Even-numbered Clusters Research Articles

Pseudopotential Density-Functional Calculations for Structures of Small Carbon Clusters CN (N = 2 ~ 8)**The project supported by National Natural Science Foundation of China under Grant No. 10274055 and the Research Fund for the Doctoral Program of High Education of China under Grant No. 20020610001

We introduce a first-principles density-functional theory, i.e. the finite-difference pseudopotential density-functional theory in real space and the Langevin molecular dynamics annealing technique, to the descriptions of structures and some properties of small carbon clusters CN (N = 2 ~ 8). It is shown that the odd-numbered clusters have linear structures and most of the even-numbered clusters prefer cyclic structures.

Polynitrogen clusters containing five-membered rings

Possible structures of N 1 5 cluster were examined by ab initio (MP2) and density functional theory (DFT) methods with the 6-31G* basis set. Their stabilities were compared together with other polynitrogen clusters N n (n= 8, 10-14) reported in the literature. The order of stability was made respectively according to even or odd numbers of the total nitrogen atoms in clusters. It is found that both for even-numbered clusters N 2 n (n = 4-7) and odd-numbered clusters N 2 n + 1 (n = 5-7) the thermodynamically most stable isomers are all based on pentazole units; for each one of N n (n = 8, 10-15) clusters, the more conjugated the five-membered ring the more stable is the isomer; and, the more side-chains the N 5 ring links the less stable is the isomer. Another finding is that the larger the cluster the less stable is the cluster for every series of clusters of (a) containing two five-membered rings with an even number of total nitrogen atoms [N 1 0 (D2d), N 1 2 (C 2 h ), N 1 4 (C 2 h )], (c) containing one five-membered ring and a side-chain with an even number of total nitrogen atoms [N8 (C s ), N 1 0 (C s ), N 1 2 (C s ), N 1 4 (C s )], (d) containing one five-membered ring and a side-chain with an odd number of total nitrogen atoms [N 1 1 (C s ), N 1 3 (C s ), N 1 5 (C s )], (e) chain clusters with an even number of total nitrogen atoms [N8 (C 2 h ), N 1 0 (C 2 h ), N 1 2 (C 2 h ), N 1 4 ( 2 h )], and (f) chain clusters with an odd number of total nitrogen atoms [N 1 1 (C 2 v ), N 1 3 (C 2 v ), N 1 5 (C 2 v )]. For another series of clusters with two five-membered ring units [N 1 1 (C 2 ), N 1 3 (C 2 v ), and N 1 5 (C 2 v )] (series b) the N 1 3 (C 2 v ) shows the best stability. It is also found that the even-numbered nitrogen clusters are more stable than the odd-numbered ones in comparison of series (a) with (b), (c) with (d), and (e) with (f).

First-principles simulations for structures and optical spectra of carbon cluster C 8

We apply a finite-difference pseudopotential density functional theory in real space and the Langevin molecular dynamics annealing technique as well as the adiabatic time-dependent density functional theory within the local density approximation (TDLDA) to the descriptions of structures and optical absorption spectra of carbon clusters C 8. It is shown that the odd-numbered clusters have the linear structures and most of the even-numbered clusters prefer cyclic structures. The calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations.

Structures and stability of N13 cluster

Quantum chemical studies for the nine N13 isomers with low spin were carried out at the UHF/6-31G*, UB3LYP/6-31G* and UMP2/6-311G* levels of theory. The most stable N13 isomer is structure 1 with C2v symmetry, which contains two separated pentazole rings connected by three nitrogen atoms. The results show that structures 1, 2, 3, 4 and 5 which are composed of the pentazole ring are more stable than the open chain structure 6 and structures 8 and 9 which contain the four- and six-membered rings. This suggests that the pentazole ring is a fundamental stable structural unit, which is applicable not only for the even-numbered nitrogen clusters, but also for the large odd-numbered clusters.

