Number Of Structural Isomers Research Articles

SinC13-n (n = 1 – 12) Clusters: An All-electron DFT Investigation

The geometrical and electronic structures of SinC13-n (n = 1 – 12) nanoclusters have been investigated using all-electron density functional theory (DFT) with the generalized gradient approximation (GGA). The binding energies, highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps, and the vibrational frequencies have been computed. We note that the binary clusters have a number of isomeric structures with lower symmetries and the stability of the clusters increases as the number of carbon atoms increases. As the number of silicon atoms increases, the lowest-energy structures of the SinC13-n (n = 1 – 12) clusters transform from planar structures to three-dimensional structures. The HOMO-LUMO gaps of the lowest-energy structures indicate that with the exception of Si6C7 and Si12C, the ground states are of high chemical stability and have the characteristics of semiconductors. In addition, the Mulliken populations show that there is significant charge transfer from the silicon atoms to the carbon atoms.

Solvated Electrons in Clusters: Magic Numbers for the Photoelectron Anisotropy.

This paper reports on a curiosity concerning magic numbers in neutral molecular clusters, namely on magic numbers related to the photoelectron anisotropy in angle-resolved photoelectron spectra. With a combination of density functional calculations and experiment, we search for magic numbers in Na(H2O)n, Na(NH3)n, Na(CH3OH)n, and Na(CH3OCH3)n clusters. In clusters of high symmetry, the highest occupied molecular orbital can be delocalized over an extended region, forming a symmetric charge distribution of high s character, which results in a pronounced anisotropy in the photoelectron angular distribution. We find magic numbers at n = 6 and 4 for sodium-doped dimethyl ether and ammonia clusters, respectively, but not for sodium-doped water and methanol clusters, which is likely a consequence of the degree of hydrogen bonding and the number of structural isomers.

Statistical Investigation of the Mean Size Distribution of AB2/B f Type Hyperbranched Polymer

A statistical method was applied to investigate the number of isomeric structures of hyperbranched polymers formed by the polymerization of an AB 2 type moiety with Bf polyfunctional core moieties (abbreviation as AB2/B f type). By means of the kinetic model described by a Smoluchowski-like coagulation equation, the explicit expressions of z-average mean-square radii of gyration are evaluated as a function of the conversion of functional groups. The numerical calculation shows that the mean size of the AB 2/B f type hyperbranched polymers will increase with the increase of the conversion of A groups or the reaction time, furthermore increasing sharply at the end of the reaction. When the reaction is quantitatively completed, the z-average mean-square radii of gyration of AB 2/B f type hyperbranched polymers show a maximum. The results are similar to those for star branched polymers, rather than those of hyperbranched polymers made by the ABf type monomers without cores; the former had finite values and the latter reached infinite values when the reaction was quantitatively completed. These theoretical analysis conclusions will be important for effectively controlling the mean sizes or the average degrees of hyperbranched polymers by varying the number of the Bf type polyfunctional core moieties in experimental research.

Density-functional investigation of 3d, 4d, 5d impurity doped Au6 clusters

The general features of the geometries and electronic properties for 3d, 4d, and 5d transition-metal atom doped Au6 clusters are systematically investigated by using relativistic all-electron density functional theory in the generalized gradient approximation (GGA). A number of structural isomers are considered to search the lowest-energy structures of M@Au6 clusters (M = 3d, 4d and 5d transition-metal atoms), and the transition metal atom locating in the centre of an Au6 ring is found to be in the ground state for all the M@Au6 clusters. All doped clusters, expect for PdAAu6, show large relative binding energies compared with a pure Au7 cluster, indicating that doping by 3d, 4d, 5d transition-metal atoms could stabilize the Au6 ring and promote the formation of a new binary alloy cluster.

