Unraveling real-time chemical shifts in the ultrafast regime

TL;DR

Unraveling real-time chemical shifts in the ultrafast regime demonstrates multisite XPS with a narrowband femtosecond x-ray probe to track real-time dissociation channels in CH$_3$F after strong-field ionization. The study extends the partial charges model to ultrafast dynamics, showing that binding-energy shifts $\Delta E_a$ can be described by $\Delta E_a = k q_a + \sum_{b\neq a} \frac{q_b}{R_{ab}} + l$ using Mulliken charges, while corroborating with high-level ab-initio core-hole calculations and semi-classical dynamics. It reveals distinct, temporally separated channels CH$_3$F$^+ \rightarrow$ CH$_3^+$+F and CH$_3$F$^+ \rightarrow$ CH$_2$F$^+$+H, with long-range Coulomb interactions and local charge flows shaping the observed spectra, including a characteristic F-site shift tied to distant charges. The work provides a practical framework for interpreting ultrafast core-level signals in more complex systems and establishes time-resolved XPS as a powerful probe of out-of-equilibrium chemistry when coupled with a PC-model interpretation.

Abstract

Traditional x-ray photoelectron spectroscopy (XPS) relies upon a direct mapping between the photoelectron binding energies and the local chemical environment, which is well-characterized by an electrostatic partial charges model for systems in equilibrium. However, the extension of this technique to out-of-equilibrium systems has been hampered by the lack of x-ray sources capable of accessing multiple atomic sites with high spectral and temporal resolution, as well as the lack of simple theoretical procedures to interpret the observed signals. In this work we employ multi-site XPS with a narrowband femtosecond x-ray probe to unravel different ultrafast dissociation processes of a polyatomic molecule, fluoromethane (CH$_{3}$F). We show that XPS can follow the cleavage of both the C-F and C-H bonds in real time, despite these channels lying close in binding energy. Additionally, we apply the partial charges model to describe these dynamics, and verify this extension with both advanced ab-initio calculations and experimental data. These results enable the application of this technique to out-of-equilibrium systems of higher complexity, by correlating real-time information from multiple atomic sites and interpreting the measurements through a viable theoretical modelling.

Figures (3)

• Figure 1: Time-resolved XPS to investigate the ultrafast ionization dynamics of CH$_{3}$F . a) Illustration of the main transient state channels in CH$_{3}$F after IR strong-field ionization, corresponding to a stable CH$_{3}$F$^+$ cation (bottom panel), a CH$_2$F$^+$ and H dissociation (middle panel), or a CH$_3^+$ and F dissociation (top panel). After the IR ionization step, a femtosecond x-ray pulse ionizes the 1s electrons and enables to investigate the local chemical shifts at the F and C sites (blue and green arrows and circles respectively). The vertical energy bar illustrates the relative energy of the channels in increasing order. b) and c) Experimental time-resolved XPS traces at the F and C sites, respectively, and corresponding lineouts at selected time delays. Positive delays corresponds to the laser pump pulse arriving earlier than the x-ray probe pulse. The laser-dressing region between -60 and 110 fs is highlighted in grey in (c). The measured peaks are identified by using a high-precision level of theory (dashed blue lines, see Methods) and are shown in table \ref{['table:BEs']}. A shift of 0.3 eV has been applied to the calculated lines in the lineouts panel (c) as explained in section S2 of the SM. (d) Time-resolved XPS traces for the F site, zoomed into the -100 to 400 fs delay region. The laser dressing region between -60 fs and 110 fs is highlighted in grey.
• Figure 2: Dynamical chemical shift during C-F bond elongation. a) Calculated partial charges (Mulliken charges) at the location of the F, C and H atoms, for a single C-F dissociation trajectory. b) Measured time-dependent chemical shift of atomic F (golden dots, shaded region corresponds to the standard deviation) and fitted function based on the Coulomb interaction model (grey line), described in the main text. (c) and (d) Calculated binding energy based on PC model applied with the calculated Mulliken charge (red line) and Dyson intensity (blue colorscale for F and green for C), calculated through the ab-initio model including core-hole states. A shift of 0.5 eV is applied to the calculations in panel (c) as explained in section S3-C of the SM. Dotted lines in (a), (c), and (d) mark the delays for the representative snapshots shown in the inset of (c) and (d). A weak satellite feature between 306 and 310 eV is observed in (d) for delays below 25 fs.
• Figure 3: Effects of the hydrogen detachment on the ultrafast chemical shifts. a) Photoelectron spectra averaged between 2800 and 6000 fs and fitting of pseudo-Voigt profiles of the individual measured peaks (error bars represent the standard deviation). CH$_3$F$^+$ and CH$_2$F$^+$ are highlighted with shaded areas (cyan and brown respectively) and show a binding energy difference of 2.1 eV (see section S1-C in the SM for additional information on the data treatment and fitting). b) Time-evolution of the CH$_3$F$^+$ (cyan) and CH$_2$F$^+$ (brown) peaks showing the C-H bond dissociation rate for the CH$_3$F$^+$ cation, fitted with an exponential with a decay constant of 1450 $\pm$ 360 fs (grey dotted line) (c) Calculated Mulliken partial charges at the location of the F, C and H atoms, during a selected trajectory of C-H bond cleavage at 225 fs. For visualization purposes, we now use the sum of the charge of the H atoms instead of the average, as done in Fig. 2(a). (d) Calculated binding energy based on a PC model (red solid line), and dyson intensity calculated through the ab-initio approach including core-hole states (blue colorscale). Orange and purple lines in (c) and (d) mark the delays for the representative framed snapshots shown below (d). Similar to fig. \ref{['fig:CF']}(d), a weak satellite feature is observed at larger binding energies between 225 and 250 fs. This feature is also present at shorter time delays, but at binding energies beyond 708 eV (see figure S15 in the SM).