Core-level interatomic Coulombic decay in van der Waals clusters

Andreas Hans ,1,2,* Catmarna Küstner-Wetekam,1 Philipp Schmidt,1 Christian Ozga,1 Xaver Holzapfel,1 Huda Otto,1 Christina Zindel,1 Clemens Richter ,3 Lorenz S. Cederbaum,4 Arno Ehresmann,1 Uwe Hergenhahn ,3,5,† Nikolai V. Kryzhevoi ,4,‡ and André Knie 1,§ 1Universität Kassel, Institut für Physik und CINSaT, Heinrich-Plett-Straße 40, 34132 Kassel, Germany 2Nano and Molecular Systems Research Unit, Faculty of Science, University of Oulu, P.O. Box 3000, 90014 Oulu, Finland 3Leibniz-Institut für Oberflächenmodifizierung (IOM), Permoserstraße 15, 04318 Leipzig, Germany 4Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany 5Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany

large, may even compete with Auger decay [10]. In the related electron transfer mediated decay (ETMD), an electron from the environment is transferred to the ion and the environment gets ionized [11]. In contrast to ICD, ETMD neutralizes one charge of the initial ion and transfers two charge units to the environment.
In systems with a core vacancy, ICD or ETMD usually attracts attention as one part of various cascades starting with Auger transitions [12][13][14][15][16][17]. Yet, core vacancies can also directly decay by ICD. These so-called core-level ICD processes were recently studied both theoretically and experimentally in aqueous solutions and hydrogen-bound clusters using electron spectroscopy. They manifest themselves as shoulders or separate peaks on the high-kinetic-energy side of the local Auger peaks [18][19][20][21][22][23][24].
Although such processes were also predicted in van der Waals bound solid Ar, their rates were estimated to be extremely small (about seven orders of magnitude smaller than the local Auger decay rates), suggesting that these processes are elusive [25]. Indeed, experimental attempts failed to observe core-level ICD following 2p ionization in Ar dimers [26] and large Ar clusters [27]. However, since noble gas clusters are commonly used as prototype systems in studies on interaction of matter with ionizing radiation, the direct nonlocal decay of core vacancies may have immediate implications. Especially in the emerging field of x-ray imaging with high-intensity free electron laser (FEL) radiation, processes like core-level ICD have not yet been considered to contribute to charge distribution and nanoplasma formation [28,29]. Here, we unambiguously demonstrate the occurrence of core-level ICD in van der Waals systems by presenting an observation of these processes in 2p core-ionized Ar clusters. This observation became possible by the application of highly sensitive electron-electron and electron-electronphoton coincidence spectroscopies. The experimental results are supported by theoretical calculations.
In the present experiment, the 2p vacancies were created by photoionization. The dominant relaxation channel of a 2p hole is the Auger decay to localized one-site dicationic states with two outermost 3p vacancies [ Fig. 1(a)]: As presented below in detail, also direct core-level ICD is possible in clusters, leading to two-site delocalized dicationic states [ Fig. 1(b)]: The experiment was performed at the BESSY II storage ring of the Helmholtz-Zentrum Berlin (HZB) using linearly polarized synchrotron radiation of the U49-2 PGM-1 beamline. A setup for electron-photon coincidence experiments as recently described in detail ( [30], configuration A) was used, including the procedure of data acquisition and elimination of random coincidences. It combines a magnetic bottle timeof-flight electron spectrometer [31] and a mirror assembly for enhancing the solid angle of photon detection. A singlephoton detector equipped with a CsTe photocathode was used, sensitive for photons in the range from about 120 to 300 nm (about 4.0 to 10.4 eV) [32]. In the present experiment, the setup was used for the acquisition of coincidence events of two electrons and one photon.
