An "inverse" harpoon mechanism.

Electron-transfer reactions are ubiquitous in chemistry and biology. The electrons' quantum nature allows their transfer across long distances. For example, in the well-known harpoon mechanism, electron transfer results in Coulombic attraction between initially neutral reactants, leading to a marked increase in the reaction rate. Here, we present a different mechanism in which electron transfer from a neutral reactant to a multiply charged cation results in strong repulsion that encodes the electron-transfer distance in the kinetic energy release. Three-dimensional coincidence imaging allows to identify such "inverse" harpoon products, predicted by nonadiabatic molecular dynamics simulations to occur between H2 and HCOH2+ following double ionization of isolated methanol molecules. These dynamics are experimentally initiated by single-photon double ionization with ultrafast extreme ultraviolet pulses, produced by high-order harmonic generation. A detailed comparison of measured and simulated data indicates that while the relative probability of long-range electron-transfer events is correctly predicted, theory overestimates the electron-transfer distance.

INTRODUCTION

Long-range electron-transfer (LRET) reactions play a fundamental role in many processes in gas phase (–), solution (–), and surface chemical reactions (–). In the prototypical harpoon mechanism proposed by Magee and Polanyi, LRET from a metal atom to a halogen species occurs at a long distance and pulls the reactant molecules toward each other by the long-range Coulomb force (–, ). The high alkali-halogen collision cross sections, as high as ~150 Å2 (, ), indicate the very long distances at which such LRET can occur. Simple models offer valuable qualitative insight about different LRET reactions (, , ). Nevertheless, quantitative understanding, e.g., the relation of experimentally measured cross sections to the LRET distance distributions, is nontrivial (, ).

Coulomb explosion (CE) imaging can provide information about molecular-scale distances. Attosecond-scale multiple ionization and removal of all valance electrons has been achieved by passing a fast ion beam through a thin film (, ). Measuring the kinetic energy release (KER) of the instantaneously formed atomic ions, which are repelled from each other by the long-range Coulomb force, provides information about the distances within the parent molecule geometry. In contrast, noninstantaneous multiple ionization with an intense laser pulse revealed a charge-exchange resonance that enhances the second ionization of H2 at specific long internuclear distances that are reached by the molecule within the laser pulse duration and reflected in low KER (). Correspondingly, the KER in an LRET-triggered CE can offer an experimental probe of the distance at which the electron transfer occurs and test LRET models at different levels of theory.

The dynamics following double ionization of isolated methanol molecules offers an opportunity to observe such an LRET-triggered CE. Partial removal of valence electrons can also trigger fascinating structural rearrangement dynamics such as forming H3+ ions from isolated organic species. This initially unexpected product is ubiquitously observed in many systems and with different ionization methods, including electron impact (–), highly charged ion impact (, ), intense field laser ionization (–), and single-photon double ionization (SPDI) with extreme ultraviolet (EUV) pulses (–). Mebel and Bandrauk () proposed a roaming H2 mechanism for explaining H3+ formation. He considered double ionization of an allene molecule, after which a neutral H2 emerges from the dication and roams around until proton capture forms the trihydrogen ion and triggers a CE event. Initial intense-laser studies suggested roaming on the picosecond time scale for methanol dication (). However, time-resolved experiments indicated that ultrafast roaming dynamics time scale was much faster, on the order of ~100 fs (, , ). This controversy was resolved using low-intensity SPDI of the molecule formed by ultrafast EUV pulses. The experimental effort was complemented by nonadiabatic ab initio molecular dynamics (NA-AIMD) simulations (), based on extended multistate complete active-space second-order perturbation theory (XMS-CASPT2) (, ). The theoretical branching ratios and KER distributions for the H3+ formation, CO bond cleavage, and other CE channels followed the experimentally measured quantities. Furthermore, the researchers proposed that the ultrafast H3+ formation by proton transfer is in direct competition with LRET, resulting in HCOH+ + H2+ products. Therefore, they hoped that a direct comparison of this channel’s simulated and experimental KER distributions could provide a direct probe of the LRET distances. However, this channel’s small experimentally measured yields were at odds with the theoretically predicted branching ratio (, ), preventing analysis of the KER distributions in terms of LRET distances.

