Photoemission Chronoscopy of the Iodoalkanes

TL;DR

This study applies attosecond streaking to the I4d photoemission channel of iodoalkanes to extract absolute time delays and test their dependence on functional-group size. The absolute delays are obtained from relative I4d–He1s delays, via the relation $ au^{tot}_{ ext{He1s}} = au^{abs}_{ ext{I4d}} + au^{clc}_{ ext{I4d}} - au^{tot}_{ ext{He1s}}$, with measurements conducted at photon energies of $90$, $105$, and $118$ eV and interpreted against EWS delays computed from scattering theory. Across iodomethane to 2-iodobutane, the results show no robust monotonic increase of the I4d delay with ligand size; delays generally decrease with photon energy, and 1-/2-iodobutane converge to values close to the atomic reference, challenging prior semi-classical predictions that the molecular environment uniformly amplifies the delay. The work highlights limitations of $ ext{LDA/HF}$-based scattering calculations for the giant resonance and motivates the development of time-dependent, multi-electron approaches (e.g., R-matrix TD) to accurately describe molecular photoemission delays in this regime. Overall, the findings suggest that the functional-group effect on I4d chronoscopy is molecule-specific and not simply governed by ligand size, with implications for using photoemission delays as probes of local chemical environments.

Abstract

Time delays in photoemission are on the order of attoseconds and have been experimentally determined in atoms, molecules and solids. Their magnitude and energy dependence are expected to yield fundamental insights into the properties of the systems in which they're measured. In a recent study Biswas \textsl{et al.} (Biswas, S., Förg, B., Ortmann, L. et al. Probing molecular environment through photoemission delays. Nat. Phys. 16, 778-783 (2020)) determined the absolute photoemission time of the I$4d$ level in iodoethane via attosecond streaking spectroscopy, finding the presence of a functional group to increase the photoemission time delay, suggesting a correlation between the size of the functional group and time delay based on a semi-classical calculation. Here we experimentally study the dependence of the I$4d$ photoemission time on the functional group in the iodoalkanes from iodomethane up to 2-iodobutane at three photon energies across the giant resonance in the I$4d\to\varepsilon f$ photoemission channel, finding that the presence alone of a functional group does not necessarily increase the photoemission delay, and that overall no clear correlation between its size and the photoemission time delay can be established.

Figures (13)

• Figure 1: Experimental determination of the absolute time delay of the I$4d$ photoemission in the iodoalkanes. A Exemplary spectrogram recorded in a mixture of 2-iodopropane and Helium at $90\,\mathrm{eV}$ photon energy. The relative photoemission time $\Delta\tau_{\mathrm{I}4d-\mathrm{He}1s}$ is the lateral shift of the two streaking features with respect to each other and is extracted from the spectrogram via a multivariate fitting procedure. B With $\Delta\tau_{\mathrm{I}4d-\mathrm{He}1s}$ experimentally determined the absolute photoemission time of the I$4d$ level $\tau_{\mathrm{I}4d}^\mathrm{abs}$ can be determined via the illustrated timing scheme. The photoemission time of the He$1s$ photoemission is known ossiander2017attosecond and can be calculated with great precision, and the measurement-induced $\tau_{\mathrm{I}4d}^\mathrm{clc}$ can be calculated analytically nagele2011time. C Ball-and-stick models of the iodoalkanes under study. Iodine atoms are rendered in violet, Carbon atoms in dark gray and Hydrogen atoms in light gray.
• Figure 2: Absolute photoemission time delays of the I$4d$ photoelectrons in the iodoalkanes in comparison with the results of other experiments ossiander2018absoluteDissMarcusbiswas2020probing. The black curve represents the atomic calculation by pi2018attosecond, gray diamonds are the semi-classical calculation for atomic iodine, and salmon points are the molecular calculation from biswas2020probing. Horizontal error bars for our data are given by the XUV reflector's bandwidth and only plotted once for clarity.
• Figure 3: Correlating the absolute I$4d$ photoemission time delay with the ligand size as measured by its mass. While Ref. biswas2020probing predicts an increase of the I$4d$ photoemission delay with ligand mass we find that $\tau^\mathrm{abs}_{\mathrm I 4d}$ tends to decrease (primary and secondary iodoalkanes at $90\,\mathrm{eV}$, secondary iodoalkanes at $105\,\mathrm{eV}$) or to initially decrease and go through a shallow minimum for 1-iodopropane as seen for the primary iodoalkanes at $105\,\mathrm{eV}$ and $118\,\mathrm{eV}$. The gray dashed lines have been added as a guide to the eye.
• Figure 4: Comparison of our experimental result for iodomethane with a quantum scattering calculation on the HF+LDA level of theory (ePolyScat). The inset shows the calculated cross section in comparison to the experiment on iodomethane by olney1998quantitative. It is easily seen that the giant resonance is not rendered adequately.
• Figure S1: Example of the delay retrieval procedure, here applied to a spectrogram of a mixture of iodoethane and Helium at a photon energy of $118\,\mathrm{eV}$. The left panel shows the leftmost time slice in the spectrogram in blue and the stick spectra used to model the He$1s$ and I$4d$ feature in yellow and red, respectively. The measured spectrogram and its delay derivative are shown in the second and third panels. The rightmost panel shows the fit of eq. \ref{['rTDSE']} to the experimental data.