Odd-numbered Clusters Research Articles

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.

FT-ICR Studies of Laser Desorbed Carbon Clusters.

Atomic and molecular clusters are being recognized as playing an important role in the thin-film deposition process and phase-change phenomena. Furthermore, small clusters are the most adequate system for the verification of quantum molecular dynamics calculations such as the interference of light and matter. Hence, experimental treatments of such atomic and molecular clusters are now desired. In order to examine such clusters, we have implemented a Fourier transform ion cyclotron resonance (FT-ICR) spectrometer directly connected to a laser-vaporization supersonicexpansion cluster beam source. The heart of the FT-ICR spectrometer was made of ICR cell cylinder centered in a strong homogeneous magnetic field of a 6 Tesla superconducting magnet. The atomic cluster beam was generated outside of magnetic field by the laser vaporization of a solid sample disk, followed by cooling with supersonic expansion of pulsed helium gas. The ionized cluster was carried by helium gas and directly injected to the magnetic field. By measuring the ion-cyclotron frequency, which was inversely proportional to the ion mass, a very highresolution mass spectrum can be obtained. The high mass-resolution was demonstrated for positive mass spectra of silicon, carbon, and metal-carbon binary clusters and negative mass spectra of metal-carbon binary clusters. For bare carbon positive clusters, we found the special condition where the odd-numbered clusters were observed in the range of C30 to C50 and the continuous change to C60-dominant condition and 'normal' even-numbered distribution. An example of mass spectrum measured by the directinjection FT-ICR apparatus is shown in Figure A-1. Here, a graphite sample with about 1 % of Sc, which is the typical composition used for macroscopic metal-containing fullerene, was vaporized by the 2nd harmonics of Nd: YAG laser and the positive clusters were trapped and analyzed by the FT-ICR spectrometer. If we ignore the metal-composite clusters, the distribution of bare carbon clusters was almost the same as typical pure carbon clusters. One the other hand, almost all of Sc-carbon composite clusters had only one Sc atom and even number of carbon atoms: ScC2n in the range of 76 2

An analytical solution of isotopomeric enumerations for C2v cyclic odd-numbered carbon clusters Cn

The current experimental and computational research in carbon clusters pointed out a need for enumeration of all possible12C/13C isotopoments of the C2v cyclic odd-numbered carbon clusters Cn. It is shown that the number of the isotopomers is given by 2k−1(2k−1+1) withk=(n+1)/2. Some illustrative computed structure and energy data for the clusters are reported, too.

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···.

DELAYED IONIZATION OF FULLERENES AND FULLERENE DERIVATIVES UPON LASER DESORPTION AND SURFACE COLLISION

Delayed electron emission has been observed upon laser desorption for several fullerenes, endohedral metallofullerenes, and large carbon clusters formed by coalescence reactions. Odd-numbered carbon clusters and fullerene derivatives with exohedral functional groups do not show delayed ionization under similar conditions, presumably due to lower dissociation energies. Thus, delayed electron emission is suggested to be a characteristic indicator for strongly bound fullerene structures. Measurements of the rate of delayed electron emission are used together with structural information from other sources to calculate ionization potentials for these species. Selective observation of delayed electron emission from scattered [Formula: see text] after surface impact and neutralization of [Formula: see text] on graphite confirms an earlier report of this process by Whetten et al.6

On the vibrational spectrum of C 9, C 11 and C 13

The harmonic frequencies and infrared intensities of C 9, C 11 and C 13 have been calculated using SCF and complete active space SCF (CASSCF) methods. The ordering of the harmonic frequencies in C 9 is predicted wrongly unless at least the π HOMO and LUMO are included in the active space. Infrared intensities depend crucially on the size of the active space. For linear odd-numbered clusters C 13 and larger, the computed SCF spectrum is qualitatively wrong. The recent observation of a band near 1809 cm −1 in the gas phase is explained using our CASSCF results on C 13.

Accurate ab initio total atomization energies of the Cn clusters (n=2–10)

The total atomization energies of the carbon clusters Cn (n=2–10) have been calculated ab initio using augmented coupled-cluster methods and basis sets of spdf and spdfg quality. The values agree to within experimental uncertainty with recent Knudsen effusion measurements for Cn (n=2–7), but suggest actual values on the high side of their experimental range. For the odd-numbered clusters, an additivity approximation holds very well, and extrapolated ∑D0 values are proposed for C11, C13, C15, C17, and C19.

Molecular orbital study of pyrolytic carbons based on small cluster models

Molecular orbital calculations are applied to the Raman scattering and ESR of pyrolytic carbons on the basis of small cluster models. The E 2 g and A 1 g modes of C-C stretching vibrations of coronene, hexabenzocoronene, and circumcoronene, which belong to D 6 h carbon clusters, are shown to appear around the 1550 cm −1 and 1360 cm −1 bands, respectively. The unpaired electrons observed in pyrolytic carbons are attributed to the bond-alternation defects on odd-numbered carbon clusters that are more easily mobile than those of trans-polyacetylene.

