Clusters C1 Research Articles

Photocurrent responsive properties of a series of charge-transfer materials with nano-sized CdS/Se clusters and ruthenium complex dyes

Large cadmium chalcogenido clusters C2 (Cd32) and C1 (Cd17) CdQ (Q = S, Se) with photoactive dye cations [Ru(Phen/Bpy)3]2+ are prepared under solvothermal conditions (Phen = 1,10-phenanthroline, Bpy = 2,2′-bipyridine). All the C2 compounds are 3-D polymeric structures, while the C1 compounds are discrete Cd17 clusters. Two of the 3-D C2 clusters can be considered as homosized nano CdSe@CdS core–shell particles (2.0 nm radius) with Cd4Se10 core. Charge-transfer interaction is found between [Ru(Phen/Bpy)3]2+ cations and CdQ cluster anions. The photocurrent behaviors indicate that (1) the current intensities are greatly increased for the dye cation functionalized Cn clusters, (2) the current intensities of the 3-D C2 clusters are larger than those of the discrete C1 clusters, and (3) the current intensities of the selenide clusters are larger than those of the sulfide clusters.

Ultraperformance Liquid Chromatography Tandem Mass Spectrometry Determination of Cyanogenic Glucosides in Trifolium Species

Cyanogenic glucosides were analyzed by ultra-high-performance liquid chromatography combined with mass spectrometry in 88 Trifolium species grown at the same site. On the basis of the occurrence of cyanogenic glucosides and the linamarin/lotaustralin ratio species could be grouped into five clusters. Cluster C1 included 37 species, which did not contain cyanogens. Cluster C2 (22 species) included plants containing only lotaustralin. In clusters C3 (14 species), C4 (13 species), and C5 (2 species) both linamarin and lotaustralin were present but at different ratios. In C3 and C4 the linamarin/lotaustralin ratio was below 1, whereas in cluster C5 the ratio was much higher. Generally, the total content of cyanogens was below 500 μg/g dry matter. Only in Trifolium repens var. biasoletti and Trifolium montanum extremely high cyanogen concentrations were observed. There was no general rule of occurrence of cyanogens. Samples of the same species from different countries accumulated cyanogens or could be free of these compounds.

Screen-based media use clusters are related to other activity behaviours and health indicators in adolescents

BackgroundScreen-based media (SBM) occupy a considerable portion of young peoples’ discretionary leisure time. The aim of this paper was to investigate whether distinct clusters of SBM use exist, and if so, to examine the relationship of any identified clusters with other activity/sedentary behaviours and physical and mental health indicators.MethodsThe data for this study come from 643 adolescents, aged 14 years, who were participating in the longitudinal Western Australian Pregnancy Cohort (Raine) Study through May 2003 to June 2006. Time spent on SBM, phone use and reading was assessed using the Multimedia Activity Recall for Children and Adults. Height, weight, muscle strength were measured at a clinic visit and the adolescents also completed questionnaires on their physical activity and psychosocial health. Latent class analysis (LCA) was used to analyse groupings of SBM use.ResultsThree clusters of SBM use were found; C1 ‘instrumental computer users’ (high email use, general computer use), C2 ‘multi-modal e-gamers’ (both high console and computer game use) and C3 ‘computer e-gamers’ (high computer game use only). Television viewing was moderately high amongst all the clusters. C2 males took fewer steps than their male peers in C1 and C3 (-13,787/week, 95% CI: -4619 to -22957, p = 0.003 and -14,806, 95% CI: -5,306 to -24,305, p = 0.002) and recorded less MVPA than the C1 males (-3.5 h, 95% CI: -1.0 to -5.9, p = 0.005). There was no difference in activity levels between females in clusters C1 and C3.ConclusionSBM use by adolescents did cluster and these clusters related differently to activity/sedentary behaviours and both physical and psychosocial health indicators. It is clear that SBM use is not a single construct and future research needs to take consideration of this if it intends to understand the impact SBM has on health.