Here, we resolve the apparent contradiction between theory and experiment, thereby producing an experimental verification of the theoretical prediction concerning the “inverse” harpoon mechanism. In contrast to the prototypical harpoon mechanism, in which LRET is followed by attraction, the inverse harpoon results in substantial distance-dependent repulsion due to the presence of the same-charge ions. Furthermore, as shown below, the analysis of the experimental momentum correlations in three-body breakup events reveals a dominant secondary dissociation of the HCOH+ radical cation, showing that the “missing” HCOH+ + yield can be observed in the three-body dissociation channel

The measured three-body momentum correlations allow the reconstruction of the KER of the initial two-body CE events, facilitating the direct comparison with NA-AIMD. Once these missing events are accounted for, we find that the simulation correctly reproduces the measured branching ratios between the produced by the inverse harpoon mechanism and the competing proton capture mechanism generating ions. However, the simulated KER distribution peaks over 1 eV lower than the experimental measurement, suggesting that theory overestimates the LRET distance.

RESULTS

It is valuable to consider a simple LRET model for the inverse harpoon mechanism. The full blue line in Fig. 1 shows the repulsive long-range Coulombic potential as a function of the distance of the HCOH+ and CE products. The dashed red curve shows the attractive charge-induced dipole potential between the HCOH2+ dication and the neutral H2 molecule. The weak attraction of the neutral H2 follows a dependence on R, its distance from the dication that is treated as a point charge, and the induced dipole of a neutral with a polarizability α (). In the asymptotic limit, the potential difference between the CE channel and the higher-lying limit of the neutral + dication system is estimated to be ~2.2 eV, the difference between the ~15.4-eV ionization potential of H2 and the calculated ~17.6-eV adiabatic second ionization potential of hydroxymethylene. This attractive potential prevents the escape of the neutral H2 and enables the roaming dynamics that culminates either by proton capture and the formation of or by LRET and the formation of a product. Because of the high ionization potential of hydrogen, the two potentials cross at a relatively long ~12-a.u. (atomic units) distance, with little difference between the polarizability of H2 parallel and perpendicular to the molecular axis (). The Coulombic explosion, initiated at such long distance, can release up to ~2.2 eV as kinetic energy of the dissociating fragments.

Fig. 1.

Simple model of long-electron transfer from the neutral H2 to the HCOH2+.

The blue line indicates the repulsive Coulombic potential curve, while the dashed red curve indicates the attraction between the dication and an induced dipole on the neutral.