Large Odd-Numbered Carbon Clusters from Fullerene-Ozone Reactions

The odd-numbered carbon clusters C(119), C(129), and C(139) have been observed in the mass spectra of toluene extracts of fullerene soots and of the products of ozone-fullerene reactions. Specifically, ozone-C(60) reactions yield C(119), ozone-C(70) reactions yield C(139), and ozone-(C(60)/C(70)) reactions produce C(119), C(129), and C(139). These unexpected species correspond to dimers of C(60), C(60)/C(70), and C(70), respectively, less one carbon atom, and are stable gas-phase ions with behavior similar to that of fullerenes. The results suggest a new route to functionalization and derivatization of fullerenes through controlled ozone-catalyzed cage-opening reactions.

Direct infrared and visible absorption spectroscopy of stoichiometric and nonstoichiometric clusters of indium phosphide

Resonant two-color and one-color photodissociation spectroscopy is performed on neutral InxPy clusters with x+y=5 to 14 atoms. Absorption spectra of 29 different InxPy clusters are obtained for excitation energies between 0.84 and 1.84 eV. The absorption behavior is qualitatively similar for all of these clusters. An optical-gap-like absorption feature is observed at the blue end of the spectra, particularly for clusters which contain an even number of atoms. This feature shifts as a function of cluster size, but has an onset close to the band gap of bulk crystalline InP. Weaker absorptions are observed tailing to the red. A distinct absorption peak is also observed near the bulk InP band band gap for odd-numbered clusters with a stoichiometry of Inx+3Px. An empirical fitting of the low energy absorption tails reveals a correlation between the optical behaviors of these tiny clusters and amorphous semiconductors.

Ab initio MRD-CI study of GaAs -, GaAs 2(±), Ga 2As 2(±) and As 4 clusters

Using pseudopotentials and double zeta basis sets with s, p diffuse functions and two sets of d functions, MRD-CI calculations were performed on As 2 (±), As 4 (+), GaAs −, GaAs 2 (±) and Ga 2As 2 (±). This study complements previous theoretical investigations on Ga (±) to Ga 4 (±) and GaAs (+). For As 4 tetrahedral symmetry was assumed, and Re of X 1A 1 determined as 4.73 a 0. Vertical ionization potentials to several states of As 4 + were calculated. For GaAs 2, GaAs 2 + and GaAs 2 −, ground and one low-lying state were geometry-optimized, both in C 2v (Ga-As-As), and linear symmetry (GaAsAs, C ∞h and AsGaAs, D ∞h). The lowest state of GaAs 2 is 2B 2 in C 2v. For Ga 2As 2, the lowest state and low-lying excited states were optimized in various geometries. The most stable state has rhombic structure ( 1A g in D 2h), but T-form and other forms (C 2v, C ∞v, D ∞h) are only 1–2 eV less stable. In D 2h symmetry, several low-lying excited states of Ga 2As 2 were studied. The ground states of Ga 2As 2 + and Ga 2As 2 − were found to be 2B 2u, and 2B 2g, respectively. Trends in ionization potentials (IP), electron affinities (EA), atomization energies and fragmentation energies for the molecules Ga x As y and the pure compounds Ga n and As n up to 4 atoms, were studied. Ga x As y clusters, with x + y even, have higher IP's than odd-numbered clusters. An experimentally observed alternation of EA, whereby an odd number of atoms have higher EA than their even neighbors, is confirmed. The mixed compounds Ga x As y have atomization energies between those of Ga n and As n ( x + y = n), usually closer to those of Ga n . Fragmentation of Ga x As y occurs such that As-As bonds are retained, and if possible, also Ga-As bonds, since the dissociation energy of As 2 is higher than that of GaAs, which in turn is higher than that of Ga 2. Calculated fragmentation energies agree qualitatively with experimental observations about the composition of 3-atomic and 4-atomic clusters Ga x As y .

Laser photoionization and spectroscopy of gas phase silver clusters

Silver clusters containing up to 40–50 atoms are produced by laser vaporization in a pulsed-nozzle molecular beam source and studied with laser photoionization mass spectroscopy. A variety of Nd:YAG pumped dye laser and UV excimer laser wavelengths are used to achieve ionization. Ionization dynamics are studied by varying the laser wavelength and fluence. Bracketing experiments under single-photon ionization conditions are used to estimate ionization potentials as a function of cluster size. An even-odd ionization potential alternation is observed with odd-numbered clusters (N=3, 5, 7 ...) having lower ionization potentials than adjacent even-numbered species. Shell closings at clusters containing 2, 8 20 and 40 electrons are observed consistent with a one-electron shell model picture of cluster electronic structure. Resonance-enhanced ionization produces a vibrationally resolved spectrum for the trimer, Ag3, yielding an electronic state assignment and excited state vibrational frequencies. Fragmentation in dimer ionization via theE state at 249 nm establishes the dissociation energy of Ag2+ to be <2.1 eV.

