Electron Dynamics in the Core-Excited ${\mathrm{CS}}_2$ Molecule Revealed through Resonant Inelastic X-Ray Scattering Spectroscopy

We present an experimental and theoretical study of resonant inelastic x-ray scattering (RIXS) in the carbon disulphide ${\mathrm{CS}}_2$ molecule near the sulfur K-absorption edge. We observe a strong evolution of the RIXS spectral profile with the excitation energy tuned below the lowest unoccupied molecular orbital (LUMO) absorption resonance. The reason for this is twofold. Reducing the photon energy in the vicinity of the LUMO absorption resonance leads to a relative suppression of the LUMO contribution with respect to the emission signal from the higher unoccupied molecular orbitals, which results in the modulation of the total RIXS profile. At even larger negative photon-energy detuning from the resonance, the excitation-energy dependence of the RIXS profile is dominated by the onset of electron dynamics triggered by a coherent excitation of multiple electronic states. Furthermore, our study demonstrates that in the hard x-ray regime, localization of the S 1s core hole occurs in ${\mathrm{CS}}_2$ during the RIXS process because of the orientational dephasing of interference between the waves scattering on the two sulfur atoms. Core-hole localization leads to violation of the symmetry selection rules for the electron transitions observed in the spectra.

Popular Summary

The behavior of molecules exposed to x-ray radiation is of interest to physicists, chemists, and biologists in light of the many technological and medical applications of the process. A key question is how the electrons and atoms in molecules respond to the x-ray radiation and whether one can follow this response in real time. Tracing extremely fast x-ray-induced electron dynamics in a molecule occurring on attosecond (${10}^{-18}\mathrm{s}$) time scales may be accomplished using very short x-ray pulses; this technique is currently in development. Here, we theoretically and experimentally study the rearrangement of the ${\mathrm{CS}}_2$ molecule in order to demonstrate alternative access to fast electron dynamics.

Resonant photoexcitation of electrons in the sulfur K shell excites the ${\mathrm{CS}}_2$ molecule to a highly unstable state that decays via the emission of x-ray radiation. The x-ray emission spectra carry information about the electronic structure and the dynamic processes occurring in the core-excited molecule. Detuning the excitation photon energy below the absorption resonance effectively reduces the delay of emission from ${10}^{-15}\mathrm{s}$, as determined by the lifetime of the excited state, to the low-attosecond time scale. By tracing the evolution of the emitted x-ray spectra, which persists for detunings of up to 10 eV, we show that more core-excited states are involved in the inelastic x-ray scattering when the energy detuning is increased. We predict that at large detunings, a coherent excitation of multiple electronic states launches electron dynamics on the attosecond time scale determined by the spacing between the coherently excited intermediate states.

Our work demonstrates that resonant x-ray emission spectroscopy can be effectively used in studies of electron dynamics in core-excited molecules. Our theoretical predictions, which may be tested in the foreseeable future, propose an alternative experimental approach in the rapidly developing field of attophysics.

Figure 1

Experimental partial x-ray fluorescence yield of the sulfur K hole in the ${\mathrm{CS}}_2$ molecule, constructed by integration of the S $K_{\beta }$ emission spectrum over the 2445–2485 eV energy range, at fixed incidence photon energy. The emission spectra are recorded at the scattering angle $\theta =\pi /2$, in the direction of the incident polarization. The absorption resonances are assigned according to [27] as transitions from the S 1s shell to the LUMO $(3{\pi }_u)$, followed by $(6{\sigma }_u)$, $(7{\sigma }_g)$, and Rydberg orbitals.

