Probing the structural evolution of ruthenium doped germanium clusters: Photoelectron spectroscopy and density functional theory calculations.

We present a combined experimental and theoretical study of ruthenium doped germanium clusters, RuGen(-) (n = 3-12), and their corresponding neutral species. Photoelectron spectra of RuGen(-) clusters are measured at 266 nm. The vertical detachment energies (VDEs) and adiabatic detachment energies (ADEs) are obtained. Unbiased CALYPSO structure searches confirm the low-lying structures of anionic and neutral ruthenium doped germanium clusters in the size range of 3 ≤ n ≤ 12. Subsequent geometry optimizations using density functional theory (DFT) at PW91/LANL2DZ level are carried out to determine the relative stability and electronic properties of ruthenium doped germanium clusters. It is found that most of the anionic and neutral clusters have very similar global features. Although the global minimum structures of the anionic and neutral clusters are different, their respective geometries are observed as the low-lying isomers in either case. In addition, for n > 8, the Ru atom in RuGen(-/0) clusters is absorbed endohedrally in the Ge cage. The theoretically predicted vertical and adiabatic detachment energies are in good agreement with the experimental measurements. The excellent agreement between DFT calculations and experiment enables a comprehensive evaluation of the geometrical and electronic structures of ruthenium doped germanium clusters.

Cluster is a new state of aggregation, which can be regarded as the intermediate phases between atoms or molecules and bulk solids12. A systematic study of clusters can provide valuable information on the evolution of the structural and electronic properties when isolated atoms or molecules become larger agglomerations, and bridge many fields of physics, such as atomic, molecular, and condensed-matter physics3. The central issue in cluster science is the determination of the true global minimum structures4. However, as the size of cluster increasing, finding the global minimum geometries becomes increasingly difficult due to the much increased complexity of the potential surface as well as the rapid increase of the number of low-lying isomers56. Luckily, the combined experimental and theoretical photoelectron spectroscopy approach has become a very effective method to identify the cluster structures, which has successfully determined the true global-minimum structures for various clusters ranging from small or medium-sized cluster to large sized cluster789101112.

Among the various classes of cluster materials, germanium-based clusters have attracted considerable experimental and theoretical attention because of that germanium is one of the most potential alternatives to silicon in microelectronic industry1314. However, pure germanium clusters can not form stable fullerene-like cage structures and are unsuitable as a building block of self-assembly materials1516. In order to generate and stabilize Ge cage structures, numerous experimental and theoretical investigations have been performed on transition metal (TM)-doped germanium clusters, similar to the case of TM-doped silicon clusters1112171819202122232425. It is found that the TM-doped germanium clusters reveal different growth pattern from the TM-doped silicon clusters1926. The critical size of TM-encapsulated Si structures is generally suggested to appear at n = 1210272829, while the TM-doped Ge clusters can form endohedral structures when n ≤ 10171819202122232425. Using solution chemistry methods, Wang et al.17 successfully synthesized the intermetalloid CoGe103− cluster with a D pentagonal prism structure. Zhou et al.18 performed experimental measurements by using the standard Schlenk-line techniques and reported another pentagonal prismatic Zintl ion cage encapsulating an interstitial iron atom, FeGe103−. Based on the anion photoelectron spectroscopy in combination with density functional theory (DFT) calculations, Deng et al.11 studied the structural, electronic and magnetic properties of VGe (n = 3–12) clusters and suggested that the endohedral structures occur from n = 9 and a D distorted hexagonal prism cage structure is formed at n = 12. They also observed that the critical size of the transition from exo- to endohedral structures is n = 9 for both anionic and neutral CoGe (n = 2–11) clusters12. Despite the much advances of 3d TM-doped germanium clusters, relatively little is known about the 4d TM-doped germanium clusters.

