Formation of Al + (C 6 H 6 ) 13 : The Origin of Magic Number in Metal–Benzene Clusters Determined by the Nature of the Core

Abstract

Open AccessCCS ChemistryRESEARCH ARTICLE1 Dec 2019Formation of Al+(C6H6)13: The Origin of Magic Number in Metal–Benzene Clusters Determined by the Nature of the Core Hanyu Zhang†, Arthur C. Reber†, Lijun Geng, Daniel Rabayda, Haiming Wu, Zhixun Luo, Jiannian Yao and Shiv N. Khanna Hanyu Zhang† Beijing National Laboratory of Molecular sciences (BNLMS), State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences; University of Chinese Academy of Sciences, Beijing 100190, (China) †These authors contributed equally to this work.Google Scholar More articles by this author , Arthur C. Reber† Department of Physics, Virginia Commonwealth University, Richmond, VA 23284, (United States). †These authors contributed equally to this work.Google Scholar More articles by this author , Lijun Geng Beijing National Laboratory of Molecular sciences (BNLMS), State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences; University of Chinese Academy of Sciences, Beijing 100190, (China) Google Scholar More articles by this author , Daniel Rabayda Department of Physics, Virginia Commonwealth University, Richmond, VA 23284, (United States). Google Scholar More articles by this author , Haiming Wu Beijing National Laboratory of Molecular sciences (BNLMS), State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences; University of Chinese Academy of Sciences, Beijing 100190, (China) Google Scholar More articles by this author , Zhixun Luo *Corresponding authors: E-mail Address: [email protected], E-mail Address: [email protected] Beijing National Laboratory of Molecular sciences (BNLMS), State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences; University of Chinese Academy of Sciences, Beijing 100190, (China) Google Scholar More articles by this author , Jiannian Yao Beijing National Laboratory of Molecular sciences (BNLMS), State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences; University of Chinese Academy of Sciences, Beijing 100190, (China) Google Scholar More articles by this author and Shiv N. Khanna *Corresponding authors: E-mail Address: [email protected], E-mail Address: [email protected] Department of Physics, Virginia Commonwealth University, Richmond, VA 23284, (United States). Google Scholar More articles by this author https://doi.org/10.31635/ccschem.019.20190033 SectionsSupplemental MaterialAboutAbstractPDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareFacebookTwitterLinked InEmail The identification of highly abundant, “magic” species in the mass spectra of clusters have proven to be valuable in nanoscience, leading to the discovery of new stable species such as fullerenes and the electronic shell structures of metallic clusters. However, identifying “magic” clusters formed via noncovalent interactions faces challenges of poor clustering and difficulties in structure determination. Using a customized ultrafast, deep-ultraviolet laser ionization mass spectrometer, we report the finding of aluminum–benzene complex (Al+Bz13; Bz = benzene) as a magic cluster in the spectra of Al+Bzn (n ≤ 40) clusters, and herewith compared with the mass spectra and stability of vanadium–benzene complex (V+Bzn; n ≤ 40) clusters. Theoretical investigations, using Amsterdam Density Functional with dispersion correction, identified the structure of the dominant Al+Bz13 and revealed that the origin of the magic number Al+Bz13 is due to the geometric structure of Bzn shell enclosure of Al+, contrary to the V+Bzn clusters in which Bzn molecules formed a sandwich complex with the V+ core in V+Bz2. The differences in the structures of the clusters became apparent from their distinct characteristic features, revealed by Bz as a solvent around Al+ being strikingly different from the observed Bz solvent shell for V+, attributable to the variances in solvation numbers of 3 or 4 for aluminum and 2 for vanadium. These results provide new details into coordination chemistry and a strategy to dissect the interactions of metal ions in solvents like benzene. Download figure Download PowerPoint Introduction The structures and properties of biomolecules, supramolecular systems, organic functional materials, and catalysts often depend on the noncovalent interactions between aromatic species.1–5 Specifically, cation–π interactions have long been recognized as a major force for molecular recognition in supramolecular chemistry, where the hydrophobic effect, hydrogen bonding, and ion-pairing play a determining role in the macromolecular structure and donor–acceptor interactions.6–10 Furthermore, it has been illustrated that the cation–π