Luzon et al. () proposed that following the initial CE event, the hydroxymethylene HCOH+ radical cation may undergo subsequent fragmentation because of its internal excitation. Two dissociation pathways can be considered: COH+ + H and CHO+ + H, where, hypothetically, the latter is energetically more favorable by ~1.6 eV (). Experimental evidence for these hypotheses can be obtained from the coincidence fragment imaging of the three-body CE events, where the ion momenta are directly imaged on a time- and position-sensitive detector, while the third neutral H momentum is derived from the measured recoil of the ions’ center of mass (, , ). Figure 2 shows the mass-scaled Dalitz plot representation of the measured three-body momentum correlations in the product channel. The Dalitz representation shows the energy partitioning between the three fragments (–), where, for the mass-scaled representation, the three εCOH, εH, and εH axes indicate the respective energy fraction that each fragment carries relative to the maximal kinetic energy it can receive while conserving total momentum (). Thus, the vertical coordinate η2 = 2εH − 1 indicates the kinetic energy fraction of the cation, while the horizontal η1 coordinate reflects the energy partitioning between the other two products (see the Supplementary Materials for more details). In this representation, an uncorrelated three-body breakup obeying total momentum conservation exhibits a uniform distribution confined within the unit circle (, , ). The color scale indicates the measured probabilities, weighted relative to a uniform uncorrelated dissociation. The products carry nearly their maximal possible KER fraction, consistent with the proposed sequential mechanism of a relatively high KER CE event, followed by a secondary low KER dissociation of CHOH+. Complete depolarization of a much delayed secondary dissociation due to CHOH+ rotational motion would appear as an uncorrelated distribution with respect to η1. However, the measured data shown in Fig. 2 clearly favor the left-hand side of the Dalitz plot. The longitudinal lines in Fig. 2 indicate the contours of equal Jacobi angle β between the two dissociation vectors, where the β = 0 limit (η1 > 0) corresponds to a colinear dissociation of both H and in the same direction, while the β = π limit (η1 < 0) corresponds to a colinear fragmentation, with H and ejected in opposite directions. Considering the reported 7:1 preference of the versus the H2D+ + CHO+ in the SPDI of deuterated CH3OD methanol (), it is reasonable to assume that the roaming H2 is similarly more likely to undergo inverse harpoon and ejection of the cation while on the carboxyl rather than the hydroxyl side. Thus, the preference for β > π/2 indicates that the secondary dissociation was from the opposite hydroxyl side, preferentially resulting in rather than the product correlation. This is consistent with the preferred ejection of the energetically favorable CHO+ over its COH+ isomer that is dynamically preferred in the trihydrogen formation channel ().

Fig. 2.

Dalitz plot of H2+ + CHO+ + H channel showing the measured momentum correlations.

The ɛCOH, ɛH, and ɛH2 axes of each fragment (kinetic energy divided by the maximal energy allowed by momentum conservation) are indicated on the Dalitz plot. Dotted longitudinal lines indicate contours with equal Jacobi angles, β. Two representative momentum correlations are depicted, both assuming that the H2+ is ejected from the carbon side, while the H is ejected from the oxygen (or carbon side), resulting in respectively obtuse (or acute) β angles with correspondingly negative (or positive) η1 values.

The identification of sequential dissociation events based on their three-body momentum correlations allows evaluating the KER of the initial dissociation, by neglecting the recoil of the heavy CHO+/COH+ ion from the light H atom. Accordingly, it is possible to reconstruct the complete distribution of KER associated with inverse harpoon events, including both the measured two-body events and the contribution of three-body events that underwent a subsequent dissociation of the CHOH+ ion. Figure 3A shows the complete distribution of KER assigned to formation by an inverse harpoon mechanism, where full bars indicate the partial contribution of intact hydroxymethylene cations and empty bars indicate the reconstructed KER of the initial ejection event from sequential three-body breakup events. Both distributions appear to be similar with no indication that a higher KER in the initial dissociation event contributes to the stabilization of the hydroxymethylene product. The measured KER is significantly higher than the indicated ~2.2-eV KER that could be expected on the basis of the simple model presented in Fig. 1. The higher KER can be tentatively interpreted as efficient LRET at shorter distances than the ~12-a.u. distance predicted by the simple one-dimensional (1D) model. In principle, this can be explained by considering excitation that would raise the potential of the HCOH2+ + H2 complex and result in LRET at a shorter distance and with higher KER. However, high-level AIMD simulations can provide a better understanding of the LRET process.

Fig. 3.

Comparing experimental and simulated KER distributions for the CE, normalized to the total yield of double ionization.

In (A), the full bars indicate the KER distribution in two-body breakup events, while the empty bars indicate the initial KER in CE events that were followed by a secondary dissociation of metastable HCOH+ products. In (B), the contributions from AIMD trajectories initiated on the ground (GS), first and higher excited states of CH3OH2+ are presented in red, green, and blue bars, respectively. The vertical arrow indicates the KER predicted by the simple 1D model.