An ultralow-energy negative cluster ion beam system and its application in preparation of few-layer graphene

We developed a cluster ion beam system that produces negative cluster beams of C1–C10 with ion current of 4.5 nA-50 μA at extraction voltages ranging from 6 to 20 kV. The system uses the injector of a tandetron accelerator and was established by inserting an electrostatic scanner on its ion-optical line and modifying its Faraday cup into a substrate holder. Utilization of clusters enables ultrashallow ion implantation at energies as low as 600 eV/atom without deceleration. Small carbon clusters C2 and C4 were implanted into Ni/SiO2/Si substrates and following post-thermal treatment graphene was obtained. Raman spectroscopy showed characteristic 2D peaks with G-to-2D peak ratios revealing formation of 2–3 layers of graphene. The Raman data reveals clear effect of nonlinear cluster-surface interaction in ion beam synthesis of two-dimensional nanomaterials.

On the diameter of partition polytopes and vertex-disjoint cycle cover

We study the combinatorial diameter of partition polytopes, a special class of transportation polytopes. They are associated to partitions of a set X = {x1, . . . , xn} of items into clusters C1, . . . , Ck of prescribed sizes κ1 ≥ · · · ≥ κk. We derive upper bounds on the diameter in the form of κ1 + κ2, n − κ1 and \({\lfloor \frac{n}{2} \rfloor}\). This is a direct generalization of the diameter-2 result for the Birkhoff polytope. The bounds are established using a constructive, graph-theoretical approach where we show that special sets of vertices in graphs that decompose into cycles can be covered by a set of vertex-disjoint cycles. Further, we give exact diameters for partition polytopes with k = 2 or k = 3 and prove that, for all k ≥ 4 and all κ1, κ2, there are cluster sizes κ3, . . . , κk such that the diameter of the corresponding partition polytope is at least \({\lceil \frac{4}{3} \kappa_2 \rceil}\). Finally, we provide an \({O(n(\kappa_1 + \kappa_2(\sqrt{k} - 1)))}\) algorithm for an edge-walk connecting two given vertices of a partition polytope that also adheres to our diameter bounds.

The combined effect of ultraviolet B radiation and temperature increase on phytoplankton dynamics and cell cycle using pulse shape recording flow cytometry

Temperature and ultraviolet radiation B (UVB) are expected to increase in the next few decades and will mostly affect mid and high latitudes. In order to study the combined effect of temperature and UVB increase, on the phytoplankton community in the Saint Lawrence Estuary, duplicates of four different treatments were applied to 2 m 3 mesocosms to simulate an overall 3 °C and a 77.8% UVB increase, and combined. Samples were collected every 6 h over 10 days and the phytoplankton community was then analysed using a conventional flow cytometer and a Cytosense flow cytometer. Flow cytometry distinguished 9 clusters (Pico, Nano I, C3, C4, CHAINS, C6, C7 and C8) of cells sharing similar optical properties with average sizes varying from 1.3 μm up to 101 μm for chain forming cells. Compared to untreated enclosures, the high UVB treatment induced lower cell abundances (up to − 40%) for clusters Pico, Nano I, C4, CHAINS and C7, followed by an unexpected cell abundance increase in all the clusters during the last 3 days of the experiment (up to 46%). This increase was sustained by faster calculated periodicities of the cell optical characteristics and abundances, linked to a shorter cell cycle. In the samples from the high temperature treatment mesocosms, a positive delay was observed for the cell abundance increase in clusters CHAINS, C6 and C8, combined with higher average abundance values (up to 67% with respect to untreated mesocosms). During the last 3 days of the experiment, abundances decreased compared to the values observed in the high UVB mesocosms, with a slower trend in the periodicities, suggesting that high temperature inhibits the cell cycle. The combined temperature and UVB treatment emphasized the effects observed under high temperature treatments, maintaining temperature positive effects ( i.e. higher abundances) on clusters C3, CHAINS, C6 and C8 suggesting a compensation from the positive temperature effects over the negative ( i.e. lower abundances) UVB effects. Increasing temperature induced a negative effect on the abundance of clusters C4 and C7. In this case, trends in C6 and C8 cell periodicities were faster than under normal conditions while Nano I, C4 and C7 cycles were slower. Cells < 3 μm were negatively affected by the combined exposure (up to − 55% compared to untreated mesocosms) while most of the larger cells were positively affected (up to 75% compared to untreated mesocosms), suggesting a shift to an herbivorous food web ( sensu Legendre and Rassoulzadegan, 1995). Results suggest that changes in cell cycles due to increases in temperature or UVB exposure may play an important role in controlling abundance.

