Atomic-resolution imaging of carbonyl sulfide by laser-induced electron diffraction

Probing the structure of small to medium-size molecules in the gas phase is a formidable challenge. Femtosecond x-ray diffractive-imaging experiments have been recently demonstrated at free-electron lasers (FELs) Küpper et al. (2014); Glownia et al. (2016) and first electron-diffraction experiments using relativistic electron beams have been performed Weathersby et al. (2015); Yang et al. (2016). Alternatively, new laser-based approaches are being developed that make use of strong-field ionization with intense and ultrashort laser pulses. In a strong laser field, an electron can tunnel ionize near the peak of the oscillatory laser field and is then accelerated in the field. Depending on the ionization time within the laser period, the electron can be driven back by the laser field and elastically scatter from its parent ion Corkum (1993). The scattered electron is accelerated again in the laser field, reaching a very high kinetic energy. This process is responsible for the appearance of a recollision plateau in the photoelectron momentum distribution. Extracting the differential scattering cross section (DCS) of the molecule from the angular distribution of these high-energy electrons allows to derive the molecular structure Spanner et al. (2004); Blaga et al. (2012).

Laser-induced electron diffraction (LIED) has been first applied in atoms Okunishi et al. (2008); Xu et al. (2012), in diatomic molecules Blaga et al. (2012); Xu et al. (2014) and more recently in polyatomic molecular systems, such as acetylene Pullen et al. (2015), ethylene Ito et al. (2017), and benzene Ito et al. (2016). To extract structural information from a LIED experiment, the returning electron wavepacket should have a de Broglie wavelength comparable with the bond lengths that occur in the molecule. This is typically achieved using a mid-infrared laser field, as the ponderomotive energy $U_{\text{p}}/\text{eV}=9.33\,I/(10^{14}~\text{W}/\text{cm}^{2})\,\lambda^{2}/\text{\textmu{m}}^{2}$ scales quadratically with the laser wavelength.

While coupled rotational-electronic wavepacket dynamics in NO Walt et al. (2017) and ultrafast bond breaking in acetylene dications in the presence of the strong ionizing laser field Wolter et al. (2016) have been recently characterized by LIED, the suitability of this technique for retrieving transient molecular structures following photoexcitation has yet to be demonstrated. In this context, carbonyl sulfide (OCS) is a particularly interesting system. Photoexcitation of ground-state OCS ($X^{1}\Sigma$) in the (220–250 nm) UV wavelength range has been intensively investigated Brouard et al. (2007); Suzuki et al. (1998); Sivakumar et al. (1985) and is known to be dominated by a transition to the $A^{{}^{\prime}}$ state, leading to fragmentation of the molecules predominantly into $\text{CO}(X\,^{1}\Sigma^{+})+\text{S}(^{1}D_{2})$ Brouard et al. (2007). Non-adiabatic coupling along the bending coordinate is responsible for the formation of low-speed $\text{S}(^{1}D_{2})$ fragments Suzuki et al. (1998) and the production of rotationally excited CO fragments Sivakumar et al. (1985). Therefore, OCS can serve as a benchmark to test the suitability of the LIED method for recording molecular movies of molecular dynamics, in this case imaging of molecular dissociation involving bending motion.

Interestingly, strong-field ionization of OCS, performed with 800 nm radiation and intensities above $10^{15}~\text{W}/\text{cm}^{2}$, showed evidence for a bending deformation of the molecule during Coulomb explosion Sanderson et al. (2002). This suggests that the molecular geometry can substantially change both during and after ionization, with a large impact on the retrieval of the molecular structure in a LIED experiment. Therefore, it is important to test the ability of the LIED technique to image the structure of the OCS molecule in its equilibrium geometry before performing any dynamical investigation.

