An illustration of the dipole-field/QM approach (see also Ref. 25): The ground-state of a photoacid such as HPTS (a) is modeled using ground-state phenol (b). Excited-state HPTS (c) is modeled as ground-state 2,4,6-tricyanophenol (d). The three cyano groups are not explicitly modeled; however, their electron-withdrawing effects are represented by the three external dipole moments shown in (d). The photoexcitation-induced nonequilibrium hydration is modeled by transforming equilibrated phenol into DF/QM 2,4,6-tricyanophenol.
Calculated mean square displacement (top) and oxygen–oxygen pair correlation function (bottom) from a 0.55 ns MD simulation of a system comprising 2,4,6-tricyanophenol and 47 water molecules [see text and Fig. 6(b) of Ref. 25]. The raw MSD data are shown in dashed black. The blue and red lines represent linear regression fits of the first 300 ps and of the entire MSD trajectory, respectively. Results computed for pure water (see text) are shown for comparison in magenta. The experimental values, including error bars, are shown in black and correspond to pure water (see text).
Examples of nonequilibrium MD trajectories of the ionization indicator r defined in Eq. (3). All trajectories start in the covalent state, i.e., r(0) = 0. Note that for the trajectories shown here the phenolic O–H bond breaks very soon after the phenol → 2,4,6-tricyanophenol transformation. Note also that the proton translocation process is extremely rapid. Different colors were utilized to emphasize that trajectories were started from different initial configurations. The top, left panel also illustrates the formation of a contact ion-pair. The beginning of this trajectory was shifted by 10 ps in order to improve clarity.
The relevant timescales involved in the acid hydration process can be computed from the nonequilibrium MD trajectories (a) and the autocorrelation of the equilibrium fluctuations of the instantaneous hydration number (b,c) (see text). In panel (a), the first data point was taken from a simulation of equilibrated phenol. Panel (c) represents a zoom of panel (b) from 0 to 4.5 ps. Note the improved performance of the triexponential over the biexponential fit at early times.
The proton translocation times observed in the present equilibrium (black) and nonequilibrium (blue) trajectories of model 1. Equilibrium values are reported on the opposite side of the y-axis in order to improve clarity. Three values obtained in the nonequilibrium calculations are extremely close and are not reported individually. The red and green boxes group together values that were obtained when the first proton-acceptor water molecule was four-fold (red) vs three-fold (green) H-bonded.
Representative snapshots along the concerted proton translocation pathway: (a) The covalent form of the moderately strong phenol is intact; (b) and (c) transient structures involving the concerted motion of two protons. Note that the intervening water molecules are four-coordinated. (d) The excess proton is finally trapped by a three-coordinated water molecule. The total process takes 200 fs and involves the participation of three intervening water molecules.
Representative snapshots along the sequential translocation pathway: (a) The covalent form is intact; (b) and (c) transient Zundel (b) and Eigen (c) structures. It is important to note that the Eigen forms are three-fold H-bonded in this case. (d) When the excess proton reaches the third solvation shell, the acid is considered to have dissociated. The total translocation takes 2.6 ps in this case, i.e., the excess proton resides ∼1.3 ps on each of the two intervening water molecules.
A graphical illustration of the difference between sequential (black points) and concerted (red points) proton translocation: In the first case one can clearly see three species corresponding to the covalent, contact ion-pair, and solvent-shared ion-pair forms. In contrast, the contact ion-pair structure forms only transiently along the concerted trajectory: The transition path time (see text) from the covalent to the solvent-shared species (see the four points shown in green) takes only 60 fs. Both segments of trajectory were obtained from a 550 ps equilibrium MD simulation of 2,4,6-tricyanophenol (see text). The points displayed in red and green were shifted by 0.2 Å in both coordinates to enhance clarity. In addition, two points shown in green were shifted back by 0.2 Å (see points in blue and text) in order to help the comparison with the data depicted in black.
A pictorial representation of two proton translocation mechanisms in water: (a) H+ diffusion in water takes place sequentially and is driven, among other things, by a decrease in the coordination number of a neighboring water molecule from C.N. = 4 to C.N. = 3; (b) a presolvated, moderately strong phenol can transfer a proton to a four-coordinated water molecule. The subsequent concerted proton translocation process is stopped by an under-coordinated water molecule which acts as a trap.
A schematics of the elementary kinetic steps and the associated timescales that are involved in the (photo) dissociation of hydroxyarene acids, according to literature data and the present findings. Colors are employed to signify the following: Red is utilized when a molecule is in a high hydration state, i.e., C.N. ≈ 4 and ≈ 2.3 for oxygen atoms from water and phenolic moieties, respectively. In contrast, blue is employed to show that molecules are found in a low hydration state, i.e., C.N. ≈ 3 and ≈ 1.3 for the previously mentioned species. Superscripts are used to denote the nature of the excited-state: a star means a locally-excited state while a dagger represents a charge-transfer state (see text). The nature of the interaction between acid, base and solvent molecules is shown using the notation employed in Eq. (1): The symbol ∥ represents and encounter-pair while • represents a reactive pair. The elementary steps denoted by 2-4 (or 2′-4′) and 5 follow the same notation used in Eq. (1). Timescales are given for the intramolecular charge redistribution (ICT), hydration (h), reaction (r), and ion-pair separation (s) by solvent processes (see text).
Summary of the results obtained in the present nonequilibrium calculations. The details of the pKa calculations are provided in the Appendix. The definition adopted here for a “concerted” dissociation trajectory is provided in Sec. III B. The dipole moment values are for each pseudocyano group.
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