Photodissociation and photoionization of sodium coated C $_\mathsf{60}$ clusters

(C60) m Na n clusters are produced in a tandem laser vaporization source and analyzed by photoionization and photofragmentation time-of-flight mass spectroscopy. At low sodium coverage, the special behavior of (C60) m=1,2Na n clusters $(n\leq 6m)$ is consistent with a significant electron transfer from the first six adsorbed atoms towards each of the C60 fullerenes and an ionic-like bonding in this size range. However, the stability of the (C60)Na3 + cation is found much more pronounced than the one of (C60)Na7 + predicted to be a magic size under the hypothesis of a full charge transfer from the metal atoms to the C60 molecule. When more sodium atoms are present, metal-metal bonds tend to become preponderant and control the cluster properties. Relative to the number of sodium atoms, an odd-even alternation in their stability is explained by the high dissociation rates for even-numbered clusters. The even clusters evaporate neutral sodium atoms whereas odd ones prefer to evaporate Na2 molecules. The hypotheses for the growth of a sodium droplet that does not wet the fullerene surface or for the formation of a concentric metallic layer are discussed in the light of this study.

High Aggregation Number Silver Clusters by Matrix-Assisted Laser Desorption/Ionization: Role of Matrixes on the Gas-Phase Reduction of Silver Ions

Singly positively and negatively charged silver-cluster ions were effectively produced under matrix-assisted laser desorption/ionization (MALDI) conditions up to the aggregation number of n ≅ 200, using reductive polar organic matrixes and silver trifluoroacetate (AgTFA). It was found that the matrix greatly influences the resulting cluster ion abundances. The effect of the matrixes with various chemical structures on the cluster formation was systematically investigated. It was also observed that the ion intensities decreased sharply at particular cluster numbers called “magic” numbers, independently of the matrix used, and this is in good agreement with the jellium model theory. The highest observed magic numbers were achieved with HABA [2-(4-hydroxyphenylazo)benzoic acid] and are 139 and 137 for positively and negatively charged cluster ions, respectively. The fragmentations of both singly positively and negatively charged clusters ions were also studied. It was found that even-number clusters lose one...

Guided ion beam studies of the reactions of Vn+ (n=2–13) with D2: Cluster–deuteride bond energies as a chemical probe of cluster electronic structure

The kinetic energy dependencies of the reactions of Vn+ (n=2–13) with D2 are studied in a guided ion beam tandem mass spectrometer. Products observed are VnD+ for all clusters and VnD2+ for n=4–13. All reactions are observed to exhibit thresholds, except for formation of VnD2+ for n=4,5,7,9,11–13. The enhanced reactivity of the odd-sized clusters towards D2 chemisorption is nicely correlated with the D0(Vn+–V) bond energies. The odd-number clusters are less stable and more reactive, suggesting that they are open shell, whereas the even-number clusters, which are more stable and less reactive, appear to be closed shell. Threshold analyses of the endothermic reactions lead to Vn+–D binding energies (n=1–13), which reach values comparable to the bulk phase for larger clusters. The Vn+–D bond energies show odd–even oscillations anticorrelated with D0(Vn+–V) for n<5, but roughly parallel with D0(Vn+–V) for n>5. Magnitude differences in the two series of bond energies suggest that the metal–metal bonding has appreciable 3d–3d contributions. The variation in the Vn+–D bond energies with cluster size is explained using promotion energy arguments.

Anomalous Photofragmentation of Fullerene Doped in SilicaAerogel-Enhanced Formation of Odd-Numbered ``Fullerene'' Fragments

Photofragmentation of fullerene-dopedsilica aerogels has been investigated by the excimer laser ablationreflectron time-of-flight mass spectrometric technique. Greatenhancement in the formation of odd-numbered `fullerene' fragmentshas been observed in the negative-ion channel for the chemicallydoped aerogel sample. Generally, odd-numbered species C57,C55, C53 and C51 appeared in the mass spectra.Under optimal experimental conditions C55 can be even moreintense than the neighbouring even-numbered carbon clusters. Incontrast, for the physically-doped sample, just like pristineC60, only weak odd-numbered fragments were observed. In thepositive-ion channel, the behaviour of all these samples is similar,no odd-numbered species was ever detected. A mechanism related to theinteraction between the fullerene dopant and the silica aerogel hostis suggested for the anomalous enhancement of the odd-numberedcluster formation. A preliminary discussion on the structures of theodd-numbered `fullerene' fragments is given.