Density functional theory study on (LiNH2)n (n = 1–5) clusters

Geometrical structures and relative stabilities of (LiNH(2))(n) (n = 1-5) clusters were studied using density functional theory (DFT) at the B3LYP/6-31G* and B3LYP/6-31++G* levels. The electronic structures, vibrational properties, N-H bond dissociation energies (BDE), thermodynamic properties, bond properties and ionization potentials were analyzed for the most stable isomers. The calculated results show that the Li-N and Li-Li bonds can be formed more easily than those of the Li-H or N-H bonds in the clusters, in which NH(2) is bound to the framework of Li atomic clusters with fused rings. The average binding energies for each LiNH(2) unit increase gradually from 142 kJ mol(-1) up to about 180 kJ mol(-1) with increasing n. Natural bond orbital (NBO) analysis suggests that the bonds between Li and NH(2) are of strong ionicity. Three-center-two-electron Li-N-Li bonding exists in the (LiNH(2))(2) dimer. The N-H BDE values indicate that the change in N-H BDE values from the monomer a1 to the singlet-state clusters is small. The N-H bonds in singlet state clusters are stable, while the N-H bonds in triplet clusters dissociate easily. A study of their thermodynamic properties suggests that monomer a1 forms clusters (b1, c1, d2 and e1) easily at low temperature, and clusters with fewer numbers of rings tend to transfer to ones with more rings at low temperature. E(g), E(HOMO) and E(av) decrease gradually, and become constant. Ring-like (LiNH(2))(3,4) clusters possess higher ionization energy (VIE) and E(g), but lower values of E(HOMO). Ring-like (LiNH(2))(3,4) clusters are more stable than other types. A comparison of structures and spectra between clusters and crystal showed that the NH(2) moiety in clusters has a structure and spectral features similar to those of the crystal.

Integrative genomic analyses of neurofibromatosis tumours identify SOX9 as a biomarker and survival gene

Understanding the biological pathways critical for common neurofibromatosis type 1 (NF1) peripheral nerve tumours is essential, as there is a lack of tumour biomarkers, prognostic factors and therapeutics. We used gene expression profiling to define transcriptional changes between primary normal Schwann cells (n = 10), NF1-derived primary benign neurofibroma Schwann cells (NFSCs) (n = 22), malignant peripheral nerve sheath tumour (MPNST) cell lines (n = 13), benign neurofibromas (NF) (n = 26) and MPNST (n = 6). Dermal and plexiform NFs were indistinguishable. A prominent theme in the analysis was aberrant differentiation. NFs repressed gene programs normally active in Schwann cell precursors and immature Schwann cells. MPNST signatures strongly differed; genes up-regulated in sarcomas were significantly enriched for genes activated in neural crest cells. We validated the differential expression of 82 genes including the neural crest transcription factor SOX9 and SOX9 predicted targets. SOX9 immunoreactivity was robust in NF and MPSNT tissue sections and targeting SOX9 – strongly expressed in NF1-related tumours – caused MPNST cell death. SOX9 is a biomarker of NF and MPNST, and possibly a therapeutic target in NF1.