Very recently, Espinoza-Quintero et al.30 successfully synthesized the 12-vertex endohedral cluster RuGe123−, a previously unknown 3-connected polyhedral geometry of D-symmetry, by the reaction of an ethylenediamine solution of K4Ge9 with [Ru(COD){η3-CH3C-(CH2)2}2] (COD = 1,5-cyclooctadiene). In order to confirm the geometries and electronic properties observed in their experimental measurements, Goicoechea and McGrady31 performed DFT calculations on MSi12 and MGe12 and concluded that the bicapped pentagonal prism structure of RuGe123− dominates the structural landscape for high valence electron counts (57–60). Nevertheless, up to now, there are no systematic investigations on neutral or single charged Ru-doped germanium clusters. There are still several essential open questions about the Ru-doped germanium clusters: How clusters grow with the increasing number of germanium atoms? What is the size of the smallest endohedral cage structures? What are the charge properties of the endohedral cage structures?

As an effort to address the above questions, here we report a combined photoelectron spectroscopy and DFT study on Ru-doped germanium clusters: RuGe− and RuGe (n = 3–12). The vertical detachment energy (VDE) and adiabatic detachment energy (ADE) of RuGe− are estimated from their photoelectron spectra. The structures of RuGe− and RuGe are assigned by the comparison of the theoretical simulations and experimental measurements. The thermodynamic stabilities of the obtained global minima are checked by analyzing the average binding energies (E) and the second energy difference (∆2E). The natural population analysis is conducted to trace the negative charge dense regions in the neutral and anionic forms.

Results and Discussion

Experimental results

The photoelectron spectra of RuGe− clusters from n = 3 to 12 measured at 266 nm photons are presented in Fig. 1. In each spectrum, the first peak represents the transition from the ground electronic state of the cluster anion to that of the corresponding neutral species, and the other peaks with higher binding energy denote transitions to excited electronic states of the neutral clusters. The VDE is evaluated from the first peak. Meanwhile, the ADE of each cluster is estimated by adding the instrumental resolution to the binding energy which is the interaction of the binding energy axis and a straight line drawn along the leading edge of the first peak. The experimental VDE and ADE values of RuGe− clusters from photoelectron spectra in Fig. 1 are summarized in Table 1.

Figure 1

Experimental photoelectron spectra of RuGe− (n = 3–12) clusters recorded with 266 nm photons.

Table 1

Vertical detachment energies (VDEs) and adiabatic detachment energies (ADEs) of the ground state RuGe− (n = 3–12) clusters estimated from their photoelectron spectra.

Cluster	VDE (eV)		ADE (eV)
	Exp.	Theo.	Exp.	Theo.
RuGe3−	2.08 ± 0.08	1.98	1.80 ± 0.08	1.97
RuGe4−	2.12 ± 0.08	2.08	1.83 ± 0.08	2.37
RuGe5−	2.32 ± 0.08	2.64	2.08 ± 0.08	2.41
RuGe6−	2.75 ± 0.08	2.64	2.45 ± 0.08	2.77
RuGe7−	2.53 ± 0.08	2.58	2.27 ± 0.08	2.49
RuGe8−	3.10 ± 0.08	2.97	2.89 ± 0.08	2.68
RuGe9−	2.89 ± 0.08	3.17	2.53 ± 0.08	2.78
RuGe10−	3.17 ± 0.08	3.33	2.73 ± 0.08	3.11
RuGe11−	3.14 ± 0.08	3.19	2.79 ± 0.08	2.96
RuGe12−	3.81 ± 0.08	3.62	3.11 ± 0.08	3.41

In the spectrum of RuGe3−, the first peak occurs at around 2.08 eV, which gives the VDE. After this, there is a weak peak at 2.57 eV and then a broadened area with several obscure peaks between 3.00 and 4.00 eV. From the photoelectron spectrum of RuGe4−, the VDE is about 2.12 eV. The second peak at 2.52 eV is stronger than the first one whereas the third weak peak occurs at 2.90 eV. The spectrum of RuGe5− reveals that the VDE is about 2.32 eV and a second smaller peak locates at 2.95 eV. For RuGe6−, the VDE is about 2.75 eV and the front three peaks of the photoelectron spectrum are very close, followed by a broadened area between 3.90 and 4.40 eV. In the case of RuGe7−, the spectrum exhibits a major peak at 2.53 eV, which is the VDE. For RuGe8−, the VDE is about 3.10 eV followed by a sharp peak at 3.62 eV. The photoelectron spectrum of RuGe9− reveals the first weak peak at about 2.89 eV and a second small peak at 3.54 eV. The spectrum of RuGe10− is similar to that of RuGe9−, in with a VDE is 3.17 eV and a second peak at 3.58 eV. In the case of RuGe11−, there is a broad area between 2.80 and 3.30 eV and the VDE is about 3.14 eV. For RuGe12−, the intensity slowly increases from 2.60 to 3.81 eV and the VDE is around 3.81 eV.

