Functional [6]pericyclynes: synthesis through [14+4] and [8+10] cyclization strategies

Critical analysis of possible strategies for the synthesis of novel carbo-benzene derivatives suggests several [(18-n)+n] routes for the preparation of hexaoxy[6]pericyclyne precursors. Beyond the previously attempted [9+9] symmetrical scheme (n=9), the a priori most selective strategies are those for which n=1, 4, 7, 10, 13, and 16. They involve a cyclizing double-propargylation of a C(18-n) omega-bis-terminal-skipped oligoyne containing (19-n)/3 triple bonds with a C(n) omega-dicarbonyl-skipped oligoyne containing (n-1)/3 triple bonds. To complement the previously used [11+7] strategy, the [14+4] and [8+10] strategies were thus explored. They proved to be efficient, affording seven novel hexaoxy[6]pericyclynes corresponding to six different substitution patterns. These compounds were obtained in 7-15 steps as mixtures of stereoisomers. Thus, by using dibenzoylacetylene as the C(4) electrophile, a [14+4] strategy allowed the synthesis of two hexaphenyl representatives with two or four free carbinol vertices. This approach also afforded tetraphenyl representatives in which the two remaining carbinoxy vertices were substituted with either two alkynyl or one 4-anisyl and one 4-pyridyl groups. By using the hexacarbonyldicobalt complex of butynedial as the C(4) electrophile, a [14+4] strategy also allowed the isolation of a tetraphenylhexaoxy[6]pericyclyne with two adjacent unsubstituted carbinol vertices. A regioisomer with two opposite unsubstituted carbinol vertices was obtained through an [8+10] strategy and its oxidation afforded the corresponding pericyclynedione. Several attempts at synthesizing diphenylhexaoxy[6]pericyclynes with four unsubstituted carbinoxy vertices are described. Only an [8+10] strategy allowed the generation of a fragile diphenylhexaoxy[6]pericyclyne with four adjacent unsubstituted carbinoxy vertices, which could be partly characterized. These results show that the synthesis of the nonsubstituted hexahydroxy[6]pericyclyne, the ring carbo-mer of [6]cyclitol, is a difficult challenge.     

Flattening of rhodium vertices in mixed rhodium-nickel carbonyl clusters: relationships to borane and zintl ion structures

The flattened deltahedra and related polyhedra found in hypoelectronic bare group 13 metal cluster anions are also found in some anionic mixed rhodium-nickel carbonyl clusters. In all cases the rhodium vertices rather than the nickel vertices are involved in the flattening process so that the rhodium vertices contribute four internal orbitals and the nickel vertices three internal orbitals to the skeletal bonding of the cluster. Thus, the 11-vertex cluster Rh(5)Ni(6)(CO)(21)(3-) has a D(3h) triflattened pentacapped trigonal prismatic structure similar to that found in the In(11)(7-) anion of the intermetallic K(8)In(11). Similarly the polyhedra in the 11-vertex cluster RhNi(10)(CO)(19)(3-) and the 9-vertex cluster Rh(3)Ni(6)(CO)(17)(3-) are both derived from a 10-vertex isocloso polyhedron by capping (for RhNi(10)(CO)(19)(3-)) or vertex removal (for Rh(3)Ni(6)(CO)(17)(3-)) followed by flattening all of the rhodium vertices. A D(3h) icosahedron with flattened rhodium vertices is found in the 12-vertex cluster Rh(3)Ni(9)(CO)(22)(3-).     

Some examples of unusual skeletal bonding topologies in metallaboranes containing two or three early transition metal vertices

The metallaboranes (CpM)(2)B(n)H(n+4) (M = Cr, Mo, W; n = 4, 5; Cp = eta(5)-C(5)H(5), eta(5)-C(5)Me(5)), (CpW)(2)B(7)H(9), (CpRe)(2)B(7)H(7), and (CpW)(3)B(8)H(9) have the 2v or 2v + 2 skeletal electrons for closo or isocloso deltahedra (v = number of polyhedral vertices) if the early transition metal vertices are assumed to contribute four or more internal orbitals rather than the usual three internal orbitals for BH vertices. The polyhedra for the metallaboranes (CpM)(2)B(n)H(n+4) (M = Cr, Mo, W; n = 4, 5) are derived from (n + 1)-gonal bipyramids by removal of an equatorial vertex. The deltahedra for the larger metallaboranes (CpW)(2)B(7)H(9), (CpRe)(2)B(7)H(7), and (CpW)(3)B(8)H(9) are derived from the corresponding B(n)H(n)(2)(-) deltahedra (n = 9 and 11 in these cases) by sufficient diamond-square-diamond processes to provide vertices of degrees > or = 6 for each of the CpM vertices. Reasonable skeletal bonding topologies in accord with the availability of skeletal electrons and orbitals consist of surface 2c-2e and 3c-2e bonds supplemented by metal-metal bonding through the center of the polyhedron.     

