Analysis of the measured spectra of 2 and 3 coincident neutral products indicated the overwhelming predominance of 3-body events. A conservative upper limit to the contribution of the 2D2O product channel was found to be ~1% of the detected MN events (see SM for more details). This, compared with the >2% 2H2O yield in the undeuterated system,13 indicated that the dynamical isotope effect results in substantial suppression of the proton (deuteron)-transfer MN mechanism. Bogot et al demonstrated that momentum conservation is insufficient to distinguish between the two possible 3-body product channels, and used the estimated KER to distinguish between the contributions of 2OH + H2 and the lower lying H2O + OH + H channels.13 Here, we implemented principal component analysis (PCA) to distinguish between the 3-body channels based on the measured momentum conservation and KER, as well as energy partitioning between the light and heavy fragments (as described in more detail in the SM). Figure 3a shows the measured event distribution as a function of the leading PCA components that exhibits two distinct features. The feature on the left-hand-side was assigned to 2OD + D2 events and the resulting KER distribution is shown in Fig 3b. Similarly, we assigned the feature on the right-hand-side to the D2O + OD + D channel, which exhibits the KER distribution shown in Fig 3c. The dashed vertical lines in 3b and 3c indicate the maximal kinetic energy available for each channel. Accordingly, we conclude that similar to the undeuterated system, the excess energy in these channels is predominantly released as KER, indicating the low internal excitation of the neutral products. The width of the measured distributions is consistent with the undeuterated measurements, and is attributed primarily to the instrumental resolution.13 Interestingly, the branching ratio between the atomic D vs. molecular D2 channels was found to be ~2:1. This, compared with the 3:1 obtained for the analogous H vs H2 channel ratio measured for the undeuterated system.13 The difference is consistent with suppression of a substantial ~30% proton-transfer contribution to the H2O + OH + H channel. Nevertheless, one cannot exclude the possibility of a dynamical isotope effect also on the MN mechanism proceeding via electron-transfer. In the SM, we show that the branching ratio reported for the undeuterated system was reproduced also when applying the PCA method implemented here.
Analysis of momentum correlations in 3-body breakup events can provide additional valuable insights about the underlying mechanism.5,7,38–42 The Dalitz plot analysis uses the kinetic energy partitioning between the three fragments to represent the momentum correlations, such that an uncorrelated dissociation, abiding total energy and momentum conservation, appears as a uniform distribution within the unit circle. The Dalitz plot was originally developed and applied to dissociation into three equal masses.38–40 Here, we implement a generalized, mass-scaled Dalitz-plot analysis that uses , the kinetic energy fractions of each mass , relative to the maximal kinetic energy it can carry in the center of mass frame while conserving the total momentum.5,7,15,41,42 Figure 4a shows the measured Dalitz plot of the D2O + OD + D events. The vertical axis corresponds to , the scaled KE fraction carried away by the D atom, while the partitioning of the remaining energy between and depends on the horizontal axis. For convenience, all three axes are indicated in Fig 4. The Dalitz plot representation is particularly useful for identifying sequential dissociation mechanisms that exhibit a distinctive feature in the momentum correlations.6,7,15,43,44 The KE fraction of the direct product of the first dissociation event is independent of the energy partitioning between the two products of the second dissociation. Furthermore, if the dissociation occurs on a time-scale that is long compared with the rotations of the unstable intermediate, albeit short compared with the time of flight to the detector, the energy partitioning will be random within the boundaries defined by total energy and total momentum correlations. To help illustrate how such correlations appear on a Dalitz-plot, we performed Monte Carlo simulations of a sequential D2O + OD + D breakup, in which the OD and an intermediate [D3O] dissociate with an initial KER corresponding to the expected IP – EA difference.26–28 The remaining available energy for this channel was released in the 2nd dissociation of [D3O] à D2O + D, which was simulated to occur after complete depolarization of the 2nd dissociation direction. The resulting Dalitz plot distribution is shown in Fig 4b, it exhibits a strip of events that is perpendicular to the axis with ~75% KE fraction carried away by the OD product, independent of the energy partitioning between the D2O and D fragments. Figure 4c shows a simulation of the same sequential breakup, while including realistic experimental conditions including the possibility of exchange of the mass assignment of the experimentally measured heavy fragments. While such exchange has negligible effect on the measured KER distributions,13 it results in the appearance of a 2nd mirror image strip that is clearly observed also in the experimentally measured data. It is interesting to note that Gellene and Porter45 reported a substantially lower IP for D3O compared with 5.4 eV that was theoretically predicted.27,28 The latter value was found to be in good agreement the initial KER of 3.6 ± 0.1 eV that best fitted the experimental Dalitz plot, and corresponds to an IP of 5.4 ± 0.1 eV, see SM for more detail. The agreement between the simulated and measured Dalitz plots in Fig 4a and 4c, indicates that the D2O + OD + D product channel originates from a sequential mechanism via the crossing of the ionic curve and the ground electronic state of the neutral [D3O] + OD complex. The KER in the initial dissociation event can be also derived from the measured KE of the OD in the center of mass frame, peaking at ~1.9 eV, times the total mass and divided by the D3O mass (40/22). By comparing this ~3.5 eV energy gained by neutralization with the Coulombic potential, we derived the R~4 Å distance, at which the electron transfer occurs during MN towards the D2O + OD + D channel. This non-adiabatic pathway is indicated schematically in Fig 1 by the red arrows. The ~100 meV shift between the two estimates is within the experimental uncertainty, and can be partially due to a systematic contribution of the collision energy to the measured KE of the OD products.
Figures 4d-f show the measured and simulated Dalitz plots for the 2OD + D2 product channel. Here, the two heavy fragments are experimentally indistinguishable, resulting in a mirror symmetry about a central horizontal line. Nevertheless, in the simulated distribution shown in Fig 4e, we distinguish between the 1st OD originating from the hydroxide anion and the 2nd OD originating from the hydronium cation. In contrast with the D2O + OD + D channel, the energy fraction carried by the 1st OD is much lower. Correspondingly, the fraction of the light fragment is higher. In order to achieve agreement between the experimentally measured and simulated Dalitz plots, the KER in the initial dissociation was simulated to be 1.55 ±0.1 eV, a small fraction of the total ~4.06 eV KER in this channel. This in agreement with MN via the predicted 3pe [H3O*] state, situated 2.1 eV above the electronic ground state.27 The KER in the initial dissociation event can also be estimated from the measured KE of the OD in the center of mass frame, peaking at ~0.8 eV, times the total mass divided by the D3O mass, 40/22. By comparing the Coulombic potential with these ~1.45 and 1.55 eV estimates of the initial energy release, we can derive the 9 - 10 Å distance range at which the electron transfer occurs during MN towards the 2OD + D2 channel. The measured fragmentation patterns of this channel are therefore in agreement with the non-adiabatic trajectory shown by the green arrows in Fig 1, in which electron transfer occurs at the crossing of the first excited [D3O*] + OD potential with the ionic curve.