Filming enhanced ionization in an ultrafast triatomic slingshot

The study addresses how ultrafast nuclear motion during strong-field ionization distorts Coulomb Explosion Imaging (CEI) in polyatomic molecules, focusing on enhanced ionization (EI) effects. Hydrogen atoms in molecules can traverse angstrom-scale distances in tens of femtoseconds following ionization or photoexcitation, influencing key photochemical processes. While several ultrafast techniques exist, CEI uniquely measures fragment momenta of all atoms directly but suffers from distortions because multiple ionization often proceeds sequentially, allowing intermediate charge states to drive dynamics before explosion. Enhanced Ionization, where specific geometries increase ionization yield, is a major source of distortion known in diatomics and linear triatomics. The research aims to film and understand the ultrafast geometry and mechanism of EI in a bent triatomic molecule (D2O), quantify how pulse duration affects EI, and retrieve the critical geometry and trajectory responsible for EI to improve interpretation and control in CEI.

Prior work has established CEI, ultrafast electron and x-ray diffraction, and high-harmonic spectroscopy for tracking molecular dynamics, with CEI offering mass-independent momentum sensitivity. Strong-field distortions including EI were extensively studied in diatomics, where alignment and bond stretch to a critical distance enhance subsequent ionization, and reducing pulse duration can suppress EI when ionizations occur within a single pulse. EI and multielectron dynamics have been explored in triatomics (e.g., CO2, H2O), with both experimental and theoretical studies indicating EI in multiply charged states of water. Concepts such as charge resonance enhanced ionization (CREI) in H2+ inform expectations of barrier suppression at large bond lengths; however, polyatomics introduce additional degrees of freedom (bend and asymmetric stretches) and state-dependent dynamics. Recent work on water dication potentials and fragmentation dynamics provides accurate surfaces and benchmarking for trajectory-based simulations used here.

Two experimental schemes generated D2O3+ and enabled time-resolved CEI. (1) Single-pulse ionization: 800 nm pulses of variable duration τ = 6, 10, 19, 40 fs at constant peak intensity I = 2×10^15 W/cm^2 ionized neutral D2O to D2O3+, with intermediate D2O+ and D2O2+ evolving within the pulse. (2) Pulse pairs: cross-polarized 6-fs, 750 nm pulses (each I0 = 1×10^15 W/cm^2) separated by adjustable delay Δt = 10–110 fs; the first pulse created D2O2+, which evolved field-free before the second pulse formed D2O3+. Following trication formation, molecules exploded into D+/D+/O+, and 3D momenta of fragments were captured in coincidence with a position- and time-sensitive detector (MCP/hexanode). Experimental setup: ultrahigh vacuum (~6×10^-10 Torr), focused spot ~7 μm using f = 5 cm mirror; gas mixture H2O/D2O 50/50 at ~1.5×10^-9 Torr ensuring <1 molecule per shot; acquisition rate ~500 counts/s. Pulse generation and characterization: 6-fs pulses via hollow-core fiber spectral broadening (Ne gas) and chirped mirrors (central 750 nm); 10-fs via reduced broadening; 19-fs via chirp with silica wedges; 40-fs direct from Ti:sapphire system. Intensities equalized with neutral density pellicles; temporal characterization by dispersion scan (6,10 fs) and autocorrelation (19,40 fs). Pulse pairs generated with a Mach–Zehnder interferometer producing equal-intensity, cross-polarized pulses; delay extracted from spectral interferometry; dispersion managed by BK7 wedges. Data processing: Molecular-frame reconstruction defined axes by deuteron momenta (z_m: bisector; x_m: cross product of D+ momenta; y_m: z_m×x_m). Note the ambiguity between +z_m and −z_m; inversion detection inferred from time-resolved observables (β evolution to 180° then returning; oxygen momentum sign change). False-coincidence filtering used momentum-sum cutoff |P_sum| < 25 ħ/Å for D+/D+/O+; for channels without detected O^n+, applied |P_D| > 10 ħ/Å threshold. Simulation of nuclear dynamics: Wigner phase space distribution of the ground vibrational state sampled (harmonic approximation) to initiate 2048 classical trajectories on each of nine ab initio D2O2+ valence-hole states. Potentials (8 from Gervais et al., 1 from Streeter et al.) computed by icMRCI/CISD with Davidson correction, cc-pVTZ basis; fitted analytic forms represent Coulomb, polarization, screened multipole interactions. Trajectories propagated for delay Δt, then instantaneously switched to mutual Coulomb repulsion V = Σ_{i<j} q_i q_j / |r_i−r_j| with q_i = 1, preserving positions and momenta to obtain asymptotic fragment momenta; timing uncertainty from 6-fs pulse width included by ±3 fs random blur. Analysis of enhancement: Constructed 3D histogram in (Δt, β, p_D+) to localize the enhancement volume (50% isointensity surface). Weighted trajectory contributions across states to extract critical geometry distribution in (r_OD, ∠DOD). Tunneling and barrier model: Molecular electrostatic potential (MEP) for D2O3+ at critical geometry (r_OD ≈ 2.2 Å, ∠DOD = 180°) computed with ROHF/6-31G in GAMESS; DC field ε ≈ 0.17 E_h/(e a0) (~1×10^15 W/cm^2) applied along θ = 0° and 90° cuts to visualize barrier suppression; field-free 1b2 orbital density |ψ(r)|^2 computed similarly. Ionization potential (IP) of D2O2+ in field estimated via CASSCF/cc-pVTZ (Psi4) at r_OD = 2.0 and 2.5 Å and interpolated to 2.2 Å; active space 2 a1, 2 b2, 2 b1; noted uncertainties due to correlation and finite lifetimes in intense fields.