Ar clusters were produced by supersonic expansion of Ar gas through a conical copper nozzle cooled with liquid nitrogen to temperatures between 105 K and 120 K, corresponding to mean cluster sizes of N ≈ 100 and N ≈ 50 [33]. Reference spectra of atomic Ar were taken using the same source at room temperature. Note that spectra of clusters inherently contain contributions from remaining free atoms. Spectra were recorded at exciting-photon energies E = 436 eV and E = 449 eV. For further details on target preparation and the coincident detection of photoelectrons and Auger electrons see Ref. [33].
The experimental L 3 MM and L 2 MM Auger spectra of atomic Ar measured in coincidence with the respective 2p 3/2 and 2p 1/2 photoelectrons are shown in Fig. 2(a). They are separated by 2.2 eV corresponding to the spin-orbit splitting of the Ar 2p −1 core-hole state, and each component shows contributions from the 3 P 0,1,2 , 1 D 2 , and 1 S 0 final dicationic states [34]. Auger electrons with lower kinetic energies (i.e., higher binding energy final states) do not reach the detector due to the retardation voltage applied [33]. Since the electron spectrometer is not well characterized for such high retardation voltages [31], some line shapes and relative intensities of the spectral contributions may deviate from the literature values [34].
Compared to the pure atomic spectra, the electron-electron coincidence Auger spectra of a partially condensed Ar cluster jet represented in Fig. 2(b) show two new structures: the prominent shoulders at the high-kinetic-energy side of the atomic peaks and additional weak peaks at even higher kinetic energies which are well separated from the main Auger lines and only visible in a magnified presentation. Both structures appear due to electronic processes in clusters: while the former originates from Auger decays, the latter is attributed to core-level ICD processes, as explained in detail below.
The atomic and cluster contributions cannot be separated in the spectra of Fig. 2(b) because the resolution achieved does not allow for a proper separation of photoelectrons from atoms and clusters. However, for the quantification of the branching ratio of core ICD to local Auger decay it is necessary to isolate the Auger spectra from clusters. Toward this end we used electron-photon and electron-electron-photon coincident methods to efficiently eliminate the atomic contribution from the spectra.
A weak signal appears only for the Ar 2+ (3p −2 1 S 0 ) state. The situation is, however, dramatically different in clusters. Here, all localized Auger Ar 2+ (3p −2 ) states decay further by radiative charge transfer (RCT) [26,35]: The energies of the emitted RCT photons can be roughly estimated from the difference between the potential energy curves of the dicationic states at the approximate interatomic distance (∼2.7 Å) at which RCT takes place in Ar 2 [26,35]. These energies are about 6.6 eV and 8.3 eV for the 3 P 0,1,2 and 1 D 2 states, respectively, which are well within the sensitivity range of the photon detector. RCT processes involving the 1 S 0 states result however in the emission of photons of energies around 10.7 eV, for which the efficiency of the detector is extremely low, and may not be detected in the present experiment.
In Fig. 2(c), the electron-photon coincidence spectrum for the Ar cluster jet is compared to the overall electron spectrum obtained without coincidences. These spectra have photoelectron peaks on the left side of the dashed line in the kinetic energy range between 197-202 eV, which are filtered out in all other spectra in Fig. 2 [33]. As seen from these peaks, the atomic contributions (the lower kinetic energy parts in the double-peak structures) are essentially removed by the electron-photon coincidences, and the respective photoncoincident spectrum can thus be regarded as the pure cluster spectrum. Yet, the contributions from the initial 2p 3/2 and 2p 1/2 photoionizations cannot be distinguished here because only one electron was measured in coincidence with the RCT photon. However, the two Auger components can be obtained separately by making use of electron-electron-photon coincidences enabling us to filter Auger spectra for emission of an RCT photon and either the 2p 3/2 or 2p 1/2 photoelectrons. These components are shown in Fig. 2(d). As explained above, there are no contributions from the 1 S 0 Auger final states in these spectra.