The bars in Fig. 3B show the simulated KER distribution for the channel. More than 200 trajectories are initiated on each of the seven lowest singlet states of the methanol dication, in accordance with the high energy of the EUV photons (, ). The simulation is terminated once the system is significantly extended after the dissociation. Thus, delayed fragmentation of the CHOH+ product could not be observed, and the three-body channel was not significant in the simulated trajectories. Nevertheless, few trajectories did exhibit H2+ ejection that is shortly followed by HCOH+ breakup, with only four trajectories yielding CHO+ and two yielding COH+, in agreement with the trend observed in the measured three-body momentum correlations. Similar to the experimental data, the simulated KER peak is higher than the 1D model prediction, indicating shorter LRET distances.

Despite the higher KER, the underlying mechanism of all the simulated products is consistent with LRET. Figure 4A shows the relative velocity of the center of mass of the H2 atoms relative to the remaining atoms composing the CHOH+ fragment in a representative -forming trajectory as a function of time after double ionization. The LRET and resulting CE can be identified at t ~ 140 fs as the threshold time for a strong monotonic acceleration. After LRET, the relative velocity rapidly grows because of the long-range Coulomb repulsion, reaching an asymptotic dissociation value measurable as the KER. Note that, although before t ~ 140 fs the relative velocity is positive, indicating a monotonic separation of the two moieties, the deceleration as a function of time indicates the attraction of the induced dipole by the CHOH2+ dication, like the attractive dashed red curve of the 1D model in Fig. 1. Additional insight about the underlying mechanism can be drawn from the time-resolved R(H ─ H) bond length and R(C ─ H2) distance of the H2 moiety from the carbon atom shown in Fig. 4B by the full and dashed lines, respectively. It is possible to identify the time at t ~ 70 fs at which the neutral H2 emerges from the parent dication. The distance to the carbon significantly exceeds the newly formed bond length, which exhibits oscillations about the equilibrium ~1.4-a.u. bond distance of neutral H2. After LRET, the R(H ─ H) increases and oscillates around the longer ~2-a.u. bond length of the cation. At the same time, the oscillation frequencies that are initially in the range of ~3800 ± 700 cm−1, assigned to vibrationally excited neutral H2, exhibit a rapid change to the ~2100 ± 400 cm−1 range, assigned to the product.

Fig. 4.

A representative AIMD ground-state trajectory exhibiting the inverse harpoon mechanism.

(A) Time-resolved relative velocity between the centers of mass of the and HCOH+ fragments. (B) Time-resolved distances of the roaming H2 moiety from the carbon atom (dashed line) and the H─H bond length (solid line). The simulations begin at the ionization time, under the Franck-Condon sudden approximation. The cyan-shaded region marks the neutral H2 roaming time, which onset and termination by LRET are respectively identified by the intramolecular distances and relative fragment velocities.

In addition to the change of nuclear motion accompanying LRET, it is valuable to describe the time-evolving electronic structure that changes as the H2 and CHOH moieties separate. The representative trajectory shown in Fig. 4 proceeds on the ground state of the methanol dication complex. The time-evolving potential energies of the electronic ground state, as well as the two low-lying excited states around the time of inverse harpoon, are shown in Fig. 5. The observed time dependence of the electronic structure is assigned primarily to the elongation of the distance between the separating parts of the system. These three states are mainly composed of the three electronic configurations, illustrated in the inset of Fig. 5, where for each potential point, the diamond, triangle, and the square indicate each of the electronic configurations. Thus, as the neutral H2 moves away from the CHOH2+ dication, the electronic character of the ground state changes. The change of the predominant electronic configuration of the ground state facilitates the LRET, which is also supported by Mulliken charge analysis that indicates that charge transfer occurs around 138 to 140 fs. Thus, although showing higher KER, as compared with the simple 1D model, the molecular dynamics simulation supports an LRET mechanism for ejection.

Fig. 5.

Time resolved electronic structure during LRET.

The lowest three configurations and their energies as a function of time are shown for the simulated trajectory presented in Fig. 4. The vertical black dashed line indicates the same LRET time shown in Fig. 4, in agreement with the change in the electronic configuration of the ground state, on which the trajectory evolves.

