Time-resolving the ultrafast H₂ roaming chemistry and H₃⁺ formation using extreme-ultraviolet pulses

Trihydrogen (H₃⁺) is a key ion in interstellar chemistry, yet its formation pathways and time scales during organic molecule ionization remain unclear. Prior strong-field laser studies on methanol reported conflicting time scales for H₃⁺ emergence, with suggestions ranging from >1.4 ps lifetimes inferred from isotropic ejection patterns to ultrafast (~100 fs) signals potentially reflecting intermediate-state dynamics rather than final dication chemistry. Strong-field ionization introduces ambiguity due to coexisting direct and indirect mechanisms and sensitivity to laser parameters, complicating interpretation and modeling. Earlier theoretical efforts limited to ground-state dication dynamics could not reproduce observed product distributions. This work asks: what is the intrinsic time scale of H₃⁺ formation following methanol double ionization, and what mechanisms govern competition between H⁺ and H₂⁺ formation? The authors develop a single-photon EUV pump with a delayed, low-intensity nIR probe, combined with nonadiabatic AIMD on CASPT2 surfaces, to time-resolve roaming H₂ dynamics and directly probe the formation of H₃⁺ on the low-lying dication states.

Previous strong-field pump–probe and imaging experiments found isotropic H₃⁺ ejection in methanol, interpreted as rotational depolarization requiring lifetimes much longer than 1.4 ps, while other studies observed ultrafast (~100 fs) H₃⁺ signals and ~38 fs beatings attributed to vibrations of a singly ionized intermediate rather than final dication dynamics. Strong-field double ionization involves multiple competing pathways and intermediate-state dynamics that can mask true bond-making/breaking timescales. Early theoretical studies proposed a roaming neutral H₂ on the dication surface culminating in proton abstraction to form H₃⁺, akin to long-lived roaming dynamics seen in other systems. Ground-state dication AIMD predicted low (~4%) H₃⁺ yields and failed to capture channels like C–O cleavage or H₂O⁺ formation, indicating the need to include excited dication states and nonadiabatic effects. These gaps motivate a single-photon pump approach and higher-level nonadiabatic simulations to clarify mechanisms and timescales.

Experimental: An ultrafast EUV pump–nIR probe Coulomb explosion (CE) imaging setup was employed. ~7 mJ, <35 fs, 803 nm nIR pulses (1 kHz) were split into ~2.1 mJ for high-order harmonic generation (HHG) in a semi-infinite neon gas cell to produce EUV pulses (pump) and ~4.9 mJ for the time-delayed nIR probe. The EUV was spatially filtered from the nIR fundamental; the nIR was merged with the EUV at ~1° within a 3D coincidence imaging spectrometer intersecting a skimmed effusive methanol beam. The nIR intensity was kept below the strong-field CE threshold so that at long negative delays the branching ratios matched EUV-only measurements (H₃⁺ fraction 6%; three:two body ratio 3:1). Ion products were detected with time- and position-sensitive detectors for 3D recoil imaging, applying low count rates and momentum conservation to suppress random coincidences, with residuals estimated from single-ion probabilities. Temporal overlap and instrument response were characterized via the Ne²⁺ cross-correlation signal (Gaussian cross-correlation <35 fs FWHM). Time-resolved changes in three:two body ratio and H⁺+COH⁺ branching were recorded versus nIR delay; transients were fit jointly with Ae^t(1+erf(−t/ω)), fixing ω from Ne²⁺ analysis, extracting enhancement/depletion amplitudes and a common lifetime, plus a long-lived term for residual H⁺ depletion. Kinetic energy release (KER) spectra for H₃⁺+COH⁺ were compared across delay windows to assess changes in spectral shape. Theoretical: Nonadiabatic AIMD surface-hopping trajectories were run on XMS-CASPT2/(8e,2o)/(aug-cc-pVDZ) potential energy surfaces with nonadiabatic couplings computed by BAGEL and an adapted Newton-X (v1.4.0) interface. Initial neutral methanol geometries/velocities were sampled from a 300 K AIMD at CASSCF(14e,10o)/aug-cc-pVTZ (MOLCAS), yielding 100 configurations. For each, trajectories were initiated on each of the seven lowest dication electronic states (total 700 trajectories). Surface hopping allowed transitions only between adjacent adiabatic states (n→m with |n−m|=1). Time step was 0.3 fs; trajectories propagated up to 300 fs or until asymptotic monotonic inter-fragment velocities were reached; long-range Coulomb effects were included classically to refine final velocities. Fragment identities were determined from trajectory outcomes; inter-fragment velocities were computed from center-of-mass separations. Basis-set convergence checks comparing aug-cc-pVDZ and aug-cc-pVTZ for key single points (double ionization energy, excitation energies, ground-state barrier height) showed ~1% relative differences; the C–O cleavage barrier on the low-lying states is ~3 eV with a 0.02 eV basis-set difference. Simulated observables included branching ratios versus initial state, dissociation time distributions (66 H⁺+COH⁺ trajectories), neutral H₂ separation and inverse harpooning times, and model convolution with the measured instrument response for comparison to time-resolved data.