Multivariate statistical analysis of geochemical data as indicative of the hydrogeochemical evolution of groundwater in a sedimentary rock aquifer system

Summary The study of groundwater hydrogeochemistry of the Paleozoic Basses-Laurentides sedimentary rock aquifer system in Quebec produced a large geochemical dataset. Groundwater samples were collected at 153 sites over a 1500 km2 study area and analyzed for major and minor ions. The large number of data can lead to difficulties in the integration, interpretation and representation of the results. Two multivariate statistical methods, hierarchical cluster analysis (HCA) and principal components analysis (PCA), were applied to a subgroup of the dataset to evaluate their usefulness to classify the groundwater samples, and to identify geochemical processes controlling groundwater geochemistry. This subgroup consisted of 144 samples and 14 parameters (Ca2+, Mg2+, Na+, K+, HCO 3 - , Cl−, SO 4 2 - , Fe2+, Mn2+, Br−, Sr2+, F−, Ba2+, HS−). Seven geochemically distinct clusters, C1–C7, resulted from the HCA. Samples from clusters C3, C4, C6 and C7 are mostly located in preferential recharge areas. The majority of these samples have Ca–Mg–HCO3 recharge groundwater (C3, C6, C7) and Na–HCO3 evolved groundwater (C4). Samples from the other three clusters (C1, C2, C5) are characteristic of an aquifer system under confined conditions. The majority of these samples have Na–HCO3 evolved groundwater (C1, C5) and Na–Cl ancient groundwater that exhibits elevated concentrations in Br− (C2). In addition to recognizing the importance of hydrogeological conditions on groundwater geochemistry, the distribution of clusters also showed the importance of the geological formations on minor and trace elements, such as Fe2+, Mn2+, Sr2+, F− and Ba2+. The first five components of the PCA account for 78.3% of the total variance in the dataset. Component 1 is defined by highly positive loadings in Na+, Cl− and Br− and is related to groundwater mixing with Champlain Sea water and solute diffusion from the marine clay aquitard. The high positive loadings in Ca2+ and Mg2+ of component 2 suggest the importance of dissolution of carbonate rocks in this aquifer system. From their characteristic loadings, the first two components are defined as the “salinity” and “hardness” components, respectively. Components 3–5 are related to more local and geological effects. The integration of the HCA and the PCA, with conventional classification of groundwater types, as well as with the hydrogeological and geological contexts, allowed the division of the region into four main geochemical areas, providing an improved regional picture of the aquifer system dynamics and hydrogeochemical evolution of groundwater. The following factors were recognized as influencing the evolution of groundwater identified in every geochemical area: (1) geological characteristics including sedimentary rock type and till mineralogy; (2) hydrogeological characteristics represented by the level of confinement and the hydraulic gradient; and (3) the geological history including the latest glaciation and the Champlain Sea invasion. With its integrated approach, this hydrogeochemical study contributes to the characterization and understanding of complex groundwater flow systems, and provides an example of the long-term geochemical evolution of hydrogeological systems after a major perturbation, in this case seawater invasion.

Extent and Pattern of Genetic Diversity for Morpho-agronomic Traits in Ethiopian Highland Pulse Landraces: I. Field Pea (Pisum sativum L.)