Here, we present an LIED measurement on OCS molecules, photoionized by strong 2 µm wavelength laser pulses. Different from previous investigations Blaga et al. (2012); Pullen et al. (2015); Wolter et al. (2016), the experiment was performed using a velocity map imaging spectrometer Eppink and Parker (1997) that allowed the detection of all electrons with kinetic energies up to 500 eV. Our new experimental apparatus was benchmarked by strong-field ionization experiments on argon and krypton. DCSs extracted from measured photoelectron angular distributions for a recolliding electron energy of 100 eV were compared to results from partial-wave calculations for scattering of electrons by atoms performed using the Elsepa package Salvat, Jablonski, and Powell (2005), and agree very well. The same procedure was applied to the experimental data for OCS. Fitting the calculated DCS to the experimental one with the O-C and C-S bond lengths and the $\angle\text{(O-C-S)}$ bending angle as adjustable parameters, we were able to confirm the linear structure and were able to extract the internuclear distances of the molecule to a precision better than 5 pm. Our experimentally determined values agree very well with reported bond lengths of the OCS molecule Dakin, Good, and Coles (1947) and suggest that accurate structures can be retrieved for OCS using the LIED technique.

The experiments were performed using 2 µm radiation pulses, obtained from an optical parametric amplifier pumped by 800 nm laser pulses from a commercial amplifier system, delivering 30 mJ, 38 fs (full width at half maximum, FWHM) pulses at a repetition rate of 1 kHz. The linearly polarized 2 µm laser pulses were focused into a beam of nearly pure ground-state OCS molecules at the center of a high-energy velocity map imaging spectrometer (VMI) using a CaF₂ lens with a 25 cm focal length, see Fig. 1 . The laser polarization axis was aligned in the plane of the detector, corresponding to the vertical axis in all images presented, vide infra.

The molecular beam was formed by supersonic expansion of a mixture of OCS in helium with a mixing ratio 1/2000 and a constant pressure of 90 bar, using an Even-Lavie valve running at a repetition rate of 250 Hz. In the experiments performed on atoms, a pure sample of either argon or krypton was expanded into vacuum, where the stagnation pressure was limited to 1 bar to avoid cluster formation. An electrostatic deflector Kienitz et al. (2017) was operated at $\pm 13.5$ kV to spatially separate OCS molecules from the helium carrier gas Chang et al. (2015). We note that this device is ideally suited for quantum-state selection and the preparation of structurally pure samples, even of complex molecules Chang et al. (2015); Teschmit, Horke, and Küpper (2018); Trippel et al. (2018). Here, the deflection provided the sample of OCS molecules in their rotational ground-state Nielsen et al. (2011); Karamatskos et al. (2018).

Photoelectrons from strong-field ionization (SFI) by the 2 µm laser pulses were accelerated into a 10 cm long field-free flight tube before being detected on a 77 mm diameter dual microchannel-plate/phosphor-screen assembly. The projected 2D electron momentum distributions were recorded using a CCD camera and inverted using an Abel-inversion procedure based on the BASEX algorithm Dribinski et al. (2002) in order to yield 3D electron momentum distributions.

In order to validate our experimental methodology, experiments were first performed for pure samples of rare-gas atoms. Projected 2D electron momentum distributions recorded in argon and krypton and corresponding slices through their 3D momentum distributions are presented in Fig. 2 a, d. The laser intensity was $\mathord{\sim}1\times 10^{14}~\text{W}/\text{cm}^{2}$, which corresponds to a Keldysh parameter of $\gamma=\sqrt{I_{\text{p}}/2U_{\text{p}}}\approx 0.38$, with the ponderomotive energy $U_{\text{p}}=37.3$ eV, and $I_{\text{p}}=11.2$ eV the ionization potential, indicating that the experiment was performed deep into the tunneling regime. The angle-resolved photoelectron spectra were averaged over $10^{6}$ laser shots. To account for rest gas, an image obtained without atomic beam was subtracted from the 2D electron momentum distributions prior to Abel inversion.

