Imaging molecules from within: Ultrafast angström-scale structure determination of molecules via photoelectron holography using free-electron lasers

A scheme based on (i) upcoming brilliant x-ray free-electron laser (FEL) sources, (ii) innovative energy and angular-dispersive large-area electron imagers, and (iii) the well-known photoelectron holography is elaborated that provides time-dependent three-dimensional structure determination of small to medium-sized molecules with Ångström spatial and femtosecond time resolution. Inducing molecular dynamics, wave-packet motion, dissociation, passage through conical intersections, or isomerization by a pump pulse this motion is visualized by the x-ray FEL probe pulse launching keV photoelectrons within a few femtoseconds from specific and well-defined sites, deep core levels of individual atoms, inside the molecule. On their way out, the photoelectrons are diffracted generating a hologram on the detector that encodes the molecular structure at the instant of photoionization, thus providing “femtosecond snapshot images of the molecule from within.” Detailed calculations in various approximations of increasing sophistication are presented and three-dimensional retrieval of the spatial structure of the molecule with Ångström spatial resolution is demonstrated. Due to the large photoabsorption cross sections the method extends x-ray-diffraction-based time-dependent structure investigations envisioned at FEL’s to new classes of samples that are not accessible by any other method. Among them are dilute samples in the gas phase such as aligned, oriented, or conformer-selected molecules, ultracold ensembles and/or molecular or cluster objects containing mainly light atoms that do not scatter x rays efficiently.

Figure 1

The principle of photoelectron holography (as outlined in Ref. [18]). A photoelectron $p$ wave is emitted from one of the atoms in the molecule via absorption of linear polarized light with photon energy $\hslash {\omega }_{\gamma }$ from the $K$ shell of the emitter with emerging spherical wavefronts. In photoelectron holography a photoelectron diffraction pattern is viewed as an interference between that part of the photoemitted wave, which propagates undisturbed into the detector ${\Psi }_0$, becoming a reference wave, and the part scattered by the nearby atoms ${\Psi }_s$, becoming an object wave which carries the information about the atomic positions. ${\Psi }_0$ and ${\Psi }_s$ interfere on the detector with a phase shift $\Delta \varphi$ yielding thus an intensity distribution $I_{\mathbf{p}}=|{\Psi }_0+{\Psi }_s|{}^2$, which represents a hologram in a large portion of $\mathbf{p}$ space.

Figure 2

A sketch of the chlorine-benzene molecule (the H atoms are not shown): $a=2.01$ Å, $b=1.4$ Å, and $\beta =2\alpha ={120}^{°}$.

Figure 3

A sketch of geometry I showing the emitter (Cl atom), which is taken as the origin of the coordinate system and two “active” scatterers (C atoms) located in the $x_0$-$y_0$ plane.

Figure 4

The calculated photoelectron hologram for the geometry I. Here, a $1.7$ keV photoelectron emitted from the Cl atom is scattered by two C atoms.

Figure 5

Atomic images in the plane $x$-$z$, $6$ Å above the emitter, reconstructed from the hologram shown in in Fig. 4. As usual with inside-source holography, the emitter (indicated by a circle) sits at the origin of the image and is not reproduced.

Figure 6

A sketch of geometry II showing the emitter (Cl atom), which is taken as the origin of the coordinate system and six scatterers (C atoms) on the $x_0$-$z_0$ plane.

Figure 7

The calculated photoelectron hologram for geometry II. Here a $1.7$ keV photoelectron emitted from the Cl atom is scattered by six C atoms located on the $x_0$-$z_0$ plane.

Figure 8

Positions of the scatterers (and the mirror image) $1$ Å above the emitter retrieved from the hologram shown in Fig. 7.

Figure 9

The case of geometry I. The hologram on the detector calculated using approach 2.

Figure 10

Geometry for high-energy electron detection with the pnCCD in CAMP.

Figure 11

Response of the pnCCD on electrons of different energies as indicated penetrating 40 nm SiO${}_2$ insulating and 50 nm Al laser-light protection layers.