An experiment was conducted in 2001 at Holetta and Kulumsa, Ethiopia, to study the extent and pattern of genetic diversity in Ethiopian field pea (Pisum sativum L.) landraces. One hundred forty-eight germplasm accessions were grown in an alpha lattice design with 2 replications. Data on 12 traits were collected and analyzed. Differences among the accessions were significant for most of the traits (except number of seeds/ pod) at each location even though differences pooled over location were mostly non-significant. The accessions were grouped into five clusters of different sizes. Accessions from the southern part of the country (Arsi) distributed overall clusters while those from the northern half (North and South Wello, North Gonder and North Shewa) fell into clusters C1 to C3. Cumulative effects of a number of characters dictated differentiation of the accessions into clusters. There was no definite relationship between geographic diversity and genetic diversity as overlapping was encountered in clustering pattern among accessions from different parts of the country. Accessions from different regions might have similar genetic background and those from the same origin might also have different genetic background. Therefore, geographic diversity should not necessarily be used as an index of genetic diversity and parental selection should be based on a systematic study of genetic diversity in a specific population. Genetic distances among most of the clusters were significant that crosses between parents selected out of them are expected to generate desirable genetic recombination. Selection should also consider the special advantages of each cluster and each accession within a cluster. Future germplasm collection, conservation and breeding efforts should focus not only on inter-regional diversity but also on intra-regional diversity.

Density-functional calculations of the structures, binding energies, and spin multiplicities of Fe–C clusters

We report ab initio calculations of the structures, binding energies and spin multiplicities of the clusters Fe2, C2, FeCn (n=1–4) and Fe2Cn (n=1–3) using a density-functional method that employs linear combinations of atomic orbitals as basis sets, nonlocal norm-conserving pseudopotentials, and the generalized gradient approximation for exchange and correlation. Our results for the pure dimers and the monometallic carbide clusters are in good general agreement with those obtained in previous theoretical studies and with available experimental data. All the dimetallic carbide clusters are predicted to have cyclic planar geometries that are stabilized (except, of course, in Fe2C) by transannular bonds. In particular, the pentagonal geometry of Fe2C3, with transannular Fe–Fe and Fe–C bonds and an FeC2 unit that is almost identical to free FeC2, parallels that of Ti2C3. However, this Fe2C3 structure is almost isoenergetic with another in which the C atoms aggregate to form a quasilinear C3 substructure, as in Co2C3. This is consistent with the position of Fe in the 3d metal series, intermediate between met-car formers (Ti, V, Cr) and nonformers (Co, Ni), and with the fact that mass spectra show Fe8C12 not to be significantly more stable than FemCn clusters of several other stoichiometries.

Insulin resistance syndrome revisited: application of self-organizing maps.

Most common chronic diseases have a multifaceted aetiological background. Because currently used statistical methods have severe limitations in describing complex non-linear processes, the authors evaluated the usefulness of a multivariate method which is able to describe non-linear phenomena, the self-organizing map (SOM). The study subjects were the 1650 participants of the Kuopio Ischemic Heart Disease Risk Factor Study (KIHD). The SOM model was constructed using 25 continuous biochemical and physiological variables. The aim of the SOM algorithm, together with Sammon's mapping, is to group the data into reduced but representative format and divide the study population into homogeneous subgroups. The study population consisted of four groups (clusters) according to the method used. In the clusters C1 to C4 were 637, 445, 275 and 121 men, respectively. There were eight neurons (n = 172) which were not included to the four main clusters. The mean values of the variables related to insulin resistance syndrome in the identified SOM map were 32.1 (kg/m(2)) for body mass index (BMI), 1.01 for waist-to-hip ratio (WHR), 158.7 mmHg and 103.8 mmHg for systolic (SBP) and diastolic blood pressure (DBP), 2.8 mmol/l for triglycerides, 6.2 mmol/l for blood glucose and 22.4 mU/l for serum insulin. There was a statistically significant difference in the mean values of BMI, WHR, SBP, DBP, HDL, triglycerides and blood glucose between the cluster representing the insulin resistance syndrome and the normal cluster. This study shows that the multidimensional structures of insulin resistance syndrome can be visualized and identified at qualitative and quantitative level using the SOM algorithm.