Ground-state energy of Heisenberg antiferromagnet for spins s=(1/2 and s=1 in d=1 and 2 dimensions.

A simple real-space renormalization method yields the ground-state energy of the Heisenberg antiferromagnet. We find the ground-state energy per spin for $s=\frac{1}{2}$ (-0.4438 in 1D, -0.6723 in 2D) and $s=1$ (-1.388 in 1D and -1.907 in 2D) to three-figure accuracy, using properties of relatively small odd-numbered clusters. Our results provide reasonable proof for long-range order in the ground state of the $s=\frac{1}{2}$ Heisenberg antiferromagnet in 2D.

Structure, stability, and fragmentation of small carbon clusters

Accurate ab initio calculations are performed to study the structures and energies of small carbon clusters (Cn, n=2–10). The effects of polarization functions and electron correlation are included in these calculations. Significant odd–even alternation is found in the nature of the cluster geometries with the odd-numbered clusters having linear structures and many of the even-numbered clusters preferring cyclic structures. Energetically, odd-numbered clusters (up to C7) are found to be more stable than the adjacent even-numbered clusters. Ionization potentials are calculated and used in conjunction with the cluster energies to explain the fragmentation behavior of small carbon cluster ions.

Supersonic copper clusters

Copper clusters ranging in size from 1 to 29 atoms have been prepared in a supersonic beam by laser vaporization of a rotating copper target rod within the throat of a pulsed supersonic nozzle using helium for the carrier gas. The clusters were cooled extensively in the supersonic expansion [T(translational) 1 to 4 K, T(rotational)=4 K, T(vibrational)=20 to 70 K]. These clusters were detected in the supersonic beam by laser photoionization with time-of-flight mass analysis. Using a number of fixed frequency outputs of an exciplex laser, the threshold behavior of the photoionization cross section was monitored as a function of cluster size. The 7.9 eV photon energy of the F2 excimer laser was found to be above the ionization potential of all clusters, and the photoion mass spectrum thus produced showed the copper cluster concentration in the beam to follow a monotonically decreasing function of cluster size. The 6.4 eV ArF exciplex laser photon energy was found to be above the photoionization threshold of clusters with three or more atoms in the case of odd-numbered clusters, but only for clusters with eight or more atoms for even-numbered clusters. Extending out to clusters as large as 29 atoms, laser photoionization at 6.4 eV produced a time-of-flight mass distribution with a pronounced even/odd alternation in cluster photoion intensity. This alternation in ionization threshold behavior was attributed to an even/odd alternation in the electronic structure of the copper clusters with the highest occupied molecular orbital (HOMO) of the even clusters being considerably more strongly bonding than it is in the clusters with an odd number of copper atoms. The 4.98 eV photon energy of the KrF exciplex laser was found to lie below the ionization threshold of all clusters in the 1 to 29 atom range. An extensive survey of the ultraviolet absorption spectrum of the copper dimer was also performed with this supersonic beam source. Resonance two-photon ionization (R2PI) with mass selective detection allowed the detection of five new electronic band systems in the region between 2690 and 3200 Å, for each of the three naturally occurring isotopic forms of Cu2. In the process of scanning the R2PI spectrum of these new electronic states, the ionization potential of the copper dimer was determined to be 7.894±0.015 eV.

Odd and even numbered hydrogen ion clusters

Since the suggestion that hydrogen ion clusters of the type H+n may be present in gaseous nebulae1,2 and interstellar space3,4 and the early experiments of Clampitt and Gowland5, who discovered such clusters for 3≤n (odd) ≤99 in low temperature (3K) mass spectrometer experiments, it has sometimes been assumed that only odd-numbered clusters exist (ref. 6, and refs therein). There have been extensive studies in the past decade on the binding energy and the geometry of these ion-induced-dipole clusters. Massa et al.7 have carried out ab initio calculations on H+n, for odd values of n ranging from 3 to 15. Weak binding energies of the order of 44meV against dissociation according to H+n→H+n−2+H2 5 ≤ n (odd) ≤ 15 were found. The geometrical shape of these clusters was calculated to be dominated by a triangular nucleating centre H+3 with the relatively high proton binding energy of 4 eV. Salmon and Poshusta8 have conducted polarised-orbital valence-bond calculations on the ground state properties of H+5. Most recently, the molecular structure of H+3 has been experimentally determined by means of the beam-foil technique9. We describe here an ion-trap experiment in which we studied collisional processes of electrons with hydrogenic trapped ions of mass numbers, 1, 2, 3, 5, 7, 10, 14, and 20. Since these are the only ions observed, up to a mass limit of 40 AMU, there are serious implications for the assumption by some theoretical chemists that H+n; exists only for odd values of n.