Theoretical results

The optimized global minima of all RuGe− and RuGe (n = 3–12) clusters as obtained at the PW91/LANL2DZ level are plotted in Fig. 2. The geometries and relative stabilities of the low-lying isomers of each cluster are shown in Figs S1 and S2 in the Supporting Information (SI). The electronic states, point group symmetries and relative energies of all the considered clusters are summarized in Table S1 in the SI. The theoretical VDE and ADE values of the global minimum anions are listed in Table 1, in comparison with the experimental data. From Table 1, for all the ground state species, the computational VDE values are in good agreement with the experimental data, lending considerable credence to their structures.

Figure 2

Global minimum structures of the RuGe− and RuGe (n = 3–12), along with the point group symmetries.

The green balls are Ge atoms and the red balls are Ru atoms.

As shown in Fig. 2, the global minimum structures of the neutral RuGe clusters are nearly identical to those of RuGe− when n = 6, 7, 9, 10, 11, while the structures of RuGe (n = 3–5, 9, 12) are different from their corresponding anions. However, both the anionic and neutral RuGe−/0 clusters display the following structural trends: the global minimum RuGe−/0 clusters with n = 3–6 have exohedral or Ru-capped geometries (except for RuGe5−); RuGe7−/0 and RuGe8−/0 possess half-encapsulated structures; and endohedral geometries are adopted for the larger clusters with n = 9–12. In particular, the global minimum structure of RuGe10−/0 is a 3-connected C-symmetric polyhedral cage encapsulating the Ru atom in the center. As well as, a C-symmetric ground state RuGe12− also reveals a 3-connected polyhedral geometry, which mirrors the structure of trianionic RuGe123− reported by Espinoza-Quintero et al.30. Unfortunately, except for this, there are no more available experimental data to compare with our calculations for RuGe−/0.

Comparison between experiment and theory

In order to prove the credibility of the obtained ground state structures, the photoelectron spectra of RuGe− (n = 3–12) are simulated and displayed in Fig. 3, along with the experiment spectra from Fig. 1 for comparison. In general, the simulated spectra are in overall satisfying agreement with the measured photoelectron spectra, which certify the validity of the present theoretical results.

Figure 3

Simulated (red color) photoelectron spectra for RuGe− (n = 3–12) clusters, along with the experimental spectra (blue color) from Fig. 1 for comparison.

A uniform Gaussian broadening of 0.15 eV is chosen for all the simulated spectra.

For RuGe3−, the first two discrete peaks of the simulated spectrum are red-shifted compared to the experimental results, however, the others agree well. In the simulated spectrum of RuGe4−, the first five peaks are all in excellent agreement with the experimental measurements. For RuGe5−, the first peak is located at 2.64 eV, a little higher than the experimental value. The following peak is very broad, in accordance with experimental determination, and originates from several individual excitations. In the case of RuGe6−, the essential features of the experimental spectrum are well reproduced by DFT simulation. In the calculated photoelectron spectrum of RuGe7−, the first peak is in excellent agreement with the experimental measurement, while the others are somewhat different. In the theoretical spectrum of RuGe8−, three major peaks are obtained, which are in very good agreement with experiment. In the case of RuGe9−, the overall experimental spectrum is well reproduced by theoretical calculations; however, the first calculated peak at 3.17 eV is a little higher in energy and thus less distinct than the first experimental peak. In the theoretical spectrum of RuGe10−, three obvious peaks can be clearly seen, in accordance with the experimental data. For RuGe11−, the DFT calculation successfully reproduces the experimental trend and yields two obvious peaks. The simulated spectrum of RuGe12− has an onset very similar to the experimental spectrum, and reproduces a small shoulder before the main peak.