A novel six-vertex coordination polyhedron in the crystal structure of the CuBr2 complex of 1,6-bis(benzimidazol-2-yl)-2,5-dioxahexane

A novel polyhedron has been discovered in the coordination geometry of the CuBr₂ complex of 1,6-bis(benzimidazol-2-yl)-2,5-dioxahexane. A rhombus or lozenge- shaped base (BrNBrN) shares its edges with four BrNO triangles and its Br vertices with two BrOO triangles, all six triangles lying on one side of the base. The polyhedron may be derived from an octahedron (with a trans-Br₂, cis-O₂, cis-N₂ arrangement of vertices) by breaking the N ... N edge and bringing the N atoms into coplanarity with the Br atoms.     

Oblate deltahedra in dimetallaboranes: geometry and chemical bonding

A new series of nonspherical and very oblate deltahedra, conveniently called the oblatocloso deltahedra, is found in dimetallaboranes among which the dirhenaboranes Cp2Re2B(n-2)H(n-2) (8 相似文献   

Graph theoretical classification and coding of chemical reactions with a linear mechanism

Linear mechanisms of catalytic and noncatalytic chemical reactions which are theoretically feasible have been classified and coded using a detailed procedure for the unique numbering of cycles, edges, and vertices in the kinetic graphs. The following classification criteria are used in a hierarchical order: number of cycles and vertices, mutual connectivity of the cycles, manner of linking any pair of cycles, number of elements linking two cycles, mutual position of two cycles joined to a third one, orientation of edges, and presence of pendant vertices. All the types and classes of mechanisms are presented for reactions having up to five and four routes, respectively.     

Grid expansion: a rhombiclike [L4Fe2(Ag2)2] complex containing Ag2 dumbbells at two vertices

The pyrazolate-based ditopic ligand HL forms a strongly hydrogen-bonded corner complex dimer [Fe(II)(HL)(2)](2)(BF(4))(4) (1) with a [2 × 2] gridlike arrangement of four ligand strands. The two empty vertices can then be filled with {Ag(2)}(2+) dumbbells, yielding the unprecedented diferric complex [L(4)Fe(III)(2)(Ag(I)(2))(2)](BF(4))(6) (2) that features a rhombiclike structure with an almost planar hexagon of metal ions.     

Non-IPR fullerenes with properly closed shells

Fullerenes with properly closed shells (having exactly half their adjacency eigenvalues strictly positive) are rare. All reported examples obey the isolated-pentagon rule (IPR), usually considered a necessary condition of overall stability, and fall into three series (leapfrogs, carbon cylinders and sporadic closed shells). It is shown here that there also exist fullerenes with properly closed shells that violate the IPR ('super-sporadic' fullerenes). All have negative LUMO eigenvalues of small magnitude. Exhaustive search finds four examples with 160 or fewer vertices: one isomer of C(120), two of C(156) and one of C(160). The first three contain single pentagon pairs and the fourth, a linear triple of fused pentagons. Larger examples can be found. A capping construction gives a series of properly closed shell fullerenes of C(3)/C(3v) symmetry, each with a single fully fused triple of pentagons and ≥632 vertices. Tubular extension of the C(120) example leads a series of C(1)/C(s) isomer pairs with ≥168 vertices, retaining the single pentagon adjacency and approaching isospectrality with increasing size. Both constructions are conjectured to lead to an infinite number of super-sporadic fullerenes.     

