Ionization potentials of metal clusters studied with a broad range, tunable vacuum ultraviolet light source

The adiabatic ionization potential (AIP) provides deep insights into the electronic structure of small particles and isolated clusters.^1–3 For example, the AIP is a key property to understand the redox behavior of photo- and electro-catalysts.^4–6 To measure the AIP as precise as possible, complex and costly laser setups^7–11 or synchrotron light sources¹² are necessary in order to reach the high-energy thresholds usually required to ionize metal atoms and clusters.^12,13 These vacuum ultraviolet (VUV) light sources have the advantage of a high photon flux, making the photoionization process quite efficient. Particularly, for studying isolated clusters, this is necessary because of small particle densities in molecular beam experiments. For that purpose, it is generally necessary to analyze the clusters AIP by action spectroscopy, i.e., detecting the yield of cations in dependence of the radiation wavelength.

In this work, we show how to precisely measure the AIP of metal atoms and clusters with a VUV monochromator, equipped with a commercial xenon flash lamp, by recording the photo-ion yields via time-of-flight (TOF) mass spectroscopy. This method proved to be very simple and less cost intensive for determining ionization potentials in the VUV range.

Tin stands in the shadows of silicon regarding its usage in the semiconductor industry, but it also has many of the same desirable properties of silicon, such as widespread availability, low cost, and being non-toxic, as well as easier to process. As the microelectronic industry approaches the physical limits of miniaturization,¹⁴ small nanoclusters get more and more attention.^15–21 The advantages of tin nanoclusters as being tailorable in electronic and, therefore, physical properties due to their size-dependent behavior, makes them interesting candidates for the future of nanoelectronics^22,23 and also promising as model systems for catalysis.²⁴ Therefore, to test the new setup, the AIPs of tin clusters, Sn_n with n = 8–12 atoms, have been investigated. To calibrate the monochromator, the IPs of several atoms (Sn, Mo, V, Y, and In) were utilized. Measuring the AIP of FeSn₁₂ proves that nanoalloy clusters could also be studied with the apparatus.

The experiment is performed on a newly built apparatus, which is shown in Fig. 1. The clusters are produced in a laser vaporization source, which is described in detail elsewhere.^25,26 Here, a pulsed (10 Hz) and frequency-doubled Nd:YAG laser (20–30 mJ/pulse) is focused on a rotating and translating target rod (99.9% Sn, Alpha Aesar). A pulsed valve (Parker Series 9) is used to introduce helium (5.0 grade, Westfalen AG) into the nucleation chamber in order to cool down the generated plasma rapidly so that clusters are formed. This helium-cluster mixture is then expanded into high vacuum through a 20 mm long nozzle, with a diameter of 2 mm.

After the cluster beam is formed and skimmed, the charged clusters are deflected by applying a voltage of 5 kV to an electrode so that only neutral clusters reach the ionization region. The ionization region is spatially separated from the time-of-flight mass spectrometer (TOF-MS) by an aperture to avoid photofragmentation products that arrive at the acceleration region of the TOF-MS. Photoionization of the neutral clusters is performed by a xenon flash lamp (Excelitas FX-1165, 120–1100+ nm), mounted on the entrance slit of a vacuum monochromator (Acton Research Corporation, Model VM-502). The VUV-radiation is coupled orthogonally to the expansion direction of the molecular beam into the apparatus. Due to the specification of the grating, the wavelength range of the light source is 130–550 nm. To change the wavelength of the radiation, a high-precision linear motor (Physik Instrumente M-227.50), which replaces the default stepper motor of the monochromator, has been used to turn the grating. This device allows a minimum step size of 0.05 μm and a unidirectional repetition accuracy of 0.1 μm. This enables one to set the wavelength with a precision of about 10⁻³ nm, which is much smaller than the lowest achievable bandwidth of the monochromator. The main benefit of this replacement is that it allows for an easier software-based control of the grating tuning. The spectral resolution of the monochromator is defined by the dispersion of the grating (2400 lines/mm), which is 4.2 nm/mm. For a minimal width of Δ = 5 μm of the entrance and exit slits, this results in a lowest achievable bandwidth of 0.03 nm (⁠$2⋅Δ⋅4.2$ nm/mm). In practice, this bandwidth cannot be reached because of the low photon flux following the reduction of the slit width. For the investigation of the tin clusters, a slit width of at least 120 μm is necessary, which results in a bandwidth of 0.7 nm. Since the choice of the bandwidth depends on the intensity of the investigated clusters, for the experiments performed here, values of 0.7 nm (n = 10) for Sn₁₀ and 1.4 nm for the other species have been set. For a wavelength range of 165–220 nm (7.5–5.6 eV), this results in a resolution R = λ/Δλ of 236–314 and 118–157, respectively. Therefore, the utilized parameters allow one to determine the ionization potentials with an uncertainty of equal to or better than 0.07 eV.