The LMM Auger spectra of Ar clusters have been studied in several previous works [26,27,36,37]. Pure cluster spectra have been obtained and thoroughly investigated in Ref. [36] with respect to cluster size, scattering, and postcollision interaction effects. The pure cluster Auger spectrum shown in Fig. 2(c) agrees well with them. Compared to previous studies, the considerable advance of the present work is the separation of the pure cluster Auger spectrum into the L 3 MM and L 2 MM components [ Fig. 2(d)]. Both have similar structures and in particular the L 3 MM component is twice as intense as the L 2 MM one. Note that due to the coincidence condition imposed, the present spectra in Fig. 2(d) are free of influences of photoelectron recapture and scattering.
To support the assignment of the two weak peaks in the 212-218 eV kinetic energy region [ Fig. 2(b)] to core-level ICD, we first consider their energy separation to the respective pure cluster Auger peaks. They should be related to the energy difference between one-site and two-site dicationic states in clusters. In Ar 2 , this energy difference is expected to be about 8 eV [26], which is a little larger than the 7.1 eV inferred from the current spectra. This discrepancy is likely associated with cluster size and polarization screening effects [38]: in larger clusters the energy separation between one-site and two-site dicationic states should decrease because of a larger polarization screening shift experienced by the former states.
The branching ratio of core-level ICD and local Auger processes is an important parameter for many applications. We have determined it as follows. For each of the 2p 1/2 and 2p 3/2 components, the pure atomic [ Fig. 2(a)] and pure cluster [ Fig. 2(d)] Auger spectra were added with individual variable scaling factors, until the best fit with the cluster jet Auger spectrum [ Fig. 2(b)] was found. Then, the areas of the pure cluster Auger contribution and the ICD peak (including the scaling factors) were integrated and compared. Finally, we account for the absence of the 1 S 0 channel in the electronelectron-photon coincident spectra [ Fig. 2(d)], which has an intensity on the order of 10% of the total L 2,3 M 2,3 M 2,3 area. The intensity of the local Auger decay was corrected by 10%, yielding the final result for the core-level ICD to local Auger decay branching ratio of (0.8 ± 0.2)%.
To further support the above interpretation of the experimental spectra, we have calculated Auger spectra of several size-selected Ar n (n = 2-7, 13,19) clusters. The cluster geometries were taken from the Cambridge Cluster Database [39]. In order to exclude the effect of different interatomic FIG. 3. Calculated averaged Auger spectra of Ar clusters of different sizes plotted on the double-ionization energy scale. All spectra exhibit two well-separated structures attributed to different decay processes: local Auger decay (higher DIPs) and core-level ICD (lower DIPs). The relative intensities of the core-level ICD peaks grow with increasing cluster size.
separations on the spectra computed in the present work, the same nearest-neighbor distances of 3.76 Å, corresponding to the Ar-Ar bond in Ar 2 , were used in all clusters. The spectra were computed using a combination of the ab initio secondorder algebraic diagrammatic construction [ADC (2)] method [40,41] in conjunction with a reduced relativistic pseudopotential basis set [42], and the two-hole population analysis [43]. An overview of the main steps of the computational protocol is given in Ref. [33]. For more details, see previous publications [19,20,23].
The calculated spectra are plotted on the double-ionization potential (DIP) scale in Fig. 3 as a function of cluster size. The spectra are averaged over the number of atoms present at different sites in a cluster and normalized to the maximum intensity. Like the experimental spectra, the calculated ones exhibit two well-separated features. The high-energy and intense multipeak structure is attributed to Auger processes since all dicationic states contributing here are of a one-site character. In contrast, the low-energy and faint double-peak structure (missing in an isolated atom) entirely contains delocalized dicationic states and is thus assigned to interatomic decay processes. Both spectral structures move toward lower DIPs with increasing cluster size due to polarization screening [38]. The shift is, however, larger for the localized states so that the energy gap between these two spectral structures gradually decreases, corroborating the above supposition. Besides the energy shifts, also the intensity ratio of the ICD and Auger peaks changes notably. In Ar 2 it is only 0.09%, explaining the failure to observe core-level ICD in experiments on dimers earlier [26], but reaches 0.35% and 0.47% in Ar 13 and Ar 19 , respectively.