Structural growth sequences and electronic properties of manganese-doped germanium clusters:MnGen (2–15)

The structural growth sequences and electronic properties ofMnGen (n = 2–15) clusters have been investigated using density functional theory (DFT)within the generalized gradient approximation (GGA). An extensive searchof the lowest-energy structures was conducted by considering a number ofstructural isomers for each cluster size. In the ground-state structures ofMnGen clusters, the equilibrium site of the Mn atom gradually moves from the convex, surface to interiorsites as the Ge cluster size varies from 2 to 15. The threshold size for the formation of cagedMnGen and the sealedMn-encapsulated Gen structure is n = 9 and n = 10, respectively. Maximum peaks were observed forMnGen clustersat n = 3, 6, 10, 12 and 14 with the size dependent on the second-order energy difference, implying thatthese clusters are relatively more stable. The electronic structures and magnetic properties ofMnGen inthe ground-state structures are discussed. The doped Mn atom makes the HOMO–LUMO gap of theGen clusters smaller, due to hybridization between the p states of theGe atom and the d states of the Mn atom. Most of the Mn-dopedGen clusters carry a magnetic moment of about1.0 μB, exceptthat MnGe6 andMnGe11 have a magneticmoment of about 3.0 μB. Charge transfer between Mn and Ge was also observed.

Structural transition of hexagonal tube to rocksalt for (MgO)3n, 2≤n≤10

The structures of (MgO)(3n) (2<or=n<or=10) clusters are studied using density functional theory (DFT). The starting structures are generated from empirical genetic algorithm simulations. The lowest-energy structures of (MgO)(3n) are then obtained from a number of structural isomers by using DFT optimization. It is found that when n<or=5 hexagonal tube is the most stable structure, and when n>or=6 (except 7) the rocksaltlike structure is favored, which is the same as that of the bulk. The n=7 is an interesting case, where the structure again is the hexagonal tube as the most stable structure. However, from the second order difference of the average atomization energy, we find that the n=7 case is thermodynamically unstable with respect to disproportionation to the smaller and larger clusters. The result may be the reason that it is not observed in the experiment. Therefore, we can conclude that the geometry transition really takes place at n=6. The rocksalt is the most stable structure for a large range of n numbers, from the (MgO)(3x6) cluster to bulk magnesium oxide. The result is different from Wilson's previous prediction because of the use of the ionic potential.

Lowest-energy structures and photoelectron spectra of In nP n ( n = 1–12) clusters from density functional theory

Lowest-energy structures of In n P n ( n = 1–12) clusters have been determined from a number of structural isomers using all-electron density functional calculations. The In–P alternating hollow cage-like structures emerge at n = 7. Size-dependent cluster properties such as binding energy, HOMO–LUMO gaps, electron affinities, and photoelectron spectra have been computed and discussed. The simulated electron affinities and photoelectron spectra agree reasonably with experiments. With exceptionally low electron affinity and large HOMO–LUMO gap, In 3P 3 was identified as a magic-numbered cluster of relatively higher stability, in agreement with experimental observations.

Structural and electronic properties of Bin (n = 2-14) clusters from density-functional calculations

The structural and electronic properties of Bi n (n = 2-14) clusters have been systematically studied using gradient-corrected density-functional theory. For each cluster size, a number of structural isomers were constructed and optimized to search for the lowest-energy structure. The competition of several structural patterns such as cages, superclusters, and layered structures leads to the alternating appearance of these configurations as global minima. Although the tendency of Bi to form puckered-layer structures is already well-known, the electronic states of Bi n clusters are still far from that of the bulk. As well, a remarkable even-odd atom number oscillation is observed in the structural and electronic properties of the clusters, implying that the stability of Bi n clusters is mainly dominated by the electron shell effect rather than by geometrical packing. The theoretically calculated values for electron affinities agree well with available experimental data.

Structure and magnetic properties of cobalt doped () clusters

The structure and magnetic properties of cobalt doped Sin (n=2–14) clusters have been systematically studied using density functional theory (DFT). For each cluster size, extensive search of the lowest-energy structure has been conducted by considering a number of structural isomers. The equilibrium site of the Co atom in the ground-state structures of SinCo clusters gradually moves from convex, surface, to interior sites as the number of Si atom increases from 2 to 14. Starting from Si10Co, Co atom is fully encapsulated by the Si outer cages. The magnetic moment of Co atom in SinCo clusters is completely quenched at n=7, due to charge transfer and strong hybridization between 4s and 3d states of Co and 3s and 3p states of Si.

