Time-resolved x-ray absorption spectroscopy with a water window high-harmonic source

See allHide authors and affiliations

Science  20 Jan 2017:
Vol. 355, Issue 6322, pp. 264-267
DOI: 10.1126/science.aah6114

An x-ray view of C–F and S–F bond breaks

X-ray absorption spectroscopy is a useful probe of element-specific dynamics in molecular reactions. However, the required x-ray fluxes have rarely been available outside expensive dedicated facilities such as synchrotrons. Pertot et al. developed a tabletop laser-based high-harmonic source that extends far enough into the x-ray region to probe carbon K-edge and sulfur L-edge absorptions with femtosecond temporal resolution. They used this source to track the previously elusive dissociative dynamics of gaseous carbon tetrafluoride and sulfur hexafluoride after laser-induced ionization.

Science, this issue p. 264


Time-resolved x-ray absorption spectroscopy (TR-XAS) has so far practically been limited to large-scale facilities, to subpicosecond temporal resolution, and to the condensed phase. We report the realization of TR-XAS with a temporal resolution in the low femtosecond range by developing a tabletop high-harmonic source reaching up to 350 electron volts, thus partially covering the spectral region of 280 to 530 electron volts, where water is transmissive. We used this source to follow previously unexamined light-induced chemical reactions in the lowest electronic states of isolated CF4+ and SF6+ molecules in the gas phase. By probing element-specific core-to-valence transitions at the carbon K-edge or the sulfur L-edges, we characterized their reaction paths and observed the effect of symmetry breaking through the splitting of absorption bands and Rydberg-valence mixing induced by the geometry changes.

The application of x-ray sources to the study of the structure of matter has led to some of the most prominent advances in science in the 20th century, be it by diffraction (1) or spectroscopy (2). In the 21st century, the temporal dimension has been added to x-ray measurements, both at synchrotrons (3) and through the recent development of free-electron lasers (47). In parallel to these efforts, incoherent tabletop hard x-ray sources have been applied to picosecond time-resolved studies (8, 9). An alternative approach to generating soft x-rays with the advantages of full temporal and spatial coherence, as well as perfect temporal synchronization, is provided by high-harmonic generation (HHG). Very early efforts were successful at generating a modest soft x-ray (SXR) flux from titanium:sapphire drivers (1012). Considerable progress came through the extension to longer-wavelength drivers (1318). However, time-resolved measurements with such sources have so far remained out of reach.

Here, we describe a femtosecond time-resolved experiment using SXR supercontinua reaching into the water window. Using a long-wavelength driver (1.8 μm) with exceptional average power (2.5 W; i.e., 2.5 mJ at 1 kHz), we generate SXR supercontinua ranging from 100 to 350 eV, thus covering the chemically and biologically important K-edge of carbon. We use this source to study dissociation reactions of molecular cations that have previously not been resolved in time, by transient absorption at the K-edge of carbon and all L-edges of sulfur simultaneously. This development considerably extends pioneering work on transient absorption in the extreme ultraviolet (1922). These studies were limited to photon energies below 100 eV, and therefore to the L-edge of silicon and the M- and N-edges of heavier elements.

Our measurements probe the spatial structure of unoccupied orbitals and associated changes along the photochemical reaction pathways. Exploiting the sensitivity of x-ray absorption near-edge structure (XANES) spectroscopy to chemical shifts, we follow the evolution of the unoccupied valence orbitals of molecules from the neutral to the cation and along the reaction path to the final products. Using the sensitivity of dipole selection rules to molecular symmetry, we observe a splitting of some of the initially triply degenerate orbitals of CF4 and SF6 to doubly degenerate or nondegenerate orbitals as a consequence of the symmetry lowering induced by photodissociation.

In our experimental setup, we focus a mid-infrared femtosecond pulse centered at 1.8 μm into a differentially pumped high-pressure neon gas cell (Fig. 1A). A toroidal mirror images the SXR generation region into a target gas cell, where it is superimposed with a near-infrared (NIR) pulse centered at 800 nm. The SXR absorption of CF4 (Fig. 1B) is dominated by overlapping transitions from the carbon 1s shell to the 5t2 and 6t2 unoccupied orbitals of dominant σ* character that peak at 298 eV. These assignments are based on our time-dependent density functional theory (TDDFT) calculations of core-shell absorption spectra that use the LB94 functional and the QZ4P basis set (valence quadruple zeta + 4 polarization functions, relativistically optimized) and are consistent with high-resolution spectra recorded at synchrotron facilities (23). The SXR absorption spectrum of SF6 (Fig. 1C) is dominated by transitions from the sulfur 2p1/2 and 2p3/2 shells to the a1g unoccupied orbital and to the shape resonances of t2g and eg symmetry lying above the L2,3-edge. A weaker absorption feature at 240 eV is assigned to the transition from the sulfur 2s shell to the antibonding orbital of t1u symmetry, lying just below the L1 edge, which is also consistent with the synchrotron literature (24). The weak modulation observed in both spectra up to energies of 180 eV corresponds to harmonic structure. The experimentally determined resolution of E/ΔE = 308 at E = 180 eV suggests that the appearance of these spectra is not spectrometer-limited.