The deviation between the theoretical core-level ICD to local Auger branching ratios and the experimental value can be explained by the different sizes of the experimental and theoretical clusters. In the former systems, the number of bulk atoms possessing a complete coordination shell of twelve neighbors is appreciable, whereas only a very few such atoms are present in the latter clusters and the rest FIG. 4. Comparison of the experimental spectrum with the theoretical spectrum of the central atom in an Ar 13 cluster. The experimental spectrum is composed of results from electronelectron-photon coincidences (local Auger) and electron-electron coincidences (core-level ICD) to higher and lower DIPs of the vertical dash-dotted line, respectively (see Fig. 2 and text).
consist of "surface" monomers with incomplete coordination shells. The effect of bulk atoms on Auger spectra is, however, remarkable as can be inferred from Fig. 4 comparing the experimental pure cluster spectrum with a theoretical one obtained for the central "bulk" atom in Ar 13 . Both spectra are plotted on the DIP scale such that the positions of the main maxima composed of the L 2 MM 1 D 2 and L 3 MM 3 P 0,1,2 peaks coincide and are normalized to the area of the Auger states (38-48 eV). The experimental spectrum is composed of results from electron-electron-photon coincidences (local Auger region) and electron-electron coincidences (core-level ICD region).
The spectra overall agree well. A perfect agreement is not expected since the experimental spectrum originates from a wide size distribution of clusters and different sites within each cluster, which cannot be reproduced by the calculations for size-selected clusters. Qualitatively, in the DIP region above 43 eV the experimental spectrum is lacking the contribution from the 1 S 0 states (see above). The energy gap between the Auger and core-level ICD peaks is somewhat smaller in the experimental spectrum, suggesting that the polarization screening due to Ar atoms beyond the first coordination shell is not negligible. The theoretical core-level ICD to Auger branching ratio is 0.98% for the central atom in Ar 13 and thus larger than for the experiment. However, the experimental value lies reasonably between the values of the central atom in Ar 13 and the total Ar 13 cluster, which contains mostly surface atoms.
In conclusion, we have observed core-level ICD processes in van der Waals bound clusters by applying electron-electron and electron-electron-photon coincidence spectroscopy. The efficiency of these processes has been found to be about 0.8% of the Auger decay which is smaller than in hydrogen-bonded systems but not negligible as predicted earlier for van der Waals systems [25]. Our theoretical calculations support the experimental observation. They also reveal the sensitivity of core-level ICD peaks to the local environment, which can be used for probing the geometric and electronic structures of various clusters, surfaces, and interfaces. Mixed Xe-Ar clusters could be particularly attractive systems for a further study. Due to the proximity of one-site and two-site dicationic states in these clusters [44], core-level ICD peaks may partially overlap with Auger peaks acquiring thus considerable intensity through borrowing it from the Auger states [22]. In addition, core-level ETMD may be observed there. In strong contrast to homonuclear clusters considered in the present work, the energies of ETMD states and the created ions in mixed systems are distinguishable from those produced in ICD and Auger processes. Recently, core-level ETMD processes were observed in aqueous solutions [45,46]. Our report is on a successful electron-electron-photon coincidence experiment. We emphasize that this experimental method is by no means restricted to applications on core-level ICD, but generally enriches the toolbox of experimental atomic, molecular, and cluster physics.
We thank HZB for beamtime allocation and the BESSY II staff for assistance. This work was funded by the Deutsche Forschungsgemeinschaft (DFG) (Project No. 328961117 -SFB 1319 ELCH and Research Unit FOR 1789). L.S.C. is grateful to the European Research Council (Advanced Investigator Grant No. 692657) for financial support.