In a classical picture of the strong-field ionization Corkum (1993), electrons that have experienced a single recollision with the parent ion can reach a maximum kinetic energy of 10 $U_{\text{p}}$, whereas electrons that do not further interact with the parent ion – commonly called “direct electrons” – can have a maximum kinetic energy of 2 $U_{\text{p}}$. In our measurement, the direct electron yield is five to six orders of magnitude larger than the contribution from rescattered electrons, see Fig. 2 . For argon and krypton, the photoelectron spectra observed experimentally extend to a kinetic energy close to 400 eV.

Field-free DCSs of argon and krypton were extracted from our measurements following a procedure given by the quantitative rescattering theory Chen et al. (2009); Xu et al. (2010). The high-energy rescattered photoelectron momentum distribution $D(k,\theta)$ is expressed as the product of the momentum distribution $W(k_{r})$ of the returning electron (with $k_{r}$ the momentum at the instant of recollision) and the DCS $\sigma(k_{r},\theta_{r})$, with $\theta_{r}$ the scattering angle. The relationship between the measured electron momentum $k$ and $k_{r}$ is obtained by considering that the scattered electrons gain an additional momentum after the recollision, which is given by the vector potential $-A(t_{r})$ at the time of recollision $t_{r}$:

with $y$ defined as the laser polarization axis. According to the classical equations of motion and neglecting the effect of the Coulomb potential on the electron trajectories, the maximum recollision electron momentum satisfies $k_{r}=1.26A_{0}$, with $A_{0}$ the magnitude of the vector potential, corresponding to a maximum kinetic energy of $\mathord{\sim}3.17~U_{\text{p}}$, i. e., $\mathord{\sim}118$ eV for a wavelength of 2 µm and an intensity of $\mathord{\sim}1\times 10^{14}~\text{W}/\text{cm}^{2}$. The DCS $\sigma(k_{r},\theta_{r})$ for the highest recollision energy can, therefore, be extracted from the photoelectron angular distribution (PAD) by measuring the photoelectron yield on a circle with radius $k_{r}=1.26A_{0}$ Okunishi et al. (2008) and centered at $(k_{x},k_{y})=(0,\pm A(t_{r}))$. We note that this procedure yields the DCS weighted by the ionization yield.

Fig. 2 c, f shows the field-free DCS extracted for argon and krypton using this method. The results were obtained using an integration range of $\Delta{}k_{r}\approx 0.05k_{r}$ and an angular integration width of $\Delta\theta=1\,^{\circ}$. For krypton two pronounced minima at scattering angles of $94\,^{\circ}$ and $151\,^{\circ}$ are clearly observed. For argon, the DCS presents a strong dip near $124\,^{\circ}$ and a broad minimum near $60\,^{\circ}$. These results are in very good agreement with previous LIED experiments Xu et al. (2012) as well as with conventional electron-scattering experiments using an external electron source Fon et al. (1983); Fon, Berrington, and Hibbert (1984). The DCS for both atomic targets compare also very well with theoretical calculations for field-free electron–atom collisions obtained using the Elsepa package Salvat, Jablonski, and Powell (2005), shown as orange and blue curves in Fig. 2 c, f. In these calculations, the nuclear charge distribution was approximated by a point charge and the electron charge density of the atomic cation was evaluated from self-consistent Dirac-Fock calculations. Exchange and correlation-polarization potentials were neglected. The simulations were performed considering both, a neutral and an ionic, atomic target. We note that to achieve the best agreement with the experimental DCS, the magnitude of the vector potential and, therefore, the laser intensity used to extract the DCS from the PAD was fitted. Best agreement was found for intensities of $9.1\times 10^{13}~\text{W}/\text{cm}^{2}$ and $8.3\times 10^{13}~\text{W}/\text{cm}^{2}$, with corresponding return electron kinetic energies of 98 and 107 eV, for argon and krypton, respectively. These values are in close agreement with the estimated intensity based on the laser-pulse parameters used in these experiments. We attribute the difference observed between the two atomic targets to a small variation of the pulse energy between the two measurements. The comparison between the experimentally retrieved DCS and the simulated DCS, obtained for a neutral and an ionic atomic target shown in Fig. 2 c, f, reveals that a better agreement is found when considering that the returning electron interacts with a singly charged atomic ion.