Fig. 1 Soft x-ray transient absorption spectroscopy with a high-harmonic source.

(A) Experimental setup. MCP, microchannel plate. (B) High-harmonic spectrum at the carbon K-edge and transmitted spectrum through CF4 gas. (C) High-harmonic spectrum at the sulfur L-edges and transmitted spectrum through SF6 gas.

Strong-field ionization of neutral CF4 in the gas phase is induced by an ultrashort NIR pulse centered at 800 nm, focused to a peak intensity of 4 × 1014 to 5 × 1014 W/cm2. Ionization of CF4 to each of the three lowest-lying electronic states of CF4+, of respective vertical ionization energies 16.29 eV, 17.51 eV, and 18.54 eV (measured from the neutral ground state) (25), results in spontaneous dissociation into CF3+ and F (26). At positive delays, an increase of the absorbance and a red shift of its maximum are observed in the time-resolved x-ray absorption spectroscopy (TR-XAS) spectra (Fig. 2B). After reaching a maximal absorbance, the absorption spectrum progressively splits into multiple bands, as illustrated by the sample spectrum (averaged over delays of 300 to 500 fs) shown in the upper panel of Fig. 2B. Most prominently, one band is observed to shift to lower photon energies by 10 eV, terminating at 288 eV. Two further bands shift up and down by 1 eV, respectively, and a fourth band appears as a shoulder of the absorption spectrum around 302 eV. A 50% fraction of the static CF4 absorption spectrum was subtracted from the whole data set (Fig. 2B) to account for partial ionization of the probed sample. This fraction was obtained by comparing the absorption spectrum at long delays with the calculated spectra of CF3+. The delay in the appearance of the isolated absorption band of CF3+ was determined by integrating the signal at each delay over a narrow energy range and fitting an error function to the time-dependent signal. This analysis reveals a time delay of 40 ± 2 fs in the appearance of the absorption band and determines the cross-correlation time (full-width at half maximum, FWHM) to be 40 ± 5 fs (see text S2).

Fig. 2 Transient absorption spectroscopy at the carbon K-edge.

(A) An intense NIR pulse induces single ionization of CF4 to CF4+ which is unstable in its electronic ground state and dissociates into CF3+ + F. The sequence of geometries is taken from a calculated minimum-energy reaction path (see text for details). (B) Absorbance A(t) = ln[I0/I(t)] as a function of the SXR-NIR time delay. Negative time delays correspond to the SXR pulse preceding the NIR pulse. The intensity axis, as well as the color scale, are linear. The standard deviation of this data set amounts to 4%. The calculated stick spectrum in the upper panel has been shifted by –2.5 eV. (C) Orbital diagram illustrating selected transitions, as obtained from TDDFT/LB94 calculations.

The observed changes in the absorption spectrum are the signature of symmetry lowering that occurs when the initially tetrahedral CF4+ molecule dissociates into the trigonal planar CF3+ molecule. Descent-in-symmetry arguments from group theory combined with dipole selection rules show that a transition of the type C 1s → t2 in CF4 must split into two transitions of the type C 1s → Embedded Image and C 1s → e′ in CF3+, as observed in Fig. 2B and illustrated in Fig. 2C.

Further insight is obtained by comparison with advanced quantum-chemical ab initio calculations (stick spectrum in Fig. 2B and Fig. 3), which are further described in text S3. The x-ray absorption spectrum of CF4 is dominated by transitions to the 5t2 and 6t2 orbitals, which appear as two intense lines at the bottom of Fig. 3A. Along the reaction path, the transition to the 5t2 orbital first splits into transitions to three nondegenerate orbitals in CF4+. This is the signature of the Jahn-Teller effect, which causes the minimum-energy geometry to be of C2v symmetry for short (≤1.6 Å) C-F bond lengths (27). With increasing bond length, the minimum-energy geometry changes to D3h, which is accompanied by the merging of the second- and third-lowest transitions to a single line corresponding to a transition to the 5e′ orbital, which confirms the symmetry arguments given above.

Fig. 3 Calculated x-ray absorption spectra of the reaction CF4+ → CF3+ + F.