interactions give rise to enhanced binding energies, comparable to hydrogen bonds and ion pairs in drug–receptor and protein interactions.7 However, the controlled study of these weak, noncovalent interactions is difficult due to the presence of stronger competing interactions in solutions and solids.11,12 It is highly desirable that gas-phase studies provide a target for theoretical analysis that might reveal unique features in the solvation shell of aromatic molecules.13–19 Earlier studies, based on Kebarle’s analysis, illustrated that the electrostatic ion–quadrupole interaction of benzene molecules displayed a substantial enthalpy change (e.g., K+ binds to benzene with a ΔH° of −19 kcal/mol).7 Thus, it is anticipated that the identification of magic benzene clusters with enhanced mass abundance and stability would reveal important information about solvation shells and chemical structures, and could be used as inputs for developing accurate model potentials. Magic species and corresponding magic numbers typically refer to a particular cluster having unusually high stability relative to other nearby sized clusters. Depending on the experimental conditions, the stability of metal clusters is often associated with energetic stability, geometric shell closure, electronic stability, and/or chemical stability.20–24 In comparison, the stability of clusters that exist in solvents alone, like water–water or benzene–benzene, are expected to be significantly different from those of the well-known metal-solvent clusters and their respective magic numbers.25,26 Previous investigators have demonstrated that the interaction between benzene molecules was thought of as a quadrupole–quadrupole interaction where the negatively charged π orbitals are attracted to a positively charged core, leading to a stronger binding for the CH–π structural motifs than the π–π motif.27–32 Such CH–π structural motifs were also addressed in the studies of clusters of benzene with other solvents such as H2O, CH3OH, and CH4.33–35 Although the size-dependent abundance of cationic benzene clusters has been studied, the nature of magic clusters have not been elucidated fully.36–38 Structural analysis of such clusters is challenging, as first-principles methods fail to accurately localize the electron-hole, whereas force-field based methods struggle to account for the effect of ionization. To avoid these challenges, we have performed a synergistic study on the size-dependent gas-phase stability and chemical structures of Al+(Bz)n and V+(Bz)n clusters (Bz = Benzene) with n = 0–15. By encapsulating a metal ion with benzene, we performed a unified study, combining experimental (customized ultrafast, deep-ultraviolet laser photoionization mass spectrometry [DUV-LIMS]) and theoretical strategies (Amsterdam Density Functional [ADF] calculations, employing dispersion corrections of density functional theory [DFT]) by fully taking into consideration the interaction between benzene and the metal ion.39–41 We used two metal ions, one main group metal (Al) and other, transition metal (V), with different electronic characteristics; Al+ has a closed electronic shell with a configuration of 3s23p0, and a V+ has an open 3d shell with a configuration of 3d4.42–45 The difference between the electronic configurations of Al+ and V+ has been shown to account for their altered coordination number of 3 and 2, respectively, in benzene complexes.46,47 To observe the stability of the Al+Bzn and V+Bzn clusters, we employed the optional DUV-LIMS to identify clusters, based on their intramolecular noncovalent Bz–Bz or Bz with metal ions (Al+ or V+) interactions.48,49 We obtained high-resolution mass spectra of benzene clusters up to 30 molecules, on which we introduced Al+ or V+ by laser ablation of the corresponding metal target by way of molecular beam expansion. Further, we explored the capabilities of the stable species in surviving excessive exposure to helium (He) and oxygen (O2) in a rich-pressure collision cell. Simultaneously, we also performed extensive calculations using ADF/DFT to obtain the structures of the clusters. We show that the energetic analysis is consistent with the magic stability of Al+Bz13 possessing a closed geometric shell structure, and V+Bz2, which is sandwich-structured, with the differences in these two distinct metallic benzene clusters pertaining to altered coordination within noncovalent cation–π interactions. Experimental and Theoretical Methods Experimental methods A customized DUV photoionization mass spectrometry apparatus50 was developed to study the formation and stability of M+–Bz clusters (). The whole instrument system was composed of three major subsystems: (1) a laser