Proton transfer from water to ketyl radical anion: Assessment of critical size of hydrated cluster and free energy barrier in solution from first principles simulations

Ab Initio Metadynamics Calculations of Dimethylamine for Probing pKb Variations in Bulk vs. Surface Environments

“…Figure 7a shows a snapshot in which one water molecule (O1) donates a proton (H1) to the N atom, and an additional two water molecules are hydrogen-bonded to the donor water molecule (O1) in the bulk aqueous environment. Experimental gas-phase 82 and theoretical studies [57][58][59] suggest that this kind of arrangement is known to be a low-energy configuration and can serve as a critical cluster size for the proton transfer from water to an anion. A very similar type of configuration is also found at the air-water interface (Figure 7b).…”

“…61 However, our calculated free energy activation barriers are very close to previously reported values for the protonation of water to ketyl radical anion, which used a similar simulation methodology. 58 We also performed convergence tests with a 10-fs hill deposition rate, and the resulting free energy profile is shown in Figure S10. Based on our tests, we find that the free energy barrier decreases with increasing hill deposition rate.…”

Ab Initio Metadynamics Calculations of Dimethylamine for Probing pKb Variations in Bulk vs. Surface Environments

“…The deposition rate for the Gaussian hills was 10 MD steps, which allows each Gaussian hill to be spawned every 5 fs. It should be noted that for systems characterized by a high reactivity (such as ultrafast proton transfer from water to anions on a femtosecond time scale, [57][58][59] aqueous proton conduction across two-dimensional graphyne, 60 or irreversible reactions 61 ), a Gaussian hill deposition rate of every 10 MD steps is a common and sufficient choice. 62,63 However, in numerous instances, such as force-field based metadynamics simulations of alanine dipeptide or tri-peptide in vacuum, 64 dissociation of weak acids from AIMD simulations, 24 and systems having activation barriers where several picoseconds of metadynamics simulation time are required, 65 several hundred steps are used for the Gaussian hill deposition.…”

“…Figure 7a shows a snapshot in which one water molecule (O1) donates a proton (H1) to the N atom, and an additional two water molecules are hydrogen-bonded to the donor water molecule (O1) in the bulk aqueous environment. Experimental gas-phase 80 and theoretical studies [57][58][59] suggest that this kind of arrangement is known to be a low-energy configuration and can serve as a critical cluster size for the proton transfer from water to an anion. A very similar type of configuration is also found at the air-water interface (Figure 7b).…”

“…61 However, our calculated free energy activation barriers are very close to previously reported values for the protonation of water to ketyl radical anion, which used a similar simulation methodology. 58 It should be noted that a precise evaluation of the free energy requires an average over all of the free energy profiles to sufficiently explore the entire phase space spanned by the CVs. This can be carried out by increasing the simulation time until all accessible regions of the potential are explored, with trajectories crossing forward and backward several times between the reactant to the product regions.…”