For the sake of a clearer comparison to experiment, the experimental and computed VDEs and ADEs as functions of cluster size are shown in Fig. 4. In the experimental VDE curve, an overall increase can be seen from 1.98 to 3.62 eV across the different clusters, but features local minima at RuGe7−, RuGe9−, and RuGe11−. The theoretical VDEs reproduce this trend generally well, bar for the local minimum at RuGe9−. In general, the ADE value of an anionic cluster is equal to the adiabatic electron affinity (AEA) of the corresponding neutral species when their geometries are similar to each other. From experiment, it can be seen that ADE values keep rising from 1.80 to 2.45 eV for RuGe (n = 3–6); thereafter this trend slows down, with an increase from 2.53 to 3.11 eV as the number of germanium atoms increases from 9 to 12. The ADE shows oscillatory from n = 6 to 9, with local minimum at RuGe7− (2.27 ± 0.08 eV) and RuGe9− (2.53 ± 0.08 eV). Again, the experimental trend is well reproduced by DFT simulations, but with an overestimation of about 0.46 eV at RuGe4− and 0.30 eV at RuGe10− respectively. From electronic points of view, RuGe7− and RuGe9− stand out as unique species with appreciable stability. For a given neutral cluster, lower AEA corresponds to higher stability. This indicates, in other words, that the neutral RuGe7 and RuGe9 clusters are stable.

Figure 4

Vertical detachment energies (VDEs) and adiabatic detachment energies (ADEs) of RuGe−/0 (n = 3–12) clusters: blue circles, experiment; red pentacles, theory.

Stabilities and electronic properties

The thermodynamic stabilities of the RuGe− and RuGe (n = 3–12) clusters can be explored by investigating two thermodynamic parameters, namely the average binding energy and the second energy difference. The E and ∆2E of RuGe−/0 clusters are defined as follows:

where E is the energy of the corresponding atom or cluster. The behaviors of calculated E and ∆2E values as function of cluster size for RuGe− and RuGe clusters are shown in Fig. 5(a,b), respectively. From Fig. 5(a), the binding energy per atom increases monotonously, but saturates for n > 9, with increasing number of Ge atoms, suggesting that the formation of larger clusters is favorable over smaller clusters. For all cluster sizes, E values of anionic clusters are higher than those of the neutral species. This implies that as soon as a neutral cluster gains an extra electron, it becomes more stable. From Fig. 5(b), one can see stronger oscillations of the second energy difference in the anionic than the neutral clusters. An obvious odd−even oscillation for anions is found from n = 5 to 11. The peaks for RuGe6−, RuGe8− and RuGe10− indicate that these are more stable than their neighboring sized clusters.

Figure 5

Size dependences of average binding energies (E), second order difference (Δ2E) and HOMO–LUMO gaps (E) for the global minimum RuGe−/0 (n = 3–12) clusters.

The energy gap (E) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) indicates the ability of electrons to jump from occupied orbitals to unoccupied orbitals. As shown in Table S1 and Fig. 5(c), the HOMO–LUMO gap values of RuGe−/0 clusters range between 0.26 and 1.17 eV. Regarding cluster size, the E values of neutral species with n > 6 are much larger than those of the small clusters. In contrast, the E values of the larger sized anions are smaller than those of the small species. It stands out that neutral RuGe8, RuGe9 and RuGe12 have the largest HOMO–LUMO gaps, implying that they are (relatively) more stable based on their electronic structure.