Since the light intensity of the flash lamp is not constant over its full wavelength range, a photomultiplier (Hamamatsu R6836, spectral response: 115–320 nm) is used to measure the light intensity (Fig. 2). This allows one to normalize the measured cluster’s photo-ion yield with respect to the light intensity. The coarse calibration of the monochromator setting is performed by measuring the emission spectrum of the flash lamp (Fig. 2) and comparing it with the calibrated spectrum reported in the literature.²⁷ This is done with a resolution of 0.28 nm. This approach is verified by measuring the IPs of different atoms (Table I). It has been found that it is not necessary to correct the parameters of the coarse calibration further.

A typical mass spectrum for tin clusters is shown in Fig. 3. The assignment of the clusters is done based on the time-of-flight analysis of the isotopes of the Sn atom. At the cluster source settings used, the intensities for Sn_8–12 are greatest. Therefore, the photo-ion yields were measured for these cluster species. The low signal-to-noise ratios of the cluster signals are a consequence of the low photon flux achieved with the xenon flash lamp after monochromatization. We tried to quantify the available photon flux by setting the width of the entrance and exit slits to the maximum value of 4 mm (bandwidth of 23.8 nm). The light intensity has been measured at a photon energy of 3 eV with a NIST calibrated pyroelectric sensor (Thorlabs ES111C). The fluence is about 60 μJ/cm² per pulse, which results in roughly 3 × 10¹⁰ photons/cm² per pulse reaching the ionization region. Taking into account the fact that the intensity of the radiation incident on the molecular beam increases with the square of the slit width, a maximum of 2 × 10⁸ photons/cm² per pulse for photoionization are available at a bandwidth of 1.4 nm. Despite the low signal-to-noise ratio, it is possible to determine the photo-ion yields with the experimental setup. The achievable bandwidth is still comparable to the spectral resolution of synchrotron light sources, and compared to sophisticated laser systems, the setup has the big advantage that the radiation can easily be varied over a large photon energy range, i.e., measuring the photo-ion yield within a wavelength range of 180–200 nm for a monochromator bandwidth of 0.28 nm is feasible within 2 h. This is particularly important, because it guarantees good cluster stability across the whole measurement. Another advantage is that the flashlamp–monochromator unit can be adapted to existing molecular beam experiments, which is particularly interesting when access to a synchrotron-based light source is not available.

Figure 4 shows the photo-ion yields (PIYs) of the investigated clusters, as well as the corresponding error function fits. The course of the curves on the first onset is s-shaped. The analysis of this onset using the error function fit gives the adiabatic ionization potentials of the investigated clusters. The FWHM of the error function fit for the Sn atom of 0.10 eV is about twice as large as expected from the dispersion of the grating and the widths of entrance and exit slits. This indicates that the flashlamp is not optimally aligned with respect to the entrance slit of the grating. In addition, the flash lamp does not behave like a point light source. Both effects together lead to the fact that the FWHM from the error function fit is significantly increased compared to the originally estimated value of 0.06 eV. The FWHMs of the corresponding error function fits of the studied clusters are slightly increased compared to the value found for the Sn atom. However, a lower value for FWHM is found for Sn₁₀, since the slit width could be reduced in this measurement. The obtained AIPs are (all energies are in eV) Sn₈ (6.53 ± 0.05), Sn₉ (6.69 ± 0.04), Sn₁₀ (6.93 ± 0.03), Sn₁₁ (6.34 ± 0.05), and Sn₁₂ (6.36 ± 0.05). The unusually high value of the ionization potential of Sn₁₀ is related to the particular stability of this cluster.³⁰ For Sn₉ and Sn₁₀, these values agree very well with the literature data.³¹ For Sn₈, Sn₁₁, and Sn₁₂, the values obtained in this work are up to 0.3 eV smaller than those reported in the literature.³¹ The values reported in the literature have been measured with an experimental setup using a few discrete laser lines. This enabled a lower and upper limit for the ionization potential to be determined. This procedure has already led to deviations in the investigation of the ionization potentials of some silicon clusters compared to an experiment in which photoionization efficiency curves were evaluated.¹² Concerning the determination of the adiabatic ionization potentials, the procedure based on the onset of the photo-ion yield seems to be more accurate compared to that using some discrete laser lines. Since the deviations for the tin clusters are significantly larger than the bandwidth of the monochromator, we assume that the values for the ionization potentials reported here are reliable. With increasing photon energy, additional photoionization channels arise so that no plateau in the photo-ion yield is reached. A similar behavior has already been observed for silicon clusters.¹² The course of the photo-ion yield for Sn₁₂ is particularly striking, since the two onsets are clearly visible here. To clarify whether this is related to the presence of several structural isomers that have already been observed for this cluster size,³⁰ the shape and onset of the photo-ion yield was examined in more detail using a Franck–Condon simulation.