(A) X-ray absorption spectra, calculated with the TDDFT method using the LB94 functional and the QZ4P basis set, as a function of one C-F internuclear separation along the minimum-energy reaction path CF4+ CF3+ + F calculated on the CCSD/6-31G* level of theory. The CF4 x-ray absorption spectrum is shown below the dashed line. A linear intensity scale is used. (B) Unoccupied orbitals characteristic of the final state of the x-ray transition, corresponding to the dominant absorption bands of (A). Only one of three equivalent orbitals is shown in the tetrahedral (Td) geometry of CF4+, whereas both distinct orbitals of e′ symmetry are shown for CF3+.

Figure 3A also reveals a very large shift of the lowest-energy x-ray absorption band occurring in the transition from CF4+ to CF3+. The major part of this shift originates from the changing energy of the unoccupied Embedded Image orbital, caused by its evolution along the reaction path (Fig. 3B). We next consider the complementarity of the intensity evolutions in the 5e′ and 6e′ transitions. In the tetrahedral geometry of CF4, the 5t2 orbital has dominant valence character, whereas the 6t2 orbital has dominant Rydberg character, with most of its probability located outside the sphere defined by the fluorine atoms. This arises because the high electron density at the strongly electronegative fluorine atoms creates an effective potential barrier along the radial direction. This so-called “cage effect” was first discussed in the context of XANES spectra of SF6 (see below) (28). As the CF4+ molecule dissociates, the fluorine cage opens up, going from a tetrahedral geometry to a planar one in CF3+. This evolution causes a mixing of Rydberg and valence character of the orbitals. Indeed, orbitals previously localized inside (valence) or outside (Rydberg) the cage display a mixed character after dissociation. This change causes a decrease of the overlap between the highly localized core orbital and the initially localized valence orbitals, translating into a decrease of their absorption as the cage opens. In contrast, Rydberg orbitals with initially small overlap with the core orbital exhibit an increase of their absorption as the cage opens up. Along the dissociation coordinate, the 5e′ orbital develops partial Rydberg character, whereas the 6e′ orbital acquires partial valence character (Fig. 3B). This explains both the calculated and the observed intensity variations—that is, a decreasing intensity for the transition leading to the 5e′ orbital and an increase of the transition strength to the 6e′ orbital. The appearance of the shoulder on the high-energy side of the absorption spectrum around 302 eV (Fig. 2B) is also reproduced by the calculations shown in Fig. 3A and is attributed to the 7t2 orbital acquiring partial valence character as it evolves into the 7e′ orbital of CF3+.

The good agreement between experimental and theoretical results enabled us to reconstruct the average C-F internuclear separation as a function of time during the dissociation of CF4+. These results are described in text S4 and shown in fig. S10. Moreover, the analysis of time-dependent energy shifts of the Embedded Image absorption band provides evidence for the transient excitation of vibrational modes during the dissociation process (text S4 and fig. S11).

We proceeded to demonstrate the generality of our technique by turning to the sulfur L-edges and studying the photodissociation SF6+ → SF5+ + F. The three lowest electronic states of SF6+, with respective vertical ionization energies of 15.7, 17.0, and 17.0 eV (measured as energy difference from the neutral ground state) (29), all dissociate to SF5+ + F (26).

Shown in Figure 4, C and D, are the observed TR-XAS spectra after strong-field ionization of SF6, observed at the L2,3-edge and the L1-edge of sulfur simultaneously. A 55% fraction of the static SF6 absorption spectrum was subtracted from the whole data sets (Fig. 4, C and D) for clarity, for the same reason as in Fig. 2B. The L2,3-XANES spectrum at negative delays is dominated by transitions from the sulfur 2p shell of SF6 to the unoccupied orbital of a1g symmetry, lying below the L2,3 edge, and to the shape resonances of t2g and eg symmetry lying above (Fig. 4B). These shape resonances are confined by the effective potential barrier created by the presence of the surrounding electronegative fluorine atoms (28), as we have discussed in the case of CF4. However, in SF6, they are contained within the cage and therefore have considerable overlap with the central sulfur atom, which explains their strength in the experimental absorption spectra. The a1g band shifts to lower energies by 2 eV; the t2g band splits into two main components that shift to lower energies by 2.5 and 6.5 eV, respectively; and the eg band shifts to lower energies and broadens considerably. The red shift of all of these absorption bands is consistent with an increase of the local electron density on the sulfur atom, which is a consequence of the loss of an electron-withdrawing fluorine atom. The delay in the appearance of the absorption bands of SF5+ was determined by integrating the signal at each delay over a narrow energy range and fitting an error function to the time-dependent signal. This analysis reveals time delays ranging from 34 ± 4 fs to 74 ± 10 fs in the appearance of the absorption bands and determines the cross-correlation time (FWHM) to be 45 ± 7 fs (table S1 and text S2). The absorption at the L1-edge (Fig. 4D) is dominated by the transition to a t1u antibonding orbital, which is observable because of the gerade parity of the 2s initial orbital. This band splits into two main components that shift to lower energies by 6 and 15 eV, respectively.