vaporization (LaVa) source coupled with a flow tube reactor, (2) home-made Reflection Time-of-Flight Mass Spectrometer (Re-TOF-MS), and (3) a DUV laser system for optional photoionization experiments. The Al+/V+Bzn clusters were generated in the cluster formation channel by laser ablation of metal targets of Al (99.999%) and V disks (99.9%) in the presence of 1% benzene vapor seeded in argon (Ar) buffer gas with a backing pressure of 0.4 MPa. A 532 nm laser (Nd:YAG) with an energy of 6–7 mJ/pulse and a repetition rate of 10 Hz was used for the laser vaporization experiments. The Ar buffer gas was controlled by a pulsed General Valve (Parker, Serial 9). After the generation of Al+/V+-Bzn clusters, the molecular beam was allowed for free expansion and sampling via a 2.0 mm skimmer, which separated the differentially pumped chambers. The clusters were orthogonally accelerated by the multiplate electrodes, going through deflection and focus regions, reflected by the gold-silk-weaved plate electrodes, and finally detected by a dual microchannel plate detector. The ion signals from the detector were recorded with a digital oscilloscope (HDO6000; Teledyne LeCroy, Chestnut Ridge, NY) by averaging 1000 traces of independent mass spectra. For the measurements of neutral Bzn alone clusters, a designed downstream electric field (DC 200 V) following the reaction tube was used to remove unwanted ions from the molecular beam. Then the beam of neutral clusters was ionized by the DUV laser via a “head-to-head” direction, which provided sufficient overlap between the DUV laser and the molecular beam in order to maximize the ionic abundance for mass spectrometer. The customized laser system (wavelength of 177.3 nm, pulse duration of 15.5 ps, and small pulse energy at ∼15 µJ) bore a transient low power density but high single-photon energy up to 7 eV, set to also, increase the ionic abundance and to avoid cluster fragmentation for precise mass spectrometer peak analysis. Previous studies employed the widely sufficient collisions in rich-pressure flow tubes or compact pipes method to probe cluster stability in the gas phase. In this study, we utilized a customized mini flow tube to conduct both He collision and O2 etching reactions in order to probe cluster stability. The reaction gas (99.999% high-purity He, or 5% O2 in He) was injected into the DUV-LIMS system by another pulsed General Valve to interact with foregoing clusters in the reaction tube. The amount of the reaction gas was controlled accurately by ranging the pulse width of the valve. After several hundreds of collisions (∼700 in this study), the reactants and products thermalized in the reaction tube during which the progress of the reaction dynamics was monitored for optimal metal cluster stability measurements. It is noteworthy that a proper thermalization process could be helpful to attain comparable results with theoretical calculations for the ground-state clusters. Theoretical methods We carried out first-principles calculations using the ADF/DFT set of codes, as follows:51 (1) The electron exchange and correlation contributions were included via generalized gradient approximation (GGA), as proposed by Perdew, Burke, and Ernzerhof (PBE).52 (2) We included the dispersion correction for DFT (DFT-D3-BJ) proposed by Grimme et al.53 (3) We used a TZ2P basis set and a large frozen electron core in all the computations. (4) We used the zero-order regular approximation to include a scalar-relativistic effects.54 (5) We performed geometry optimizations, initially starting from a large number of structures, and then used delocalized coordinates to aid in locating the desired M+–Bz cluster complexes. Results and Discussion Figure 1a presents a typical mass spectrum of the benzene clusters generated by a benzene vapor seeded in an argon buffer gas, followed by ionization by the ultrafast DUV laser. The benzene dimer was the most abundant, and the largest Bzn clusters with discernible intensity contained up to 30 benzene molecules. These clusters displayed a decaying abundance as the number of molecules increased and provided evidence for enhanced stability at n = 14 and 20. There were large drops in abundance at n = 15 and 21, consistent with a previous observation reported by Rusyniak et al.38 who noted prominent mass abundancies for Bz14 and Bz20 using an electron impact ionization method. As compared with the previous electron impact mass spectrometry studies, our DUV laser ionization mass spectrometry (DUV-LIMS)49 produced very clean spectra without any doubly charged mass peaks or cluster fragmentation. The ultrashort DUV laser pulses in the picosecond (ps) regime largely prevented the fragmentation of the clusters. Also, our