Figure 2

Experimental (red line) and calculated (black line) S $K_{\beta }$ RIXS spectra of the ${\mathrm{CS}}_2$ molecule for different values of the incident photon-energy detuning $\mathrm{\Omega }$ from the $1\mathit{s}\to 3{\pi }_u$ LUMO resonance. At the $3{\pi }_u$ resonance (2470.4-eV photon energy, $\mathrm{\Omega }=0\mathrm{eV}$), the major emission bands labeled as A, B, and C are assigned as transitions to the final states $|2{\pi }_g^{-1}3{\pi }_u^1⟩$, $|2{\pi }_u^{-1}3{\pi }_u^1⟩$, and $|5{\sigma }_u^{-1}3{\pi }_u^1⟩$, respectively. The error bars on the peak intensities reflect the experimental statistical error.

Figure 3

Schematic showing an analogy between the RIXS process in ${\mathrm{CS}}_2$ and the Young double-slit diffraction experiment, where the role of the slits is played by the sulfur atoms serving as the scattering centers. Dynamic symmetry breaking due to asymmetric stretching vibrations in the ${\mathrm{CS}}_2$ molecule plays only a minor role in our case and does not affect the RIXS profile.

Figure 4

The dependence of the YDS factor ${\rho }_{\text{yds}}$ [Eq. (6)] on the scattering angle $\theta =\angle ({\mathbf{k}}^{\prime },\mathbf{k})$ for S $K_{\beta }$ RIXS of ${\mathrm{CS}}_2$ with ${\mathbf{e}}^{\prime }\perp \mathbf{e}$. The DSB mechanism is responsible for the breakdown of selection rules at the small-angle scattering (shaded area), where ${\rho }_{\mathrm{yds}}\approx 1$. This is in contrast to large-angle scattering, where ${\rho }_{\mathrm{yds}}\ll 1$ and the reason for the selection-rules violation is the orientational dephasing of YDS interference. Our experiment was performed at $\theta =\pi /2$, where ${\rho }_{\mathrm{yds}}(\pi /2)\approx -0.16$ (circle) and the YDS interference is absent, which leads to violation of the selection rules.

Figure 5

Calculated S $K_{\beta }$ RIXS spectrum of the ${\mathrm{CS}}_2$ molecule at the $1\mathit{s}\to 3{\pi }_u$ LUMO resonance (black line), corresponding to the spectrum shown in Fig. 2 at $\mathrm{\Omega }=0$. The arrows show the symmetry-forbidden ungerade final states $|2{\pi }_g^{-1}3{\pi }_u^1⟩$ contributing to the dominant band A.

Figure 6

Partial S $K_{\beta }$ RIXS cross sections ${\sigma }_{\mu }(\omega ,{\omega }^{\prime })$ [see Eq. (9)] of the ${\mathrm{CS}}_2$ molecule corresponding to the scattering through the $|1{\mathit{s}}^{-1}3{\pi }_u⟩$ and $|1{\mathit{s}}^{-1}6{\sigma }_u/7{\sigma }_g⟩$ core-excited states. As a reference, the total RIXS spectrum including multielectron and interference effects is shown as the black solid line. The calculations are performed for the excitation-energy detuning from the $1\mathit{s}\to 3{\pi }_u$ LUMO resonance: (a) $\mathrm{\Omega }=0$ and (b) $\mathrm{\Omega }=-2\mathrm{eV}$. The thin curve shows the $|1{\mathit{s}}^{-1}6{\sigma }_u/7{\sigma }_g⟩$ partial contribution with intensity multiplied by 10 for visibility. The partial emission profiles ${\sigma }_{3{\pi }_u}^{\text{emis}}$ and ${\sigma }_{6{\sigma }_u/7{\sigma }_g}^{\text{emis}}$ are shifted by $\mathrm{\Delta }E\approx 3.6\mathrm{eV}$, the energy spacing between the first two absorption resonances.

Figure 7

Calculated S $K_{\beta }$ RIXS spectra of the ${\mathrm{CS}}_2$ molecule for different excitation-energy detuning values below the $1\mathit{s}\to 3{\pi }_u$ LUMO resonance. The evolution of the electron wave packet is reflected in the $\mathrm{\Omega }$ dependence of the RIXS profile for the detuning values larger than the energy spacing between the absorption bands.