Theoretical study of the vertical electron excitation of linear carbon clusters C3, C5, and C7

AbstractThe vertical electron excitation spectra of linear carbon clusters C3, C5, and C7 have been investigated by means of polarization propagator calculations using the second‐order algebraic diagrammatic construction [ADC(2)] scheme. The structure of singlet and triplet excited‐state manifolds below the lowest ionization threshold has been analyzed in detail for the smallest prototype cluster C3. The electronic spectra of all three molecules contain numerous low‐lying single and double valence excitations, reflecting strongly the correlated nature in these clusters. The density of the excited states becomes increasingly high above the onset of Rydberg excitations. A substantial mixing of various valence and Rydberg configurations in this region does not allow for simple interpretation of the final electronic states. The spectroscopic and photophysical implications of this complex situation are discussed. Where possible the computed excitation energies and oscillator strength are compared with available experimental and previous theoretical data. © 2001 John Wiley &amp; Sons, Inc. Int J Quantum Chem, 2001

Analysis of genomic diversity within the Xr-region of the protein A gene in clinical isolates of Staphylococcus aureus.

Protein A of Staphylococcus aureus contains a polymorphic Xr-region characterized by a tandem repeat of eight amino acid units. In this study, the diversity of genes encoding the repeat regions and their relatedness among S. aureus strains was analyzed. Ten different protein-A types characterized by repeat numbers 4-13 were identified in a total of 293 clinical isolates. The protein-A type with 10 repeat units (10 repeats) in the Xr-region was most frequently detected in methicillin-resistant S. aureus, whereas the majority of methicillin-susceptible strains were distributed almost evenly into protein-A types with 7-11 repeats. Strains that belonged to a single coagulase type were classified into multiple protein-A types, e.g. strains with the common coagulase types II and VII were differentiated into 7 and 8 protein-A types, respectively. Nucleotide sequence analysis of the Xr-region of 42 representative strains revealed the presence of 37 different genotypes (spa types), which were constituted by a combination of several of 24 different repeat unit genotypes. Based on the similarity in arrangement of repeat unit genotypes, 34 strains with different repeat numbers were classified into 5 genetic clusters (C1-C5). The clusters C1, C2 and C3 consisted exclusively of strains with identical coagulase types II, III, and IV, respectively. These findings suggested that the protein-A gene of S. aureus has evolved from a common ancestral clone in individual clusters independently.

Structure and Vibrations of Small Carbon Clusters from Coupled-Cluster Calculations

The vibrational spectrum of the linear carbon clusters C2−C9 and of cyclic C4, C6, C8, and C10 has been investigated using the augmented coupled-cluster, CCSD(T), method and correlation-consistent basis sets. Particular emphasis is placed on assignment of bands in matrix infrared spectra of trapped graphite vapor. The relative energetics of linear and cyclic isomers of C6, C8, and C10 were investigated at the CCSD(T) level using basis sets of [4s3p2d1f] quality. Our best calculations predict that the ground state structure of C6 is a cumulenic D3h ring and that of C8 a polyacetylenic C4h ring. Linear states are close in energy (13 ± 2 and 8 ± 2 kcal/mol, respectively), and both forms should be observable. The ground state structure of cyclic C10 clearly has D5h rather than D10h symmetry, at least for the re geometry. A linear regression of computed CCSD(T)/[3s2p1d] harmonic frequencies vs observed fundamentals for the previously assigned stretching frequencies of linear Cn clusters has a very high correla...

Antigenic Relationships among Oral Actinomyces Isolates, Actinomyces naeslundii genospecies 1 and 2, Actinomyces howellii, Actinomyces denticolens, and Actinomyces slackii