In order to examine the charge transfers, we next conduct the natural population analyses for the most stable isomers of the anionic and neutral RuGe−/0 (n = 3–12) clusters. The results are summarized in Fig. 6. For the anionic clusters, it is found that, for RuGe3−, the negative charge is localized on both Ru atom and the Ge framework. For the larger anions, there is increasing electron transfer from the Ge framework to the Ru atom. For cluster size of n = 7–12, in particular, the negative charge on the Ru atom increases significantly, suggesting that there is substantial electron transfer from the Ge framework to the Ru atom. In the case of neutral clusters, the electron transfer from the Ge atoms to the Ru atom occurs for all cluster size and the charges on Ru are much larger for clusters with n = 7–12. The electron transfer from the Ge framework to the Ru atom is related to the formation of endohedral structures.

Figure 6

Natural charge populations of the Ru atom for the global minimum structures of RuGe−/0 (n = 3–12) clusters.

Conclusions

In summary, we have reported a systematic study of the relative stability and electronic properties of ruthenium doped germanium clusters in the size range of 3 ≤ n ≤ 12. Photoelectron spectra of anionic RuGe− clusters are measured at 266 nm. Unbiased structure searches reveal quite similar global minimum structures for both anionic and neutral clusters. Excellent agreement between theoretical calculations and experimental measurements is found. The global minimum anionic RuGe− clusters with n = 3–6 as well as their neutral counterparts have Ru-capped structures (except for RuGe5−); half-encapsulated structures are found for RuGe7−/0 and RuGe8−/0; and the larger clusters RuGe−/0 (n = 9–12) feature endohedral geometries. From natural population analyses we see that, for the larger clusters with n = 7–12, the negative charge on the Ru atom increases significantly, suggesting that there is more electron transfer from the Ge framework to the Ru atom, which stabilizes the formation of endohedral cage.

Experimental and computational methods

Experiments are carried out on a home-built instrument consisting of a laser vaporization cluster source, a time-of-flight (TOF) mass spectrometer, and a magnetic-bottle photoelectron spectrometer, which have been described elsewhere32. In the laser vaporization source, the anionic Ru−Ge clusters are produced by laser ablation of a rotating translating disk target (13 mm diameter, Ru/Ge mole ratio 1:2) with a nanosecond Nd:YAG laser (Continuum Surelite II-10). To cool the generated cluster, helium gas with ~4 atm backing pressure is allowed to expand through a pulsed valve (General Valve Series 9) into the source. At the TOF mass spectrometer, the thus-formed cluster anions are mass-analyzed. The RuGe− (n = 3–12) clusters are individually selected with a mass gate, decelerated by a momentum decelerator, and crossed with the beam of a Nd:YAG laser (Continuum Surelite II-10, 266 nm) in the photodetachment setup. The magnetic-bottle photoelectron spectrometer is used to energy-analyze the electrons from the photodetachment. The resolution of the magnetic-bottle photoelectron spectrometer is about 40 meV at electron kinetic energy of 1 eV.

Theoretically, the structure searches for anionic RuGe− (n = 3–12) clusters and their neutral states are performed using CALYPSO method3334353637. This method is based on globally minimizing potential energy surfaces, merging ab initio total energy calculations with CALYPSO cluster prediction through particle swarm optimization. It has been successful in correctly predicting structures for various systems353638. The low-lying isomers of RuGe−/0 (n = 3–12) found in the searches are further optimized using DFT with the PW91 functional39. The LANL2DZ basis set is used for both Ru and Ge atoms. Spin multiplicities (up to septet and octet) are considered for refined structure optimization. Vibrational frequency calculations are used to verify the nature of real local minima. To further evaluate the relative energies of the low-lying structures, single-point calculations were carried out by employing the larger def2-TZVP basis set. Excitation energies of the neutral cluster are calculated using the time-dependent DFT (TDDFT) method at the corresponding anionic structure40. All calculations are carried out with the Gaussian 09 package41. The PW91/LANL2DZ theory show superior results in terms of structures and binding energies for the species considered here and are therefore used for direct comparison with the experiment.

Additional Information

How to cite this article: Jin, Y. et al. Probing the structural evolution of ruthenium doped germanium clusters: Photoelectron spectroscopy and density functional theory calculations. Sci. Rep. 6, 30116; doi: 10.1038/srep30116 (2016).