Defective vertices in arachno borane networks

Triangulated boron networks can be described in terms of the deviation of their local vertex environments from the degree 5 vertices found in ideal icosahedra. Vertices of degrees other than 5 or equivalent are considered to be defective vertices. This method, which was previously applied to deltahedral borane anions B(n)H(n)(2-) and nido-B(n)H(n+4) boranes, has now been applied to arachno boranes of the types B(n)H(n+6) and B(n)H(n+5)(-) (4 < or = n < or = 10). The known structures of the neutral arachno boranes B(4)H(10), B(8)H(14), and n-B(9)H(15) consist of triangulated boron networks with no defective vertices in accord with their higher stabilities relative to other neutral arachno boranes. In other structures of known arachno boranes, there are relatively small numbers of defective vertices, and these are isolated as far as possible from each other.     

Kolbeckite,ScPO4·2H2O,isomorphous with metavariscite

This study presents the first structural report of kolbeckite, with the ideal formula ScPO₄·2H₂O (scandium phosphate dihydrate), based on single‐crystal X‐ray diffraction data. Kolbeckite belongs to the metavariscite mineral group, in which each PO₄ tetrahedron shares four vertices with four ScO₄(H₂O)₂ octahedra and vice versa, forming a three‐dimensional network of polyhedra.     

Coding and enumeration of trees that can be laid upon a hexagon lattice

A tree that can be superimposed upon a hexagon lattice is called a hexagon lattice tree. A method for mechanically coding, enumerating and drawing these objects is described, and has been tested for trees with up to ten vertices. For storage and information transmission, the code uses an expanded version of theN-tuple code in which edge vector elements having one of four possible values are inserted. For establishing uniqueness, it is used in combination with a hexagon lattice reference grid whose vertices are numbered sequentially in the tightest possible outward spiral. Published rules for the derivation ofN-tuple codes by hand are commented on, and a small error pointed out.     

On ring carbomers of cyclobutane, cyclopentane, and cyclodecane and cyclization reactions through bis(alkynyl-propargyl) coupling

A copper-mediated procedure for terminal alkynyl-propargyl coupling has been applied to "skipped" bis-terminal undecatetrayne and 1,4-bis(pseudo)halobut-2-ynes with the aim of preparing ring carbomers of representative strained and loose cycloalkanes, namely [N]pericyclynes. Two unprecedented, cyclic. "skipped" polyynes with CH2 vertices have been isolated as mixtures of diastereoisomers: an isomer 1b and a dimer 2a of [5]pericyclyne 1a. The isomer 1b is a cyclotetrayne with an exocyclic allene function resulting from a unique formal SN process. Its structure has been established by 1H/13C HMQC and HMBC two-dimensional NMR analysis. According to density functional theory calculations, it is about 6 kcalmol(-1) more stable than [5]pericyclyne (1a). Compound 1b can also be regarded as a C13-relaxed [4]pericyclyne, a long sought "skipped" C12 tetrayne. The dimer 2a is a C30 ring that results from a formal SN process. It is a stable ring carbomer of cyclodecane, that is, a [10]pericyclyne, with four CH2 vertices.     

New vertex invariants and topological indices of chemical graphs based on information on distances

By applying information theory to the set of topological distances from one vertex to all other graph vertices, one obtains four new types of vertex invariants (u _i,v _i,x _i,Y _i) which are real numbers (as opposed to integers). They may be combined in many ways to afford new topological indices. One such type leads to indicesU, V, X andY which show no degeneracy for alkanes with up to 15 vertices.     

Nonbonding orbitals in fullerenes: nuts and cores in singular polyhedral graphs

A zero eigenvalue in the spectrum of the adjacency matrix of the graph representing an unsaturated carbon framework indicates the presence of a nonbonding pi orbital (NBO). A graph with at least one zero in the spectrum is singular; nonzero entries in the corresponding zero-eigenvalue eigenvector(s) (kernel eigenvectors) identify the core vertices. A nut graph has a single zero in its adjacency spectrum with a corresponding eigenvector for which all vertices lie in the core. Balanced and uniform trivalent (cubic) nut graphs are defined in terms of (-2, +1, +1) patterns of eigenvector entries around all vertices. In balanced nut graphs all vertices have such a pattern up to a scale factor; uniform nut graphs are balanced with scale factor one for every vertex. Nut graphs are rare among small fullerenes (41 of the 10 190 782 fullerene isomers on up to 120 vertices) but common among the small trivalent polyhedra (62 043 of the 398 383 nonbipartite polyhedra on up to 24 vertices). Two constructions are described, one that is conjectured to yield an infinite series of uniform nut fullerenes, and another that is conjectured to yield an infinite series of cubic polyhedral nut graphs. All hypothetical nut fullerenes found so far have some pentagon adjacencies: it is proved that all uniform nut fullerenes must have such adjacencies and that the NBO is totally symmetric in all balanced nut fullerenes. A single electron placed in the NBO of a uniform nut fullerene gives a spin density distribution with the smallest possible (4:1) ratio between most and least populated sites for an NBO. It is observed that, in all nut-fullerene graphs found so far, occupation of the NBO would require the fullerene to carry at least 3 negative charges, whereas in most carbon cages based on small nut cubic polyhedra, the NBO would be the highest occupied molecular orbital (HOMO) for the uncharged system.     