Decay pathways of small gold clusters

The decay pathway competition between monomer and dimer evaporation of photoexcited cluster ions Au + n, n = 2-27, has been investigated by photodissociation of size-selected gold clusters stored in a Penning trap. For n > 6 the two decay pathways are distinguished by their experimental signature in time-resolved measurements of the dissociation. For the smaller clusters, simple fragment spectra were used. As in the case of the other copper-group elements, even-numbered gold cluster ions decay exclusively by monomer evaporation, irrespective of their size. For small odd-size gold clusters, dimer evaporation is a competitive alternative, and the smaller the odd-sized clusters, the more likely they decay by dimer evaporation. In this respect, Au + 9 shows an anomalous behavior, as it is less likely to evaporate dimers than its two odd-numbered neighbors, Au + 7 and Au + 11. This nonamer anomaly is typical for copper-group cluster ions M + 9 (M = Cu, Ag, Au) and a similar behavior is found in the anionic heptamers M - 7. It is discussed in terms of the well-known electronic shell closing at n e = 8 atomic valence electrons.

Structure and stability of new N 7 isomers

Ab initio quantum mechanics methods have been used to examine isomers with low spin of N 7 cluster. In additional to the previously studied five N 7 isomers, five new structures were investigated in this paper. Their structures, energies, zero point energies, net charges were calculated at the UHF/6-31G ∗, UMP2/6-31G ∗, B3LYP/6-31G ∗, B3LYP/6-311+G ∗ levels. The harmonic vibrational frequencies and their infrared intensities have been predicted with SCF, MP2 and DFT methods. Two of them [structure 2 ( Cs) and 5 ( Cs)] are reasonable local minima on the N 7 energy hypersurface at the all of the levels we used. The twisted open-chain N 7 ( C 2 v ) is still the most stable in all of the twelve N 7 isomers. Based on the NBO analysis, a new non-classical Lewis structure was suggested for the twisted open-chain N 7 ( C 2 v ), which is helpful for understanding its special bond nature. The similar and different properties between the N 7 clusters and even-number nitrogen clusters were discussed.

Energy-resolved collision-induced dissociation of Cun+ (n=2–9): Stability and fragmentation pathways

Collision induced dissociation of Cun+ clusters (n=2–9) in collision with Xe is presented in the center-of-mass energy range from about 100 meV to above 15 eV. The collision energy dependence is measured for the total and the partial dissociation cross sections, and the dissociation thresholds for the dominating processes are derived. The threshold energies show pronounced odd–even alternations, reflecting a higher stability of the odd-numbered, Cu2n+1+, clusters. Further, the evaporation of a single neutral atom is found to be the energetically favorable process for the even-numbered clusters, while the loss of the neutral dimer is favorable in the case of the odd-numbered clusters. An exception is Cu9+, where the formation of Cun−1+ is energetically favorable, and the energetics of the Cun−2+ formation are in good agreement with sequential evaporation of two neutral monomers. Here we discuss the energy dependency of the total and partial dissociation cross sections, and try to give a consistent picture of the dissociation dynamics. We present binding energies for the cationic clusters from their dissociation thresholds, and use those, in combination with the literature values for the ionization potentials of Cun, to estimate the binding energies for neutral copper clusters. Finally, we compare this work to earlier theoretical calculations, as well as experimental estimations of the binding energies.

Photofragmentation studies of small selenium cluster cations Sen+ (n=3–8)

Selenium cluster cations are produced by the combination of laser vaporization and supersonic expansion techniques. Each small cluster cation Sen+ (n=3–8) is mass selected separately and subjected to one-photon laser photodissociation processes. The parent and daughter cluster ions are detected using a reflectron time-of-flight mass spectrometer. The appearance potentials of all the observed cluster fragment ions are estimated from their yield curves as a function of the laser wavelength. The neutral dimer evaporation is found to be the lowest energy photodissociation channel. In general, the odd-numbered cluster cations have much larger dissociation thresholds than those of the even-numbered cluster cations. In addition, the dissociation thresholds of the odd-numbered cations decrease with the increasing cluster size, while those of the even-numbered clusters increase with the increasing cluster size. A sequential neutral dimer evaporation mechanism is demonstrated in the photodissociation of some cluster cations at high photon energies.