• Time scale: Experimentally, a transient suppression of the H⁺+COH⁺ branching ratio exhibits a lifetime of ~70 ± 25 fs, accompanied by a correlated enhancement in the three:two body fragmentation ratio. Simulations show dissociation time distributions peaking around ~100 fs for H⁺+COH⁺ trajectories, consistent with sub-100 fs dynamics.
• Branching behavior: With EUV-only or negative delays, the H₃⁺ branching ratio is ~6% and the three:two body ratio is ~3:1. Introducing the nIR probe at positive delays yields up to ~8% increase in the three:two body ratio and up to ~12% suppression of H⁺+COH⁺ during the transient window; a residual ~2.5% H₃⁺ depletion persists at long delays, attributed to photodissociation of vibrationally hot H₃⁺ by the nIR.
• KER insensitivity: H₃⁺+COH⁺ KER spectral shapes are essentially unchanged across delay windows, indicating the nIR field toggles between channels without significantly altering the dynamics within a given channel.
• State dependence (theory): Over one-third of ground-state dication trajectories produce H₃⁺ (versus ~4% in earlier ground-state-only simulations without second-order perturbative corrections). H₃⁺ formation probability decreases with increasing initial excitation and is quenched above the third excited state where C–O cleavage becomes accessible; conversely, three-body breakup probability increases with excitation.
• Mechanism: Simulations reveal roaming neutral H₂ is bound to the CHOH₂⁺ dication due to charge effects; it cannot escape without charge transfer. Two ultrafast competing pathways operate on comparable ~100 fs timescales: (i) proton transfer (abstraction) forming H₃⁺ (observed as H⁺+COH⁺), and (ii) long-range electron transfer (“inverse harpooning”) triggering Coulomb explosion and H⁺+CHOH⁺ formation. Neutral H₂ can separate up to ~9 Å before inverse harpooning initiates CE, evidenced by sudden acceleration and charge analysis. The nIR probe promotes population to higher-lying states, quenching H₃⁺ formation and enhancing three-body breakup, consistent with the observed transients.
• Energy landscape: Low-lying dication states feature a ~3 eV barrier preventing immediate C–O bond cleavage, leading to prolonged, complex dynamics with roaming H₂; high-lying states dissociate rapidly with C–O cleavage and three-body breakup.

The combined EUV pump–nIR probe measurements and nonadiabatic AIMD simulations directly time-resolve the roaming H₂ chemistry in doubly ionized methanol and establish that H₃⁺ formation occurs on an ultrafast sub-100 fs timescale. This resolves previous conflicting strong-field results by avoiding ambiguities from multiphoton ionization pathways and intermediate-state dynamics. The nIR probe primarily acts as a state-selective switch: promoting the dication to higher excited states suppresses H₃⁺ formation while enhancing three-body breakup, without significantly altering within-channel KER profiles. The mechanistic picture that emerges is competition between proton transfer and long-range electron transfer (inverse harpooning) from the roaming neutral H₂, both proceeding on ~100 fs timescales and determining whether H⁺ or H₂⁺ fragments are produced. The findings clarify how the low-lying dication potential landscape (with a ~3 eV C–O cleavage barrier) funnels dynamics toward roaming and charge-transfer-mediated outcomes, providing a consistent framework that matches both branching ratios and time-resolved observables. This mechanistic and temporal resolution is relevant to astrochemical environments and radiation chemistry where ionization-driven hydrogen migration and H₃⁺ chemistry play key roles.

Using a single-photon EUV pump with a delayed low-intensity nIR probe and high-level nonadiabatic AIMD, the study unambiguously demonstrates that H₃⁺ formation in methanol dications proceeds on a sub-100 fs timescale. The nIR probe transiently suppresses H⁺+COH⁺ and enhances three-body fragmentation, consistent with photoexcitation to higher-lying states that quench H₃⁺ formation. Simulations on CASPT2 surfaces show a high ground-state propensity for H₃⁺ formation (>1/3 of trajectories), decreasing with excitation, and reveal ultrafast competition between proton abstraction and inverse harpooning electron transfer that governs product partitioning. The work resolves longstanding discrepancies from strong-field studies and provides a generalizable mechanistic picture of roaming H₂ chemistry in ionized molecules. Future research should extend to isotopologues (e.g., deuterated methanol) and other organic systems to dissect site-specific proton transfer pathways and generality across radiation-induced ionization scenarios.

• The explicit interaction of the transient dication with the nIR probe field is not modeled in the simulations; comparisons to experiment use convolution with the measured instrument response.
• Statistical uncertainties limit time-dependent analysis for less abundant CE channels (H⁺+CH₃O⁺, H₂⁺+CH₂O⁺, H₂O⁺+CH₂⁺); C–O bond-cleavage branching did not exhibit clear time evolution within error bars.
• Surface hopping was restricted to adjacent adiabatic states (|n−m|=1), an approximation that may neglect weaker long-range couplings.
• Trajectories were typically propagated up to 300 fs; longer-time dynamics, including potential slow channels, are inferred from asymptotic analysis rather than fully propagated.
• Residual long-time H₃⁺ depletion is attributed to photodissociation of vibrationally excited H₃⁺, but direct measurement of H₃⁺ internal energy distributions was not performed.