Functional [6]pericyclynes: aromatization to substituted carbo-benzenes

Reductive treatment of stereoisomeric mixtures of variously substituted hexaoxy[6]pericyclynes with SnCl(2)/HCl led to the corresponding substituted carbo-benzenes. Tetramethoxyhexaphenyl[6]pericylynediol and dimethoxyhexaphenyl[6]pericyclynetetrol thus proved to be alternative precursors of hexaphenyl-carbo-benzene, previously described. Another hexaaryl-carbo-benzenic chromophore with 4-pyridyl and 4-anisyl substituents was targeted for its second-order nonlinear optical properties and was obtained by aromatization of a dimethoxy[6]pericyclynetetrol. Two alkynyl substituents in para positions were also found to be compatible with the C(18) carbo-benzene ring, provided that the four remaining vertices are substituted by phenyl groups. In the protected series, bis(trimethylsilylethynyl)hexaphenyl-carbo-benzene (C(18)Ph(4)(C triple bond C-TMS)(2)) could be isolated and fully characterized, even by X-ray crystallography. In the bis-terminal series, the diethynylhexaphenyl-carbo-benzene C(18)Ph(4)(C triple bond C-H)(2) could not be isolated in the pure form. It could, however, be generated by two different methods and identified by the corresponding (1)H NMR spectra. Unsubstituted carbo-benzene C(18)H(6) remains unknown, but tetraphenyl-carbo-benzenes C(18)Ph(4)H(2) with two unsubstituted vertices proved to be viable molecules. Whereas the "para" isomer could be characterized by MS and (1)H and (13)C NMR spectroscopy only in a mixture with polymeric materials, the "ortho" isomer (with adjacent CH vertices) could be isolated, and its structure was determined by using X-ray crystallography. The structure calculated at the B3PW91/6-31G** level of theory turned out to be in excellent agreement with the experimental structure. The (1)H and (13)C NMR chemical shifts of hexa- and tetraphenyl-carbo-benzenes were also calculated at the B3LYP/6-31+G** level of theory and were found to correlate with experimental spectra. The remote NMR deshielding of peripheral protons (through up to five bonds) revealed a very strong diatropic circulation around the C(18) ring, regardless of the substitution pattern. In full agreement with theoretical investigations, it has been demonstrated experimentally that the carbo-benzene ring is "independently" aromatic, in accord with structural-energetic and -magnetic criteria.     

Menisci in a Diamond-Shaped Capillary

This paper presents a closed form analytical solution to the augmented Young-Laplace equation for the meniscus profile in a capillary formed between four equal-sized tangent cylinders centered on the vertices of a square. The solution is valid for a large class of disjoining pressure isotherms and contact angles.     

Common vertex matrix: A novel characterization of molecular graphs by counting

We present a novel matrix representation of graphs based on the count of equal‐distance common vertices to each pair of vertices in a graph. The element (i, j) of this matrix is defined as the number of vertices at the same distance from vertices (i, j). As illustrated on smaller alkanes, these novel matrices are very sensitive to molecular branching and the distribution of vertices in a graph. In particular, we show that ordered row sums of these novel matrices can facilitate solving graph isomorphism for acyclic graphs. This has been illustrated on all undecane isomers C₁₁H₂₄ having the same path counts (total of 25 molecules), on pair of graphs on 18 vertices having the same distance degree sequences (Slater's graphs), as well as two graphs on 21 vertices having identical several topological indices derived from information on distances between vertices. © 2013 Wiley Periodicals, Inc.