In CE events, higher KER indicates shorter distances. Figure 6A shows the simulated distribution of donor-acceptor distances at the time of LRET. The inverse harpoon distance of several simulated trajectories exceeds even 20 a.u., beyond the distance predicted by the simple 1D model for LRET and indicated by the vertical arrow in Fig. 6A. Nevertheless, the bulk of the distribution lies at shorter distances, in agreement with the higher KER. This variation is attributed to the dynamical effect of the geometry-dependent second ionization potential of HCOH and first ionization potential of H2. Although simulated trajectories indicate that LRET proceeds mainly on the electronic ground-state potential, the dynamically changing HCOH2+ geometry and H2 bond length result in a spread of LRET distances with preference to shorter distances that the system reaches at earlier times. The distribution extends down to ~5-a.u. distance, at which the neutral H2 can capture a proton from the CHOH2+ dication and form . For comparison, Fig. 6B shows the simulated donor-acceptor distance distribution at the instance of the competing proton capture events.

Fig. 6.

Simulated donor-acceptor distances at inverse harpoon and proton capture times.

In (A), the vertical arrow indicates the donor-acceptor distance predicted by the simple 1D model as shown in Fig. 1.

The measured KER distribution allows experimental probing of the LRET distances. Similar to the experimental data, the KER distribution obtained by nonadiabatic AIMD simulations corresponds to higher KER and shorter LRET distances as compared with the simple 1D model. Nevertheless, the simulated KER distribution shown in Fig. 3 remains lower than the experimentally measured values. Luzon et al. () proposed that the higher measured KER of the two-body breakup channel reflects the stabilization of the hydroxymethylene cation by the excess release of kinetic energy. However, analysis of the initial KER in the sequential three-body breakup shown in Fig. 3A exhibits similarly high KER. One possibility for accounting for the higher measured KER distribution could be to suggest a different assumption, in which higher-lying dication states are preferentially populated in the SPDI. The blue bars in Fig. 3B show the partial KER distribution of simulated trajectories initiated on the excited states 2 to 4. Few -forming trajectories were found to exhibit long-range inverse harpoon while on an excited state. However, similar to the simulated roaming H2 dynamics reported by Gope et al. (), most of the initially excited systems undergo nonadiabatic surface hopping to the ground state before the separation of the neutral H2. On the one hand, as can be expected, higher initial excitation exhibits higher KER than trajectories initiated on the ground and first excited state, respectively indicated in Fig. 3B by the red and green bars, while on the other hand, dynamics initiated on higher excited states, which lie above the charge transfer barrier for breaking the C─O bond, do not exhibit roaming H2 nor do they produce and (). Therefore, it is difficult to propose a biased initial state population without markedly disturbing the agreement between the measured branching ratios and the simulated dynamics, considering an equal population of the seven low-lying singlet states of the methanol dication (). It is important to note that both the experimental and simulated KER distributions shown in Fig. 3 are normalized to the total dication yield. Thus, by comparing the areas of the experimental and simulated distributions, both corresponding to ~12 ± 1%, we conclude that, although the simulated events exhibit somewhat lower KER, the branching ratio for inverse harpoon events and their competition with proton capture are successfully predicted by theory.

We can also consider the times at which LRET occurs after the double-ionization event. The blue and red bars in Fig. 7A show the respective distributions of simulated proton capture and inverse harpoon times, illustrating the close competition of the two relaxation channels of roaming H2 dynamics. EUV pump/near–infrared (IR) probe measurements allowed to time-resolve the roaming neutral H2 dynamics by observing the ultrafast depletion window of events (), taking advantage of the fact that excitation of the system to higher-lying electronic states enhances three-body breakup and quenches the roaming H2. Comparison of Fig. 7B and Fig. 7C illustrates the agreement of the simulated time window for depletion, derived assuming that it is stable after CE, and the experimental time-resolved branching ratio for formation reported by Livshits et al. (). Thus, in addition to the branching ratio, the ultrafast time scale of the simulated roaming H2 and competing proton transfer and LRET dynamics are in agreement with the experimental result.