- Strong enhancement of trication formation with longer single pulses and with pulse pairs at a specific delay: For single pulses at constant intensity (2×10^15 W/cm^2), the ratio R of D+/D+/O+ to D+/D+/O increased 27-fold when τ increased from 6 to 19 fs. With 6-fs cross-polarized pulse pairs (each 1×10^15 W/cm^2), R increased ~42× at Δt = 18 fs relative to a single 6-fs pulse at the same intensity. - CEI observables indicate ultrafast geometry changes preceding EI: Increasing τ from 6 to 19 fs decreased total KER from ~30 eV to ~20 eV (indicative of OD bond stretching), β approached 180° within ~10 fs (apparent unbending), and θ alignment peaked near 0/180° (dynamic alignment). Pulse pairs at Δt = 18 fs showed similar stretching/unbending but less alignment than long single pulses. - Time-resolved filming of dication motion reveals a rapid slingshot trajectory: Trajectory simulations and delay-dependent momentum maps identified a symmetric three-body “slingshot” motion on select D2O2+ states, where the molecule unbends and inverts about z_m, becoming linear at ~20 fs before re-bending. The oxygen momentum reverses sign during this inversion, and deuteron momentum branches correspond to slingshot vs two-body pathways. - Critical EI geometry extracted: Enhanced ionization localizes near r_OD ≈ 2.2 Å and ∠DOD ≈ 180° (range ~1.8–2.5 Å and 160–180°) coinciding with the linear, symmetrically stretched configuration reached by the slingshot trajectory at ~20 fs. - Electronic-state selectivity: Rapid slingshot trajectories predominantly occur on three D2O2+ states with 3a1 vacancies and intact 1b2: 3B1, 1B1, and 2 1A1. The 2 1A1 state (double vacancy in 3a1) contributes most strongly, with ~74% of its dissociations undergoing rapid slingshot motion (vs ~7% for 3B1 and ~12% for 1B1). - Mechanism of EI: A tunneling model at the critical geometry shows strong angle dependence of barrier suppression; when the laser polarization aligns with the molecular axis (θ = 0°), the downhill deuteron lowers the barrier near the oxygen, facilitating tunneling (or over-the-barrier) ionization of the third electron, likely from the σ (1b2 in C2v) orbital. Alignment preference around Δt ≈ 18 fs corroborates transient barrier suppression along the D–D axis. - Distinction from diatomics (H2+ CREI): In D2O2+, electron density remains localized near oxygen for symmetric stretches beyond ~2 Å across all nine states, precluding large-R charge resonance and indicating EI at smaller bond lengths than in H2+. The global barrier minimum in the model occurs at r_OD ~1.8 Å, slightly shorter than the extracted 2.2 Å, reflecting trajectory constraints in polyatomics (simultaneous bend and stretch). - Energetics: Single-pulse EI yields higher KER (peak ~21.5 eV for τ = 19–40 fs) than pulse-pair EI at Δt = 18 fs (peak ~17.5 eV), attributed to additional kinetic energy acquired on intermediate (field-dressed) potentials prior to the final ionization (~1–2 eV estimated in pulse-pair slingshot trajectories).