Stability of anisotropic missing dimer clusters on Si(001) surfaces

Two kinds of anisotropic structures of missing dimer clusters have been observed on (2×1) Si(001) surfaces: one is elongated along the dimer direction (missing dimer line) and the other along the dimer row direction (missing dimer row). The cohesive energy of missing dimer clusters was calculated as a function of the number, m, of missing dimers in a cluster, using Stillinger–Weber inter-atomic potential. The cohesive energy became positive in the range of m≥2 for missing dimer line (MDL) clusters, while that of missing dimer row (MDR) clusters became positive in the range of m≥3 but exceeded the cohesive energy of MDL clusters. MDL clusters are stabilized by alignment along the dimer direction of rebonded bonds, and the cohesive energy increases linearly with m. MDR clusters are stabilized by formation of alternate rebonded bonds along the dimer row direction, relaxing the strain energy caused by rebonded bonds. The cohesive energy of MDR clusters increases oscillating with m and the cohesive energy of a cluster in a size of 2 n became smaller than that of (2 n−1). The growth of odd-numbered MDR clusters is endothermic but the growth of even-numbered clusters is exothermic.

Formation Process of Empty and Metal-Containing Fullerenes—Molecular Dynamics and FT-ICR Studies

The formation mechanism of empty and metal-containing fullerene was studied through MD (molecular dynamics) simulations and FT-ICR (Fourier transform ion cyclotron resonance) mass spectroscopy of laser vaporized carbon cluster. Multi-body classical potential functions for metal-carbon and metal-metal interactions were constructed based on DFT (density functional theory) calculations of various forms of small clusters MCn and Mn (M = La, Sc, Ni). Using the modified Brenner potential for carbon-carbon interaction, the clustering process starting from 500 isolated carbon atoms and 5 metal atoms in gas phase was simulated under the controlled temperature condition at 3000K. The difference of clustering process of La@Cn, Sc@Cn and NiCn were compared with empty fullerene formation simulation. FT-ICR mass spectrometer directly connected to the laser vaporization cluster beam source was implemented in order to experimentally study the clustering process. The increase of cluster nozzle pressure roughly corresponded to the later stage of the molecular dynamics simulation. The FT-ICR mass spectra of metal-carbon composite clusters were compared for various sample materials used for arc-discharge generation of metal-containing fullerene and SWNT (single-wall carbon nanotube); La, Y., Sc, Gd, Ce, Ca, and Ni-Y. Positive La-C, Y-C, Sc-C, Gd-C, Ce-C binary clusters commonly showed strong MC2n+ signal in the range of 36 < 2n with intense magic numbers at MC44 +, MC50 + and MC60 +. It was speculated that the even-numbered clusters corresponded to the annealed random caged clusters observed in the MD simulation.

Photoelectron spectra of Nbn− clusters: Correlation between electronic structure and hydrogen chemisorption

Photoelectron spectra of mass-separated Nbn− clusters reveal an even/odd alternation for n=6–17, indicating a closed electronic shell of the neutral even-numbered clusters. The HOMO–LUMO gap of Nb8, Nb10, and Nb16 is found to be larger than that of the other even-numbered clusters, which correlates with the low H2 reactivities of these species. The spectrum of Nb15− is different from all other clusters in this size range, which might be an indication for a geometric bcc shell closing. The influence of the electronic structure of the clusters on the reactivity is discussed.

Preferential Association of 7-Azaindole Dimer in Acetonitrile Studied by Mass Spectrometry

Abstract The preferential association of 7-azaindole (Az) dimer was observed by the mass spectrometric analysis of clusters isolated from liquid droplets containing Az and acetonitrile. In the mass spectrum, the peaks corresponding to the even-numbered Az clusters, (Az)2,4,6,8···, were observed much more prominently than those neighboring odd-numbered Az clusters, (Az)3,5,7,9···.

PHOSPHORUS-CLUSTER CATIONS PRODUCED BY LASER ABLATION OF RED PHOSPHORUS

We report the generation of phosphorus-cluster cations containing up to 35 atoms by direct laser ablation of red phosphorus for the first time without supersonic expansion. Bare-cluster cations with an odd nymber of phosphorus atoms are preferentially produced. For even-number phosphorus atom clusters, the cluster cations with an odd number of hydrogens (present in trace amount in the source) are easily produced.