implementation of resonance-enhanced two-photon ionization increased the ionization of benzene clusters with minimal fragmentation. Figure 1 | Mass spectra of the (a) Bzn, (b) V+Bzn, and (c) Al+Bzn clusters, where the n is the number of benzene molecules in the clusters, while the peaks marked with arrows are V2+Bzn and Al2,3+Bzn clusters. The Bzn clusters in (a) were ionized by a ps-pulsed deep-ultraviolet 177 nm. Download figure Download PowerPoint Figure 1b and 1c show the representative size distributions of V+Bzn and Al+Bzn clusters in mass spectrometry, formed by introducing V+ and Al+ ions into the benzene clusters beam without applying of the DUV ionization laser. In the V+Bzn clusters, V+Bz2 was the most abundant species, reflecting its high stability. This is comparable with previous findings, as V+Bz2 is known to form a more stable sandwich structure than similar coordination compounds of alumnum47,55,56 (see for more details manifesting the stability of V+Bz2). In sharp contrast, the Al+Bz2 peak was significantly smaller than n = 1 and 3 and is one of the smallest peaks among the n < 30 in the Al+Bzn mass distribution. This observation is also in accordance with previous findings by Miyajima et al.45 that Al+Bz was the preferred product when using 193 nm photoionization, and also the study by Reishus et al.,46 which found Al+Bz3 to be the preferred product that could complete the coordination shell around the Al+. The most notable result was the high abundance of Al+Bz13 species, which was significantly higher than all the clusters in the displayed size range, making it a “magic” cluster. Between n = 3 and 13 of the Al+Bzn clusters, the abundancy decreased from n = 3 to 10, in contrast to the increase in abundance starting at n = 11, suggesting that Al+Bz11 might have exhibited enhanced stability. In the V+Bzn spectrum (Figure 1b), significantly enhanced stability was observed with V+Bz2, followed by a peak at V+Bz5, higher in abundance than n = 3 and 4. After V+Bz5, there was a gradual decrease in abundance from n = 6 to 12, proceeded by an uptick at V+Bz13 and V+Bz14. There was no clearly defined magic peak at larger sizes in the V+Bzn spectra, although V+Bz13 also exhibited mildly enhanced stability, compared with its neighboring counterpart, especially, in the He collisional experiments (Figure 2B). By comparing the spectra of V+Bzn with Al+Bzn, we observed that small V+Bz and V+Bz2 clusters dominated the spectra, with a considerable drop after n = 2, whereas the larger clusters, in general, had lower abundance. This suggests that clustering around the V+Bz2 sandwich cluster is less likely than in the AlBzn clusters where the Al ion could bind at least 3 Bz molecules (AlBzn). Several peaks corresponding to clusters with multiple metal ions, such as V2+Bzn and Al2,3+Bzn, were observed, but the intensities were significantly much lower than the monovalent metal cationic (V+Bzn and Al+Bzn) series. This finding indicated that a few double-decker sandwich compounds were produced in this experiment. Also, there were no pure V+–V+ or Al+–Al+ clusters observed, indicating that the Bz–Bz clusters rapidly reacted and converted the metal ions into M+–Bz clusters. Figure 2 | Reflection Time-of-Flight mass spectra of Bzn clusters (A) and V+Bzn clusters (B) colliding with different amount of He: (a) distribution without He, (b) small amount of He (pulse width at 250 µs), and (c) large amounts of He (pulse width at 300 µs) added into the reaction tube. Download figure Download PowerPoint Then, we examined the relative intensity of these M+–Bz clusters in rich-pressure collision experiments. Figure 2 shows the Re-TOF mass spectra of Bzn clusters (a) and V+Bzn clusters (b) colliding with different amounts of He. We found that pure benzene (Bz–Bz) clusters fragmented readily, and only benzene molecule monomers, primarily, survived after He collisions (Figure 2A). However, parallel experiments with V+Bzn clusters did not find V+Bz to be the dominant peak (Figure 2B); instead, the mass abundance of V+Bz2 gradually increased and emerged as the primary peak after sufficient He collisions due to fragmentation of this stable sandwich-cluster complex into larger clusters. The enhanced mass abundance of Bz monomer and V+Bz2, respectively, was also observed in the collision experiments, using oxygen (O2) as the reactant (). In comparison, Al+Bzn displayed a different intensity distribution outcome; with increasing O2 collisions, the size distribution changed, and the Al+Bz13 gradually became relatively more abundant in the mass spectrum, as shown in Figure 3A. We also employed O2 etching reactions to test the possibility of the metallic core removed given