Subsequently, we recorded the PAD resulting from SFI of OCS. Note that no laser alignment was used in the experiment, and hence the OCS molecules were randomly oriented prior to their interaction with the laser. The laser intensity was adjusted to observe only the parent molecular ion in an ion time-of-flight measurement (fragmentation $<1\%$) in order to minimize the influence of multiple ionization channels. The 2D momentum distribution recorded for OCS and its corresponding photoelectron kinetic-energy spectrum are shown in Fig. 3 a, b. The kinetic energy spectrum extends to 480 eV, suggesting an intensity $\mathord{\sim}1.3\times 10^{14}~\text{W}/\text{cm}^{2}$, i.e., slightly higher than in the measurements for argon and krypton.

Similarly to the atomic case, the field-free DCS was retrieved from the PAD for a return electron energy of 100 eV and is shown in Fig. 3 c. A broad minimum near $110\,^{\circ}$ is observed, similar to previously reported electron-scattering experiments with 100 eV kinetic energy projectiles  Murai et al. (2013); Michelin et al. (2000). The minimum observed at $110\,^{\circ}$ is known to be dominated by the atomic form factor of the sulfur atom, smeared out by the molecular structure Murai et al. (2013). To extract the internuclear distances of OCS from our measurement, we applied a procedure that was first introduced in reference Blaga et al., 2012 to retrieve the internuclear distance of diatomic molecules from LIED measurements. For a fixed-in-space molecule, oriented at Euler angles $\Omega_{L}$ with respect to the laser polarization axis $y$, the PAD is written as:

with $N(\Omega_{L})$ the angle-dependent ionization probability. For an isotropic molecular sample the measured signal is then given by:

Recent studies Schell et al. (2018) have shown that the shape of molecular orbitals can leave its imprint on the recollision probability. Moreover, in molecular ionization, multiple orbitals can contribute to ionization Krečinić et al. (2018); Trabattoni et al. (2018). For OCS, the HOMO (IP=11.2 eV) and HOMO-1 (15.1 eV) orbitals are separated by $\approx$4 eV and the contribution of the HOMO-1 orbital to the ionization dynamics is expected to be negligible. Since randomly oriented molecules were used in the experiment, we assume that the influence of the shape of the molecular orbital from which the electron is emitted is washed out during the propagation of the electron wavepacket in the laser field. Using this assumption, the field-free DCS in (4) can be approximated by an independent-atom model (IAM) and expressed as:

with the momentum transfer $q=2k_{r}\sin(\theta_{r}/2)$, the internuclear distances $R_{ij}$ and the scattering amplitude $f_{i}(\theta_{r})$ for atom $i$. The returning electron interacts with the molecular ion, which we modeled by a singly charged sulfur atom and neutral carbon and oxygen atoms. This is well justified as the removal of an electron from the HOMO of OCS is expected to lead to a molecular ion with a final charge mainly localized on the sulfur atom Holmegaard et al. (2010), see the appendix for further details.

Combining the IAM with the QRS yields the following expression that was used for the analysis of our measurements:

The first term corresponds to an incoherent sum over the scattering amplitudes $I_{\text{atom}}$ of the individual atoms whereas the second term corresponds to a molecular interference term. Following the standard approach (Blaga et al., 2012), we define the molecular contrast factor (MCF) $\gamma_{\text{MCF}}$ as:

In order to extract bond lengths from our measurement, we have compared the MCF extracted experimentally with simulations using expression (7). The neutral atomic scattering factors were obtained using the Elsepa package Salvat, Jablonski, and Powell (2005). To estimate the angle-dependent ionization probability $N(\Omega_{L})$ necessary to calculate the MCF, the following experiment was performed. A sequence of two laser pulses, at a wavelength centered at 800 nm and with 255 fs pulse duration, were used to strongly align the molecule prior to the 2 µm laser pulse, see reference  Karamatskos et al. (2018) for details. The angle-dependent ionization probability was then obtained experimentally by monitoring the ionization yield as a function of the angle between the molecular axis and the ionizing laser polarization, see Fig. 4 , and then used to calculate the MCF. Finally, the $R_{\text{O--C}}$ and $R_{\text{C--S}}$ bond distances were fitted in order to minimize the variance between experiment and theory using the following expression for the error:

with $\beta$ a normalization constant, $I_{\text{exp}}$ the DCS extracted from the measured photoelectron spectrum and $I_{\text{th}}$ the DCS calculated using (6). The result from this procedure is shown in Fig. 5 . The best agreement is obtained for $R_{\text{O--C}}=115\pm 3$ pm and $R_{\text{C--S}}=155\pm 4$ pm. Even for the relatively low return electron energy of 100 eV, a precision of $\pm 4$ pm is reached. These values are in very close agreement with the known values $R_{\text{O--C}}=116\pm 2$ pm and $R_{\text{C--S}}=156\pm 3$ pm obtained by microwave absorption spectroscopy Dakin, Good, and Coles (1947), which are marked by the red dot in Fig. 5 b.

As previously mentioned, we cannot a priori exclude a possible deformation of the molecule following its ionization by the intense laser field. If this deformation takes place on a timescale shorter than the duration between ionization and recollision, it would be observed in our experiment as a deformed, bent or stretched OCS geometry upon recollision. However, we did not observe any indication of stretching of the bond distances of the molecule, even when we performed an extended analysis of our measurement using the overall O–S distance as an additional fitting parameter. Best agreement was found for $R_{\text{O--S}}=270$ pm, with $R_{\text{O--C}}=114\pm 4$ pm and $R_{\text{C--S}}=155\pm 5$ pm, i. e., for the linear configuration of the molecule. This suggests that in our experiment, with intensity $\mathord{\sim}1\times 10^{14}~\text{W}/\text{cm}^{2}$ and wavelength 2 µm, corresponding to a laser period of 6.6 fs, the molecular structure remains essentially unchanged during the time interval between ionization to recollision. In this context we note that recent ab-initio calculations Bilalbegovic (2008) for laser pulses centered at 790 nm and an intensity of $1\times 10^{15}~\text{W}/\text{cm}^{2}$ have shown that the atomic distances and bending angle $\angle\text{(O-C-S)}$ are changing on a timescale longer than 10 fs, i. e., longer than the optical period in our experiment.

We have recorded angle-resolved photoelectron spectra of argon, krypton and OCS, ionized by short laser pulses at 2 µm, with a high-energy VMI. We extracted field-free differential electron rescattering cross sections at 100 eV, which are in excellent agreement with calculated DCSs for electron-atom and electron-molecule scattering. The geometry and bond distances of the OCS molecule were extracted from our measurement with a precision better than $\pm 5$ pm and in full agreement with the known structure of ground-state OCS.

It remains an open question to what extent the LIED technique can be used to retrieve multiple bond lengths and angles during molecular transformations, for instance following the photoexcitation of a molecule. Further investigations combining pump-probe schemes and LIED are ongoing to explore the possibility to use this technique to directly record a so-called “molecular movie” of these motions, in which the evolving structure is measured with femtosecond and picometer precision while the molecule is “in action”.

This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) through the priority program “Quantum Dynamics in Tailored Intense Fields” (QUTIF, SPP1840, AR 4577/4, KU 1527/3) and by the Clusters of Excellence “Center for Ultrafast Imaging” (CUI, EXC 1074, ID 194651731) and “Advanced Imaging of Matter” (AIM, EXC 2056, ID 390715994) of the Deutsche Forschungsgemeinschaft, by the Helmholtz Gemeinschaft through the “Impuls- und Vernetzungsfond”, and by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 674960 (ASPIRE). A.T. gratefully acknowledges a fellowship of the Alexander von Humboldt Foundation.