Structural Growth Sequences and Electronic Properties of Zinc Oxide Clusters (ZnO)n (n=2-18)

The structural and electronic properties of (ZnO)n (n = 2−18) clusters are studied using gradient-corrected density-functional theory (DFT). The starting structures are generated from empirical genetic algorithm simulations or handmade constructions with chemical intuition. The lowest-energy structures of (ZnO)n are then selected from a number of structural isomers via DFT optimization. For small clusters (n = 2−7), ring structures were found to be the most stable. Three-dimensional cage and tube structures become energetically preferable for larger clusters (n = 9−18), and the competition between cage and tube structures leads to the alternative appearance of these two types of structures as global minima. The size evolution of electronic properties for zinc oxide clusters from ring toward cage or tube is discussed.

Structure and electronic properties of medium-sized Ga nN n clusters ( n = 4–12)

The lowest-energy structures were obtained for Ga n N n clusters ( n = 4–12) using gradient-corrected density functional theory. For each cluster size, a number of structural isomers were constructed and optimized. Crossover from ring to cage-like structures were found at Ga 8N 8. The observed cage-like configurations consisting of six-membered rings with gallium–nitrogen alternative arrangement can be viewed as embryo of wurtzite structure of gallium nitride crystal. The size-dependence of cluster properties such as binding energy, HOMO–LUMO gaps, ionization potentials, electron affinities, and Mulliken charges have been computed and analyzed. The bonding characteristics of the Ga n N n clusters were discussed.

Atomic structures and covalent-to-metallic transition of lead clustersPbn(n=2–22)

The lowest-energy structures and electronic properties of the lead clusters are studied by density-functional-theory calculations with Becke-Lee-Yang-Parr gradient correction. The lowest-energy structures of ${\mathrm{Pb}}_{n}\phantom{\rule{0.3em}{0ex}}(n=2\text{--}22)$ clusters are determined from a number of structural isomers, which are generated from empirical genetic algorithm simulations. The competition between atom-centered compact structures and layered stacking structures leads to the alternative appearance of the two types of structures as global minimum. The size evolution of geometric and electronic properties from covalent bonding towards bulk metallic behavior in Pb clusters is discussed.

Density-functional study of structures and electronic properties of Cd clusters

The lowest-energy structures and electronic properties of cadmium clusters are studied by density-functional theory with the generalized gradient approximation. The equilibrium structures of ${\mathrm{Cd}}_{n}$ $(n=2--21)$ clusters are determined from a number of structural isomers, which are generated from genetic algorithm simulations with a tight-binding potential. Various close-packed structures are found for cadmium clusters. ${\mathrm{Cd}}_{n}$ clusters with $n=4,9,10,15,17,20$ show relatively high stability, which can be related to the electron shell model, and agrees with experimental results. The density of states for the magic number clusters can also be associated with the electronic shell. The theoretical ionization potentials of ${\mathrm{Cd}}_{n}$ compare well with experimental values. The size evolution of electronic properties from van der Waals to covalent and bulk metallic behavior in Cd clusters is discussed.

The formation of heterogeneous van der Waals complexes in helium droplets

The formation of the heterogeneous van der Waals complexes of tetracene with two and three argon atoms in helium droplets have been studied using the pick up technique. The laser-induced fluorescence spectra were measured with embedding of the chromophore tetracene molecule prior to the argon atoms and vice versa. The results indicate that once the Ar n complex is formed within the helium droplet it remains intact upon subsequent attachment of the tetracene molecule. This observation suggests a strategy of formation and study of larger hetero complexes where the possible number of structural isomers can be considerably reduced.

Ab initio Study of the Structure of the Molecular Forms of C3H4O2

The geometrical parameters, force fields, and vibration frequencies were calculated by the ab initio SCF MO LCAO technique using extensive basis sets of Cartesian Gaussian functions for a number of structural isomers of the C3H4O2 molecule. The relative energies of all the isomers were refined in terms of second-order Moller–Plesset (MP2) perturbation theory including electron correlation. For the most energetically favorable forms of the C3H4O2 molecule, geometry optimization was fulfilled in the MP2 approximation. For the main conformer, β-hydroxypropenal, possessing a chelate OCCCO fragment, the data are compared with the experimental and theoretical data available in the literature. The MP2 calculated internuclear distances and bond angles are in good agreement with the experimental values. For each form of the C3H4O2 molecule, the geometrical and electronic structure is analyzed. It is shown that the presence of an intramolecular hydrogen bond is the characteristic feature of the structure of the isomers and an additional stabilizing factor.