Therefore, calculated photoelectron spectra of the global minimum (GM) isomers are also shown in Fig. 4. The spectra were calculated by using the ezFCF software provided by Gozem and Krylov.³² For this, geometric input files are necessary, which have to be generated by quantum chemical calculations. For the clusters investigated here, these calculations have already been done in a previous work.³⁰ Briefly, a global optimization (GO) based on a genetic algorithm (GA) was performed with plane-wave DFT with the QuantumEspresso package.^33,34 The structural candidates found in this GO were further optimized with DFT. Here, the PBE0 functional and cc-pVTZ-PP basis were used.^35–37 The final structures considered for the calculation of the photoelectron spectra are shown beside the measured photo-ion yields. The geometric structures of the cationic clusters were also derived from the same treatment. For some clusters, the normal modes and the numbers of cations of the atoms had to be manually reordered for ezFCF, to calculate the diagonal Franck–Condon overlap matrix.³⁸ The vibrational temperature of the clusters, which is a necessary parameter in such calculations, has been set to 300 K because the cluster source is running at ambient conditions.²⁵ Integrating the photoelectron peaks leads to the theoretically predicted photo-ion yields, which are also presented in Fig. 4. For this purpose, each transition in the photoelectron spectrum was broadened by taking into account the finite resolution of the flashlamp–monochromator unit. For this, the obtained FWHM of the error function fit for the Sn atom of 0.10 eV was used. Since the quantum-chemically predicted values of the AIPs deviate systematically from the experimental data, the theoretically predicted photoelectron spectra in Fig. 4 have been shifted in each case to the extent that the best possible agreement between experiment and theory is achieved. Furthermore, the calculated spectra are normalized based on the error function fits for visual reasons. The experimental values of the AIP, the predicted AIPs at different levels of theory, including data from the literature, as well as the shift of the theoretical spectra, are summarized in Table II. As noted before, the data for Sn₁₀ are recorded with a photon energy range and bandwidth different from those of the other clusters.

The calculated photoionization efficiencies can well describe the first onset of the experimental photo-ion yield. With the exception of Sn_10, it is striking that the error function fits are smeared out a little more than the theoretically predicted curves. The influence of the thermal excitation of the clusters was investigated by simulating the theoretical PIY curves at different values for the vibrational temperature. It turned out that the expected broadening as a result of the finite vibrational temperature is completely masked by the intrinsic bandwidth of the experimental setup of about 0.10 eV. This can also be seen very clearly from the fact that the FWHM for Sn₁₀ is significantly reduced because measurements could be made with a smaller slit width for this cluster. The study of Sn₁₀ with a considerably steeper increase in the photoionization efficiency nicely demonstrates that the limited intrinsic resolution of the monochromator is crucial for smearing out the photoionization onset. Also noticeable is the less steep increase of the photoionization efficiency observed for the IsoI of the Sn₁₂ cluster. This may be due to an overlap of the ionization onset of IsoI Sn₁₂ with possible additional photoionization channels of IsoIII Sn₁₂.

Comparing the experimental values of the adiabatic ionization potentials with quantum-chemical predictions, independent of the cluster size, a discrepancy of about 0.3–0.4 eV is revealed if a hybrid exchange correlation functional such as PBE0 is used. This discrepancy is mainly due to the use of DFT, since the electron correlation is only partially correctly covered. It is to be expected that this discrepancy can be significantly reduced with the use of higher-correlated wave function-based methods. However, for Sn₁₂, we observe that the calculated AIP of the predicted global minimum IsoI is only about 0.1 eV lower than the experimental value of the first onset. In order to understand the step out of line of Sn₁₂, one must note that several structural isomers are predicted for Sn₁₂, which are almost energetically degenerate.³⁰ Correspondingly, it was also observed, in electrical deflection experiments, that at least two isomers are present in molecular beam experiments.³⁰ These experiments show that, in addition to the global minimum IsoI, IsoIII occurs in approximately the same weight. The quantum chemical calculations predict that the ionization potential of the IsoIII is about 0.3 eV lower than that of IsoI. This suggests that the first onset of the photo-ion yield results from IsoIII. The second increase, which is experimentally shifted by about 0.3 eV to higher photon energies, would then be due to the global minimum IsoI. Accordingly, in Fig. 4 for Sn₁₂, two error functions are taken into account, and two calculated photoelectron spectra are presented. In the experiments shown here, the weight of IsoI appears to be slightly greater than that of IsoIII.