Fig. 7.

Simulated and experimental time dependence.

(A) Comparing simulated inverse harpoon and proton capture times. (B) The simulated time window between the double ionization and the proton capture times, convoluted with the experimental time resolution. This can be directly compared to (C) the experimentally measured H3+ + COH+ branching ratio by a time-delayed near-IR probe following an ultrafast EUV pump pulse that initiates double ionization.

DISCUSSION

In summary, the inverse harpoon mechanism allows an experimental probe into the LRET distance distribution. Direct comparison of the observed 3D coincidence imaging data with different levels of theoretical modeling provides detailed insights into the intertwined nuclear motion and electronic structure dynamics during an electron-transfer reaction. In the case of LRET from a neutral H2 to a HCOH2+ dication, which we experimentally initiate by SPDI of an isolated molecule, AIMD simulations on CASPT2 potentials are found to correctly reproduce the branching ratio of LRET and the ultrafast time scale of the roaming H2 that precedes it. Nevertheless, the measured KER distribution exhibits higher energies, indicating that the simulated molecular dynamics on Born-Oppenheimer potentials may still overestimate the exact LRET distances, possibly due to the approximate surface hopping treatment of the nonadiabatic dynamics that predicts efficient transition to the electronic ground state before the H2 roaming and LRET take place. These results, confirming the inverse harpoon mechanism in this specially prepared system, pave the way for LRET reaction studies in various molecular systems. In particular, it will be possible to explore inverse harpooning in ion-surface reactions and in the emerging facilities for carefully prepared cold neutral-cation collisions (–).

Experimental and computational methods

The experimental setup for single-photon CE imaging and theoretical NA-AIMD simulations have been described earlier (–, , , ). Briefly, broad-bandwidth ultrafast EUV pulses are produced by high-order harmonic generation (HHG) by focusing sub-35-fs near-IR pulses, centered around 800 nm generated at a 1-kHz repetition rate in a semi-infinite neon gas cell (, ). The resulting EUV pulses are spatially filtered from the higher divergence near-IR (). Additional 4.5 mJ of the Solstice laser output is time-delayed, mildly focused to ~400 μm, and merged with the HHG pulse at a small ~1° angle at the center of a home-built 3D coincidence imaging spectrometer, where both beams cross a skimmed effusive beam of commercially available CH3OH samples (). The cationic products are accelerated, and their coincidence 3D momenta are imaged on a time- and position-sensitive detector (, ). True CE events are disentangled from an overwhelming dissociative ionization background based on the total momentum conservation of two coincident hits on the detector (). For two-body breakup events, the KER is evaluated in the center-of-mass frame of each pair of coincident ions, while for three-body dissociation events, the momentum vector and KER of the undetected neutral fragment are evaluated from the measured recoil of the center of mass of the detected ion pair in the laboratory frame. Because of velocity map imaging (), the center-of-mass recoil resolution in the 2D detector plane is superior to the recoil along the time-of-flight axis. Therefore, three-body momentum correlations are obtained from the projected momenta in the detector plane using the weighted Dalitz plot method (, , ).

Theoretical NA-AIMD simulations were performed using XMS-CASPT2 potentials (–). Nonadiabatic dynamics were approximated using surface-hopping molecular dynamics trajectories (), generated at the XMS-CASPT2/(8e,8o)/aug-cc-pVDZ level using the BAGEL electronic structure package () with a modified-version NewtonX (v1.4.0) program (). A more detailed description of the NA-AIMD is provided in our previous work concerning the CE dynamics on the singlet manifold of methanol dication states (). To determine the relative probability of different double-ionization product channels, we have initiated more than 200 trajectories on each of the excited states, where the initial phase-space configurations were sampled from neutral ground-state AIMD simulations at 300 K, performed on the CASSCF level using the MOLCAS package ().