An "inverse" harpoon mechanism

Abstract

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.

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.

Fig. 2.. Dalitz plot of H₂⁺ + CHO⁺ + H channel showing the measured momentum correlations.

The ɛ_COH, ɛ_H, and ɛ_H2 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.

Fig. 3.. Comparing experimental and simulated KER distributions for the H2++HCOH+ 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.

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 ${\mathrm{H}}_2^{+}$ 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.

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.

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.

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.