Plasma desorption mass spectrometry in studies of formation and sputtering of fullerenes by MeV atomic ions

An account is presented on plasma desorption mass spectrometry (PDMS) studies of different carbon-containing organic solids utilizing megaelectronvolt (MeV) atomic ions from the Uppsvala EN-tandem accelerator. Positive ions of even-numbered carbon clusters (C + n , n = 40 to > 200) are ejected as a result of the interaction of the fast MeV ions with the target. The distribution of cluster sizes suggests that stable, closed carbon-cage structures — fullerenes - are formed. Among the investigated materials that produce carbon clusters are poly(vinylidenefluoride) and fluorinated fullerenes — C 60F 2 m . For comparison purposes data from C 60 targets have been also collected and analyzed. PDMS has been used for the in situ assessment of the damaging of C 60 films by MeV heavy ions. Results on delayed electron emission from C − 60 sputtered by MeV ions from C 60 fullerene targets are also presented. A model of fullerene formation as a result of MeV ion interactions with the organic solid, including the yield dependence on primary ion charge state, is summarized. Both the data and the model suggest that fullerenes are formed as a result of a single primary ion impact and that they are ejected from an axially expanding infratrack plasma region. Results on different types of coalescence reactions in synthetic C 60 fullerene targets and in blends of pure (synthetic) C 60 with polystyrene leading to ejection of higher mass positive fullerene ions (C + k , k from 60 to more than 200) are also reported. The coalescence reactions are induced by the interaction of a single MeV ion with the solid. We argue that our data contribute to elucidating some general patterns of the fullerene formation mechanism.

Electronic sputtering of fullerenes and the influence of primary ion charge state

Even-numbered positive ion carbon clusters, fullerenes ( C 2 n , n = 20, 21, …), are formed and ejected as a result of the interaction of swift atomic ions with a solid film of organic polymer — poly(vinylidene difluoride), PVDF. Studies of that phenomenon including the dependence of fullerene yield on the incident MeV ion's stopping power and initial radial velocity distributions of ejected ions, have been reported earlier [G. Brinkmalm et al., Chem. Phys. Lett. 191 (1992) 345; Phys. Rev. B 47 (1993) 7560]. In this paper, the dependence of the yield of the ejected cluster ions from PVDF as a function of the charge state of the incident MeV ion is reported. Swift 72.3 MeV 127I ions in charge states ranging from + 13 to + 25 from the Uppsala EN-tandem accelerator are used in the experiments, and the secondary ion yield is measured in a time-of-flight mass spectrometer, equipped with an electrostatic ion mirror. The results are compared to data for secondary ions, ejected by the same primary ions, from samples of synthetic fullerenes (C 60 and C 70). No dependence of the yield on the charge state of the incoming ion is observed for the high mass even-numbered carbon clusters from PVDF, while yields of C 60 and C 70 ions from synthetic fullerene targets show a weak charge state dependence. This finding indicates that excited polymer material from layers deeper than the MeV ion charge equilibration length in the solid contributes to the formation of ejected carbon cluster ions ejected from PVDF.

Formation and Detection of Fullerene Metal Complexes Using Time-Of-Flight Secondary Ion Mass Spectrometry

We have found that metal/fullerene adduct ions of the C60 and C70 fullerenes can be formed with silver, gold, rhodium, and palladium by argon-ion bombardment of fullerenes deposited on a metal substrate, with the use of a Time-of-Flight Secondary Ion Mass Spectrometer (TOF-SIMS). The bis and tris metal/fullerene adducts formed include: Ag(C60)2+, AgC60C70+, Ag(C70)2+, Ag(C60)3+, Ag(C60)2C70+, AgC60(C70)2+, and Rh(C60)2+. In addition, the monomeric adducts AgC60+, AgC70+, AuC60+, AuC70+, RhC60+, RhC70+, and PdC60+ also have been detected. Samples prepared with a raw soot extract gave higher yields of metal/fullerene adducts in TOF-SIMS than those prepared with purified fullerenes. This result may indicate the presence of a matrix component in the raw soot which enhances the formation of fullerene metal adducts. Spectra obtained from the raw soot show peaks at every 24 daltons corresponding to even-numbered carbon clusters. These peaks occur as low as 600 daltons (C50) and as high as 3000 (C250).