Antigenic relatedness among human strains of oral Actinomyces and similar isolates from cattle has been analyzed by agglutination and immunoblotting. Whole cell agglutination placed A. viscosus serotype II, A. naeslundii serotypes II and III, Actinomyces NV, and strains from numerical taxomonic clusters C1, C2, C3, C4, and C6 into a single group. A. viscosus serotype I cross-reacted weakly with this group. A naeslundii serotype I strains and the cattle isolates Actinomyces denticolens and Actinomyces howellii were distinct. The agglutination results for A. slackii were equivocal. Immunoblots of cell wall extracts developed with non-absorbed sera showed cross-reactivity (23% to 90% antigenic similarity) among all of the strains tested, including A. israelii. The range of antigenic similarities among the group which included strains of A. viscosus serotype II, the A. naeslundii serotypes, and clusters C1, C2, C3, C4, and C6 was from 39% to 89%. Immunoblotting showed that A. howellii and A. denticolens were between 39% and 72% similar to A. naeslundii and A. viscosus. Absorption of antisera with A. israelii cell walls removed antibodies recognizing antigens common to Actinomyces and made the sera more specific. Immunoblotting with absorbed sera supported the grouping and separation of strains shown by agglutination. In some cases, serotypes could be included into a specific taxonomic cluster. A. naeslundii serotype II and Actinomyces NV most closely resembled cluster C1 strains, and A. naeslundii serotype III resembled cluster C1 strains, and A. naeslundii serotype I and A. viscosus serotype I were included into clusters C5 and C7, respectively. The results support a recent proposal that strains of A. viscosus serotype II, A. naeslundii serotypes II and III, and Actinomyces NV be included into A. naeslundii genospecies 2, that A. naeslundii serotype I should be designated A. naeslundii genospecies 1, and that A. viscosus serotype I should be retained distinct from A. naeslundii, as A. viscosus.

Reaction of small carbon clusters with hydrogen during laser vaporization of graphite

The hydrogen uptake for small carbon clusters C4 to C22 has been studied at high hydrogen pressure. This study indicate that both chain and ring structures exist in parallel.

A critical comparison of MINDO/3, MNDO, AM1, and PM3 for a model problem: Carbon clusters C2‐C10. An ad hoc reparametrization of MNDO well suited for the accurate prediction of their spectroscopic constants

AbstractDissociation energies and potential energy surface features for the carbon clusters C2 to C10 are compared with ab initio or experimental results for the semiempirical methods MINDO/3, MNDO, AM1, and PM3. Quite surprisingly, MINDO/3 gives a rather good account of the various structures and electronic states, unlike the other three methods. MINDO/3 tends towards systematic overestimates of binding energies, the other methods to systematic gross underestimates. Reparametrization of the diatomic parameters α, βs, and βp for exact reproduction of the experimental data for C3 results in much improved values for binding energies, but fails to correct the state splittings. Also reparametrizing Uss, Upp, ζs, and ζp to reproduce the ab initio linear‐rhombic energy difference in C4 results in a much improved description of the other states. For the linear structures, computed harmonic frequencies with the latter parameters are in surprisingly good agreement with experimental or correlated ab initio data, where available; experimental values are consistently overestimated by about 40 cm−1. Other results are comparable in quality to good ab initio treatments. The experimental IR bands at 2128 and 1892 cm−1, formerly assigned to C9, should be reassigned to linear C7. The intense 1997 cm−1 feature almost certainly belongs to C9; bands at 1952 and 1197 cm−1 both belong to linear C6. Tentative assignments of bands in the 1600–1850 cm−1 region to various cyclic structures of C6, C8, and C10 have been made. As such, this suggests a new and promising procedure for the theoretical study of large molecules in general, and of large clusters in particular.

Cluster calculations using muffin-tin orbitals

The linear combination of muffin-tin orbitals (LMTO) method, developed by Andersen (see Phys. Rev. B, vol.12, p.3060 (1975)) and applied previously to the electronic properties of bulk materials, has been used to calculate energy eigenvalues and charge distributions for small clusters of atoms. For a muffin-tin potential (spherically symmetrical within touching spheres surrounding the atoms, constant between them), the method reproduces accurately the results of multiple-scattering (KKR) calculations. The LMTO method has, however, several marked advantages: (1) computational times are much less; (2) false roots of the secular matrix do not occur; (3) improved convergence of eigenfunctions and energies can readily be obtained. These points are examined in detail for the clusters C2, Al5Na and Al5O.