the strong metal–oxygen bond. As a result, the enhanced mass abundance of Al+Bz13 was also noted in the experiments when O2 was used as the reactant (Figure 3B). In addition to the dominant mass abundance of Al+Bz13, there was an occasional odd–even alternation of the Al+Bzn distributions, such as Al+Bz4–8 in Figure 3A and Al+Bz9–13 in Figure 3B. Figure 3 | (A) Reflection Time-of-Flight mass spectra of Al+Bzn clusters colliding with different amount of He: (a) distribution without He, (b) small amount of He (pulse width at 250 µs), and (c) large amounts of He (pulse width at 300 µs) added into the reaction tube. The two peaks marked in * refer to nascent benzene molecule ion and the benzene dimer. (B) TOF mass spectra of Al+Bzn clusters when introduced different amounts of O2 into the flow tube reactor (details in ). Download figure Download PowerPoint To understand the origin of the size-dependent stability in the M+–Bz clusters, we performed an extensive structure search for the lowest energy structures of the Al+Bzn and V+Bzn clusters, n = 1–15. The structures of selected clusters are shown in Figure 4, and the structures for all the clusters are presented in . For the Al+Bzn clusters, we found that the first three benzene molecules bind directly to the Al+. These three clusters all exhibited enhanced benzene-binding energies, consistent with a previous study.46 After the formation of the first coordination shell with the central metal ion (gray=metal; blue=three-benzene inner core), the next two benzene molecules are able to bind above and below the three-benzene inner core in a bonding mode known as face-capping, in which the capping benzenes (in red) bind in a T-shaped geometry. Once this five-benzene molecule motif is formed, most of the remaining benzenes could bind to the next outer layer where the green benzene molecules generally point toward the Al+. Next, we show the structure of Al+Bz13. This cluster has a roughly tetrahedral four-benzene molecule core (gray=metal; blue=four-benzene inner core), instead of the standard three benzene core. As shown in , an isomer with a three-benzene core lies 0.04 eV higher in energy, indicating that the three- and the four-benzene cores are energetically competitive. A ring of six-benzene molecules (blue) with a T-shaped geometry and the CH–π arrangement of green benzene molecules is found. On top of the structure, a three-benzene molecule crown (orange) where these molecules also arrange in a CH–π structure. The second-order binding energies of Al+Bz13 are higher than all clusters n = 2–15, and significantly higher than clusters of similar size, confirming that the results of the theoretical analysis are consistent with the observed magic behavior of the cluster. Figure 4 | The structures of selected Al+Bzn and V+Bzn clusters based on Amsterdam Density Functional and long-range corrected density functional theory (ADF/DFT) calculations. Representative structures of the aluminum (Al+) and vanadium (V+) benzene complexes. Al+Bz3, Al+Bz5, Al+Bz7, Al+Bz11, and Al+Bz13 (upper) and V+Bz2, V+Bz4, V+Bz6, V+Bz10, and V+Bz13 (below). Download figure Download PowerPoint In comparison, the structures of the V+Bzn clusters follow a different growth pattern, as in all cases the two benzene molecules, shown in purple, form a highly stable sandwich structure with V+.45 In the smaller clusters, the third and fourth green benzene molecules bind along the edge of the sandwich, with additional benzene molecules, shown in red, binding with a CH–π structure to one of the sandwich benzene molecules. Notably, once again, almost all the interactions are T-shaped. Regarding the energetics of the cluster formation, V+Bz13 is found to be relatively stable the purple benzene form a sandwich compound core, with five green benzene molecules around the bottom sandwich of the complex in a T-shaped interaction. Five more T-shape-formed benzene clusters, four-gray, and one-red interact with the green clusters to form a second layer (Figure 4). Orange benzene caps the structure, again with a T-shaped interaction. Note that this structure is reminiscent of an icosahedron, with a 1–5–1–5–1 structure. Nevertheless, the T-shaped structure of benzene in V+Bz13 is as regular as in Al+Bz13 due to the asymmetric growth around the V+Bz2 core. Figure 5A presents the binding energies of benzene to the Al+Bzn, V+Bzn, and the Bzn clusters (n < 15), respectively, and Figure 5B displays the second-order binding energies of all the clusters, defined by Equation 1. Δ 2 E ( n ) = E ( M + Bz n + 1 ) + E ( M + Bz n − 1 ) − 2 E ( M + Bz n ) (1) Figure 5 | Binding energy plots derived from Amsterdam Density Functional and long-range corrected density functional