One can now ask whether only Sn₁₂ possesses different structural isomers. The electrical deflection data indicate that at least for Sn₈ and Sn₁₁, another isomer may also be present in the experiment.³⁰ A second isomer is also predicted for Sn₉, but this is significantly higher in energy than the global minimum. Interestingly, the measured photo-ion yields do not give a clear indication of the presence of a second isomer for Sn₈, Sn₉, and Sn₁₁. This is probably due to the fact that the ionization potentials of the different isomers are too similar for these cluster sizes. At least that is what the quantum-chemically calculated values indicate, since the differences in the ionization potential for Sn₈, Sn₉ and Sn₁₁ are less than a maximum of 0.1 eV and are, therefore, in the limit of what can be detected with the experimental setup presented here.

Also shown in Table II are other theoretically predicted values of the ionization potentials taken from the literature, namely, hybrid (B3LYP and B3P86) and GGA (PBE) functionals. Again, systematic deviations from the experimental values become visible. Depending on the level of theory, the ionization potentials can now be overestimated by up to 0.4 eV. This proves that the accurate experimental determination of adiabatic ionization potentials is still a very sensitive test for quantum chemical calculations and that the ionization potentials depend sensitively on the geometric and electronic structure of the clusters.

To demonstrate the capabilities of the setup, we also examined a bimetallic cluster, namely, FeSn₁₂. A tin rod with 5 % Fe was used for this study. The photo-ion yield as a function of photon energy is shown in Fig. 5. Even though the cluster intensity of FeSn₁₂ is much smaller than that of Sn₁₂, it was possible to extract the adiabatic ionization potential by increasing the bandwidth of the monochromator to 2.8 nm (0.12 eV). By applying an error function to the experimental data, a value of the adiabatic ionization potential of 7.43 ± 0.12 eV is obtained, which is much larger compared to the value of the pure Sn₁₂ cluster. Future work will address the understanding of why the addition of a non-noble transition metal such as Fe increases the ionization potential of a main-group metal cluster so much.

An experimental study of the IPs of small Sn_n (n = 8–12) clusters was performed. A xenon flash lamp, combined with a vacuum monochromator, has been used to measure the clusters’ photo-ion yield. The results demonstrate that monochromatized light emitted by a flash lamp is a low cost alternative to determine the ionization potentials. One big advantage of this setup is that a wavelength range of 150–320 nm is available for experiments. The main drawback of this procedure is the bad signal-to-noise ratio of the mass spectra due to the low light intensity. Therefore, averaging the photo-ion yield curves over tens of measurements is necessary. In the future, we will be working on our setup to increase the intensity of the generated clusters, allowing one to study different cluster sizes and also other bimetallic nanoclusters. The obtained IPs match previous experimental data for n = 9–10 and differ by a maximum of 0.3 eV compared to the literature values for other tin clusters.³¹ The origin of these deviations is not entirely clear at the moment, but the calibration of the monochromator with several atoms gives us confidence that the procedure for extracting the AIPs from the onset of the photo-ion yield is adequate. Franck–Condon simulations of the photo-ion yield match the experimental data very well, additionally indicating that the analysis of the experimental data based on an error function fit works correctly. The systematic difference between the theoretical and experimental values of the IPs was discussed. The possibility that multiple structural isomers of a given cluster size can be present in the experiment is demonstrated for Sn₁₂. Here, two structural isomers can be identified because the difference in the AIPs is large enough to be detected unambiguously by measuring the photo-ion yield.

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Grant No. CRC 1487, “Iron, upgraded”—Project No. 443703006. This work was also funded by the Federal Ministry of Education and Research (BMBF) and the state of Hesse as part of the NHR Program. The authors would like to thank the Hessian Competence Center for High Performance Computing—funded by the Hessian State Ministry of Higher Education, Research and the Arts—for helpful advice. A.M. acknowledges Andreas Lehr and Filip Rivic for the many helpful discussions and providing the data regarding the quantum chemical calculations shown in this work. Also, the authors thank A. Krylov for helpful discussions regarding ezFCF and N. Wolf for the first adoption of the software.

The authors have no conflicts to disclose.

A. Macion: Data curation (equal); Formal analysis (equal); Investigation (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). R. Schäfer: Conceptualization (equal); Funding acquisition (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.