The work directly addresses how ultrafast intramolecular motion in intermediate charge states drives EI and biases CEI measurements. By employing cross-polarized pulse pairs and comparing to single-pulse ionization, the authors temporally isolate dynamics in D2O2+ that culminate in enhanced formation of D2O3+. The simulations on accurate dication potential surfaces, benchmarked against prior photoionization studies, reproduce experimental momentum features and reveal two principal pathways: a symmetric three-body slingshot motion and an asymmetric two-body fragmentation. The EI maximum at Δt ≈ 18–20 fs coincides with the slingshot trajectory reaching a linear, symmetrically stretched geometry (r_OD ≈ 2.2 Å), where the applied field along the D–D axis transiently suppresses the tunneling barrier near oxygen. State-resolved analysis shows that EI is predominantly accessed through dication states with vacancies in the 3a1 orbital (intact 1b2), allowing rapid unbending prior to dissociation; the 2 1A1 state is especially efficient at launching slingshot motion. The angular dependence of alignment localized around the enhancement confirms the directional barrier suppression central to the EI mechanism. Compared with diatomics, EI in D2O2+ does not rely on large-R charge resonance; instead, EI occurs at relatively small bond lengths due to persistent oxygen localization, emphasizing the role of multi-dimensional nuclear motion and electronic-state selectivity in polyatomics. Differences between single- and double-pulse KER distributions imply that field-dressed dynamics and dynamic alignment contribute more strongly to EI in longer single pulses. Overall, the findings clarify how EI distorts CEI in polyatomics and how these distortions can be exploited as a selective probe of targeted nuclear motion.

The study films and elucidates an ultrafast slingshot motion in D2O2+ that produces enhanced ionization to D2O3+ within ~20 fs. The critical EI geometry is a transient linear configuration with r_OD ≈ 2.2 Å, accessed via unbending and symmetric stretching on specific dication electronic states (notably 2 1A1 with 3a1 double vacancy). A directional tunneling model shows that alignment of the laser field along the D–D axis suppresses the ionization barrier near oxygen, enabling the third ionization. Experimentally, EI is maximized with 6-fs cross-polarized pulse pairs at ~18 fs delay and also occurs with ≥19-fs single pulses, though with different KER signatures suggestive of field-dressed dynamics. These insights provide a mechanistic and geometric understanding of EI in a polyatomic molecule, informing the interpretation of CEI and offering a strategy to deliberately harness EI as a structural filter to highlight specific motions in molecular movies. Future work could tailor EI by shaping pulse duration, intensity, and polarization to select subsets of dynamics, extend the approach to other polyatomics, and integrate more complete field-dressed electronic-nuclear dynamics for single-pulse regimes.

- CEI distortions due to sequential ionization and ultrafast intermediate-state motion persist; results represent a subset of trajectories that reach the EI-favorable geometry. - Molecular-frame reconstruction has an intrinsic ±z_m ambiguity; inversion is inferred indirectly from time-resolved observables (β evolution, oxygen momentum sign flip). - In pulse-pair modeling, formation of the trication is approximated as instantaneous switching to pure Coulomb repulsion, neglecting any residual field-dressed effects during the second pulse rise time. - Timing uncertainty from finite pulse width is approximated by ±3 fs blurring; precise ionization timing within the pulse envelope is not resolved. - Tunneling model uses static-field, 1D cuts of the MEP (ROHF/6-31G) and estimated IP (CASSCF/cc-pVTZ); exchange is neglected in MEP, and differences in electron correlation between dication and trication introduce several-eV uncertainty in barrier heights. Finite lifetimes of field-dressed states are not included. - Field-dressed nuclear dynamics are not explicitly modeled for single-pulse experiments, though they likely contribute (e.g., dynamic alignment, bond softening). - Detection limitations: O^n+ not detected in some channels required alternative filtering; potential residual false coincidences minimized but not entirely eliminable. - Generalizability to other polyatomics may depend on state-specific electronic structure and accessibility of slingshot-like trajectories.