Femtosecond Nonadiabatic Confinement of Molecular Dication Yield

TL;DR

The study probes how ultrafast nonadiabatic dynamics in XUV-ionized molecular cations influence the yield of doubly charged dications. It uses an XUV pump to create electronically excited ethylene cations and a time-delayed NIR probe to drive multiphoton ionization, revealing a pronounced dication yield peak at a pump-probe delay of $14.8 \pm 1.7$ fs. The observed enhancement is attributed to resonance-enhanced multiphoton ionization (REMPI) that becomes efficient when the C=C bond in the cation expands to specific lengths around $R_{CC} \approx 1.40$–$1.52$ Å for $D_1$ and $D_2$, but is tempered by ultrafast nonadiabatic relaxation of higher-lying states. Theoretical modeling combines trajectory surface hopping with a TDSE-based multi-photon ionization treatment using the ASTRA framework, showing that the dication yield is governed by a competition between increased ionization rates due to nuclear relaxation and decay of electronic populations, indicating a general mechanism for confinement of dication production within a few femtoseconds.

Abstract

Doubly charged molecular cations often carry signatures of electronic correlation and electron-nuclear entanglement present in the parent cation. Here, we produce ethylene dications using a combination of an extreme ultraviolet pump and near-infrared probe pulses, observing a peak in the dication yield at a pump-probe delay of approximately 15 fs. Ab-initio calculations, which explicitly take into account coupled electron-nuclear dynamics induced by the pump and the multiphoton nature of the probe-induced ionization step, reproduced the observed delay in the yield. It originates from resonant enhancement of the multiphoton ionization of the electronically excited ethylene cation as the carbon-carbon double bond expands. However, this effect is tempered by rapid nonadiabatic relaxation of the excited ionic states. Our results suggest a general mechanism whereby ultrafast nonadiabatic relaxation of a molecular ion can compete with its strong-field ionization rate, confining the dication yield to a narrow temporal window of a few femtoseconds.

Figures (4)

• Figure 1: The potential energy curves (solid lines) for various electronic states in ethylene as a function of the C=C bond length (left-panel): neutral ground state (maroon), D$_0$ (black), D$_1$ (blue), D$_2$ (red), D$_3$ (green), D$_4$ (purple) in $^{13}$C$^{12}$CH$_4^+$ cation and S$_0$ (yellow) in $^{13}$C$^{12}$CH$_4^{++}$ dication. These adiabatic potential energy curves have been computed at the SA-CASSCF level using the ANO-RCC-VDZP basis set, a (12,12) active space for the neutral species, (11,12) for the cation and (10,12) for the dication. The geometry was set to be D$_{2h}$ and only the C=C distance was varied. The vertical purple arrow indicates the XUV-pump pulse. The horizontal dashed line indicates the maximum photon energy reachable by the pump, which is below the photo-double ionization threshold for ethylene. To reach the ground state in the dication, we used a multi-photon NIR probe pulse (denoted by the red arrow). It requires around $10$ to $11$ NIR photons (see the right panel for a simplified pictorial depiction) to reach the S$_0$ state in the ethylene dication from the cation prepared by the XUV-pump. Due to its multi-photon nature, the NIR-probe can initiate a resonance-enhanced multi-photon transition (REMPI), via an electronic state (magenta) below the ground state of the dication, increasing the yield.
• Figure 2: ( A) XUV-only (magenta, solid line) and NIR-only (red, solid line) time-of-flight mass spectra. In both cases, the signal has been normalized with respect to the corresponding parent cation ($^{13}$C$^{12}$CH$_4^+$) yield. The NIR-only mass spectra was collected at an approximate intensity of $8.6$ TW cm$^{-2}$. No contributions from the dication can be observed in either of the spectra. ( B) Typical two-color signal for the dication, $^{13}$C$^{12}$CH$_4^{++}$. ( C) Same as in ( B), but integrated over the corresponding mass window. The error bars indicate statistical fluctuations. The solid line represents least-squares fitting with a time-delayed Gaussian function (see Supporting Information for details). ( D) Shift $\Delta t$ in temporal appearance of the dication relative to the pump-probe zero-delay. The uncertainties come from the fitting. The dashed line represents weighted average of the individual values, with the shaded area indicating the $99\%$ confidence interval. Circles (squares): XUV pump pulses via HHG in xenon (krypton).
• Figure 3: Theoretical ethylene dication production probabilities, termed as yields (open circles) as a function of the pump-probe delay, when the cation is ionized from the D$_0$ (black), D$_1$ (blue), D$_2$ (red), D$_3$ (green), and D$_4$ (purple) electronic states. The yellow, solid diamonds denotes the combined contributions from all electronic states as a function of the delay. Note the excellent qualitative agreement with the experimental results reported in Fig. \ref{['fig2']}C.
• Figure 4: ( A) Temporal evolution of the electronic population for different cationic states (black: D$_0$; blue: D$_1$; red: D$_2$; green: D$_3$ and purple: D$_4$) weighted by the XUV-induced initial-state populations in D$_0$, D$_1$, D$_2$ and D$_3$. ( B) Temporal evolution of C=C bond lengths per current electronic state following initial ionization to D$_0$, D$_1$, D$_2$, and D$_3$. The results are weighted both by the XUV-ionization yields for each of the initial states, and by the populations of each current state at each point in time (see main text for details). ( C) Ionization probability (open circles) as a function of the C=C bond length from D$_1$ (blue), D$_2$ (red) and D$_3$ (green) electronic states. ( D) $|R_Y/R_W|$ as a function of pump-probe delays. The empty (full) circles indicate an increase (decrease) of the dication yield as a function of the delay. The time delay corresponds to the higher one in the interval analyzed. The time delays for which the yield vanishes either at the beginning or at the end of the time interval are excluded in to order avoid giving the false impression that both $\langle\mathcal{Y}_i(t)\rangle$ and $\langle w_i(t)\rangle$ contribute the same to the yield variation. In panels ( C) and ( D), the NIR-probe intensity was $7$ TW cm$^{-2}$.