theory (ADF/DFT) calculations: binding energies (a) second-order binding energies (b) of benzene to the Al+Bzn, V+Bzn, and the (Bz)n clusters; energies in eV. Download figure Download PowerPoint In the V+Bzn clusters, n = 2 is by far the most stable species due to the strong covalent bond between V+ and the two Bz molecules. Once the sandwich compound core V+Bz2 is formed, the additional benzene molecules bind weakly. For Al+Bzn, n = 2, no special stability is established; instead, the clusters n = 1 and 3 both have larger benzene-binding energies and higher abundance in the mass spectra. The small peak for Al+Bz2 is consistent with the smaller second-order binding energy for Al+Bz2, compared with Al+Bz1 and Al+Bz3. This suggests that the Al+Bzn clusters grow slowly from n = 1 to 2, and grow more rapidly from n = 2 to 3. Also, the low abundance might be caused by the low stability of the dimer Bz2, which might be attributable to the fact that the addition of Bz to the Al+ significantly lowers the ionization energy of the species and begin to rise when the relative ionization energy n > 2. It is noteworthy that Al+Bz13 acquired both prominent benzene-binding energy and second-order binding energy, presented in Figure 5a and 5b, respectively, consistent with the experimental findings, which revealed a high-intensity peak in the mass spectra, shown in Figure 3. It is also interesting to note the enhanced stability calculated for Al+Bz11, is consistent with n = 11, ending the trend of attenuation in the nascent mass distribution from n = 5 to 10 (Figures 1C and 3A-a). Further, we extended our ADF/DFT calculations to analyze the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy levels of the Al+Bzn, V+Bzn, and the Bzn clusters (n < 15), as well as their vertical neutralization energies, that is, the ionization energy in the cationic structure; see details provided in . The low ionization energy is due to the charge-transfer complex in which the HOMO of the benzene inserts into the Al 2p LUMO, pushing the HOMO of the complex to higher energy, which, in turn, lowers the ionization energy.57 Our results from the calculated vertical neutralization energies of the Al+Bzn and V+Bzn clusters (), showed that Al+Bz2 has significantly higher neutralization energy than all of the other Al+Bzn clusters, except n = 1. This means that collisions between neutral species and Al+Bz2 would cause stabilization of the system for an electron transfer to the Al+Bz2 cluster. The mass abundance does not only filter the benzene binding of the species but also reflects the stability of the M+Bzn species. For these reasons, the abundance of Al+Bz2 is smaller than expected. Essentially, V+Bz2 is the most stable species in the V+Bzn series because of the strong covalent bond of this core sandwich complex, and additional Bz molecules could only stick together by weak noncovalent interactions after the V+Bz2 core is formed. ADF/DFT theoretical calculations found that V+Bz6 was slightly more stable than the surrounding clusters, which conforms with the mass spectrometry observation in rich-pressure He collision experiments. Similarly, the V+Bz13 cluster was found to be more stable than the surrounding clusters due to the relatively ordered organization of Bz molecules around the covalent bonded V+Bz2 core. However, among the V+Bzn (n > 2) clusters, the noncovalent bonding interactions of the outer Bz molecules were always weaker than the sandwiched V+Bz2. Briefly, we found a good agreement between the calculated stability and our experimental observations of the abundances of the M+–Bz clusters. The M+Bzn clusters formed by noncovalent bonding interactions could be sensitive to collision-induced dissociation, which is not only determined by the energetics but also associated mainly with the collisional cross section. In view of this, we calculated the Van der Waals (VDW) radius of Al+Bz13 and V+Bz13, as shown in Figure 6. It is notable that, V+Bz13 bore a larger VDW radius than Al+Bz13, indicating that the dissociation of V+Bz13 (small ones such as V+Bz2) would be much faster than Al+Bz13 due to its more extensive collisional cross section. It is worth mentioning that although both Al+Bz13 and V+Bz13 clusters had relatively high second-order binding energies, we found that Al+Bz14 was relatively unstable, suggesting its likeliness to dissociate partially into the more stable Al+Bz13. On the other hand, further cluster growth from Al+Bz13 to Al+Bz14 would be least likely, since the equilibrium, presumably, favor its dissociation. In order to fully understand the growth patterns of the metal–benzene clusters, we calculated and plotted the following from our ADF measurements: (1) the d