, and isomerization events. For each reaction we compare the results from BMTI to both RRHO-based calculations and experimental data for free energies of activation and kinetic rate constants. We also discuss our algorithm and results in context of data collection for the training of machine-learning algorithms for enhanced sampling.

Figure 1. (Left) Ball-and-stick depiction of the CH<sub>3</sub>Cl + Cl<sup>-</sup> SN<sub>2</sub> reaction. (Center) Potential energy surface of CH<sub>3</sub>Cl + Cl<sup>-</sup> projected on to two representative coordinates, together with the minimum energy pathway (black), structures sampled near the transition state (TS) at 7 K (red), and structures sampled near the TS at 600 K (green). (Right) Reaction coordinate diagram showing activation free energy (kcal/mol) of the CH<sub>3</sub>Cl + Cl<sup>-</sup> SN<sub>2</sub> reaction at 7 K (orange) and 600 K (blue).

Figure 1. (Left) Ball-and-stick depiction of the CH₃Cl + Cl^- SN₂ reaction. (Center) Potential energy surface of CH₃Cl + Cl^- projected on to two representative coordinates, together with the minimum energy pathway (black), structures sampled near the transition state (TS) at 7 K (red), and structures sampled near the TS at 600 K (green). (Right) Reaction coordinate diagram showing activation free energy (kcal/mol) of the CH₃Cl + Cl^- SN₂ reaction at 7 K (orange) and 600 K (blue).

Joseph Gomes

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