Infrared photofragmentation spectra of size-selected Krn+SF6 cluster ions

Presented here are the results of an experimental study of the infrared photofragmentation patterns of size-selected Krn+SF6 cluster ions for n in the range 2⩽n⩽50. The ν3 (T1u) vibrational mode of the SF6 molecule in each cluster ion has been excited using a line-tunable CO2 infrared laser, and the subsequent fragmentation patterns were monitored for the loss of one and two krypton atoms and also for the loss of the SF6 chromophore. For ions containing more than four krypton atoms, the dominant fragmentation process observed was the loss of a single krypton atom, with the loss of SF6 being the least intense of the fragmentation channels for most clusters. For one ion, Kr3+SF6, significantly different behaviour was observed with the loss of SF6 being the dominant fragmentation route, which suggests a stable Kr3+ trimer. Fragmentation intensities were monitored as a function of laser wavelength in order to determine infrared absorption profiles for individual Krn+SF6 cluster ions. The observation of site-symmetry splittings of the triply degenerate ν3 mode and the relatively narrow linewidths suggest the presence of asymmetric, but ordered, structures. With only a maximum of three absorption features apparent for clusters consisting of less than thirty five krypton atoms, the number of structural isomers appears to be small. Comparisons are made with results previously obtained for the Arn+SF6 series of cluster ions (J. Chem. Phys., 1995, 103, 5177), and differences in spectra are attributed to the sensitivity of the SF6 molecule to its environment. Additional interpretation comes from comparisons with computer simulation studies on neutral clusters with the compositions ArnSF6 and KrnSF6 (J. Chem. Phys., 1991, 95, 6271). The appearance of SF6 loss as a minor fragmentation channel for clusters in the region of K12+SF6 is interpreted in terms of stacked structures.

Orthogonal Ru II(bpy) 3 complexes in meso-substituted porphyrins

The synthesis and characterization of mono- and bis- meso-substituted porphyrins, where the substituents are bipyridine (bpy) groups are described. Treatment of these new porphyrins with an excess of cis-RuCl 2(bpy) 2 gives rise to their respective mono- and bis-Ru II(bpy) 3 complexes. These ruthenium porphyrin complexes all exist as a number of structural isomers and this is reflected in both the proton and carbon NMR spectra. The cyclic voltammetry of these redox active systems was examined and is reported herein. The cyclic voltammetry for the ruthenium porphyrins is complex, with the usual two oxidation and two reduction waves of porphyrins mixing with the three reduction waves of the porphyrin bound Ru II(bpy) 3 and the single oxidation wave seen for the Ru II/Ru III couple. In the case of the mono-ruthenium porphyrin, this complex redox chemistry results in the presence of a reversible two-electron reduction, along with the other redox processes. The bis-ruthenium porphyrin has an even more complex redox chemistry. However, the first ligand-based reduction wave in both the mono- and bis-substituted complexes, occur at more negative potentials than those in, simple free, Ru II(bpy) 3.

Identification by gas chromatography-mass spectrometry of vinyl chloride oligomers and other low-molecular-weight components in poly(vinyl chloride) resins for food packaging applications

Material of molecular weight less than approximately 400–500 was isolated from food grade poly(vinyl chloride) resins by initial soxhlet diethyl ether extraction and subsequent size-exclusion fractionation. Analysis by packed-column gas chromatography using Hall electrolytic conductivity detection showed the presence of a series of chlorinated components which by subsequent gas chromatography-mass spectrometry were tentatively identified as vinyl chloride oligomers. The chlorinated constituents in the extracts were selectively isolated from other low-molecular-weight components by silica gel chromatography. From low-resolution capillary gas chromatography-mass spectrometry data (together with evidence from hydrogenated extracts) the structures of these oligomers were postulated as being a complete series ranging from trimer to hexamer (and probably to the octamer), each oligomer being represented by species containing a ring or a double bond and each occurring as a number of structural isomers. Other non-chlorinated compounds identified in the resins included mixed phthalates, alkanes, nonylphenol, and undecyl dodecanoate, the latter being derived from the polymerisation initiator lauryl peroxide.

Number of structural isomers in the adamantane series

Number of structural isomers in the adamantane series

On the Number of Structural Isomers in Simple Ring Compounds. II.

On the Number of Structural Isomers in Simple Ring Compounds. II.