Fig. 4 Transient absorption spectroscopy at the sulfur L-edges.

(A) An intense IR pulse induces single ionization of SF6 to SF6+, which is unstable in its electronic ground state and dissociates into SF5+ + F. The sequence of geometries is taken from a calculated minimum-energy reaction path. (B) Orbital diagram illustrating the experimentally observed transitions. (C) Absorbance A(t) = ln[I0/I(t)] at the L2,3-edge as a function of the SXR-NIR time delay. Negative time delays correspond to the SXR pulse preceding the NIR pulse. The standard deviation of this data set amounts to 4.3%. (D) Absorbance at the L1-edge of SF6. The standard deviation of this data set amounts to 6.3%. The upper panels show absorption spectra obtained by averaging over delays of 200 to 400 fs. All intensity axes shown in this figure, as well as all color scales, are linear.

The changes observed in the TR-XAS spectra of SF6 can again be assigned by group theory. SF6+ in each of its lowest three electronic states can only dissociate into SF5+ in its electronic ground state, which has a trigonal bipyramidal geometry and belongs to the D3h point group. By symmetry, the transition to the a1g orbital of SF6 should correlate with a transition leading to an Embedded Image orbital in the D3h point group of SF5+. Similarly, the t2g shape resonance of SF6 will correlate with Embedded Image and e′ or e′′ shape resonances in SF5+. Finally, the eg-symmetry shape resonance should correlate with an e′- or e′′-symmetric resonance in SF5+. These symmetry correlations precisely describe the experimental observations. The absorption bands corresponding to the unoccupied a1g orbital and the eg shape resonance are both observed to shift to lower energies, without apparent sign of splitting. In contrast, the absorption band corresponding to the t2g shape resonance is observed to split into two bands. Whereas the shift of all transitions happens almost simultaneously (figs. S12 and S13), the splitting of the t2g band is delayed by 70 fs. Calculations (text S5) suggest that this delayed splitting is caused by a higher sensitivity of the valence-type orbital characteristic of the t2g shape resonance in SF6 to bond angle changes, as compared to the a1g and eg orbitals (fig. S16). The observed splitting of the absorption band would then be driven by rapid changes in bond angles of the SF5+ unit that occur around values of 2.5 to 3 Å for the SF5+-F dissociation coordinate.

Qualitatively similar dynamics are observed at the L1 edge. By symmetry, the dominant 2s → t1u transition can only split into two transitions leading to orbitals of e′ or Embedded Image symmetries, which corresponds well to the experimental observation of a splitting into two bands. The broad absorption feature observed around 267 eV corresponds to several absorption bands, all located above the L1 edge (244.17 eV). These bands correspond to shape resonances that have a very short lifetime and hence a large natural linewidth, leading to the observation of a single very broad absorption feature.

Our results demonstrate the feasibility of TR-XAS with tabletop light sources and its potential in elucidating the dynamics of electrons and nuclei in chemical reactions. Specifically, this method nicely complements other key techniques in molecular reaction dynamics, such as time-resolved photoelectron spectroscopy (30) and time-resolved high-harmonic spectroscopy (31). We therefore anticipate TR-XAS to become a decisive technique for the investigation of nonadiabatic molecular dynamics, such as those occurring at conical intersections (32, 33). Owing to its sensitivity to elements, TR-XAS will enable time-resolved studies of electronic dynamics with atomic spatial sensitivity. Broadening the spectral coverage of our source only slightly would bring time-resolved extended x-ray absorption fine structure (TR-EXAFS) in combination with XANES experiments within reach, providing full structural and electronic information. Although demonstrated in the gas phase, our method is directly applicable to the solid state and is readily extendable to the liquid phase using flow cells (34) or flat microjets (35).

Supplementary Materials

Texts S1 to S5

Figs. S1 to S16

Table S1

Reference (36)

References and Notes

  1. Acknowledgments: We thank L. Bonacina, A. Laso, A. Schneider, and M. Moret for technical support; D. Prendergast, R. Bohinc, and J. van Bokhoven for helpful discussions on the calculation of SXR absorption spectra; and M. Reiher and C. Stein for performing supporting calculations. Supported by the ETH Zürich postdoctoral fellowship program (Y.P.); NCCR-MUST, a funding instrument of the Swiss National Science Foundation (project 200021_159875); an ERC starting grant (project 307270-ATTOSCOPE); and an ERC advanced grant (project 291201-FILATMO). Additional data supporting the conclusions are shown in the supplementary materials.
View Abstract

Navigate This Article