Investigation into the molecular structure and energetic stability of endohedral and exohedral metallofullerene derivatives of C24

Density-functional theory was applied to the investigation of the structural and electronic properties of C₂₄ fullerene derivatives. Transition metals (TMs) from groups 11 and 12, in various oxidation and spin-states, are inserted at either endohedral (TM@C₂₄) or exohedral (TM-C₂₄) sites and their subsequent energetic stabilities are assessed. With the exception of Ag@C₂₄, all derivatives are predicted to occupy a minimum on the potential energy surface. The optimized exohedral TM-C₂₄ geometries yield TM-C bond lengths that are consistent with comparable carbon-metal bond lengths, and the overwhelming majority of the derivatives result in a slight deformation of the C₂₄ cage as the bonding carbon takes on more sp³ character. All of the TM@C₂₄ equilibrium structures maintain the integrity of the cage structure with a moderate increase in the diameter. All neutral exohedral and endohedral complexes favor the low spin-state; conversely, all of the charged exohedral complexes prefer the high spin-state, with the exception of Cu-C₂₄¹⁺ molecular ion. The Group 12 charged endohedral derivatives prefer the low spin-state, whereas the Group 11 molecular ions do not necessarily exhibit a definitive trend. Analysis of the energetic data predicts that of the lowest energy endohedral molecular species only four are predicted to be energetically favorable in terms of insertion energy and an advantageous HOMO-LUMO gap: Cu@C₂₄²⁺, Ag@C₂₄¹⁺, Au@C₂₄³⁺, and Zn@C₂₄²⁺.     

嵌入La和Gd原子的Si24笼团簇的稳定性

用梯度修正自旋极化密度泛函(DFT)电子结构计算,研究了具有T_h和D_2d对称性包裹La和Gd原子的Si₂₄富勒烯的稳定性.结果表明Gd@Si₂₄具有很高的磁性而La@Si₂₄的磁性完全猝灭.这些结果有可能导致Si基富勒烯团簇新的结构类型. 关键词： 24和Gd@Si₂₄包裹团簇')" href="#">La@Si₂₄和Gd@Si₂₄包裹团簇 自旋极化密度泛函 稳定性 电磁性质     

Essential oil extraction,chemical analysis and anti-Candida activity of Foeniculum vulgare Miller – new approaches

A comprehensive study on essential oil samples of Foeniculum vulgare Miller from Tarquinia (Italy) is reported. A 24-h systematic steam distillation was performed on different harvested samples applying different extraction times. The GC-MS analysis of the residue outcome showed o-cymene, α-phellandrene, α-pinene and estragole as the major constituents. The predominance and continued presence of o-cymene makes this fennel oil a rather unique chemotype. An evident correlation between the antifungal activity and phenological stage is demonstrated. The most active fractions were particularly rich in estragole, as well as a significant amount of fenchone that possibly exerts some additive effect in the expression of overall antifungal potency. Pre-fruiting material produced oil particularly rich in o-cymene. With reference to the duration of the extraction, the maximum amount of oil was released within the first 3 h, whereas the reproductive phase material needed at least 6 h for the extraction.     

Wrapping polygons in polygons

This paper is developed toI ₂(2g).c-geometries, namely, point-line-plane structures where planes are generalized 2g-gons with exactly two lines on every point and any two intersecting lines belong to a unique plane.I ₂(2g).c-geometries appear in several contexts, sometimes in connection with sporadic simple groups. Many of them are homomorphic images of truncations of geometries belonging to Coxeter diagrams. TheI ₂(2g).c-geometries obtained in this way may be regarded as the standard ones. We characterize them in this paper. For everyI ₂(2g).c-geometry , we define a numberw(), which counts the number of times we need to walk around a 2g-gon contained in a plane of , building up a wall of planes around it, before closing the wall. We prove thatw()=1 if and only if is standard and we apply that result to a number of special cases.     

X-ray structure of 14-phenyldiquino[3,4 b;4′,3′-e][1,4]thiazine<Superscript>(1)</Superscript>

The title compound 1 (C₂₄H₁₅N₃S) crystallizes in an orthorhombic unit cell, with a = 8.2355(3), b = 19.1499(8), and c = 11.3520(5) Å, Z = 2, and space group Pnma. The pentacyclic ring system is folded mainly along the S–N(2) axis and slightly along the C(3)–C(4) and C(3′)–C(4′) axes. The butterfly folding angle between the two quinoline planes is 48.96(3)^∘ and the angle between the planes of the two halves of the thiazine ring is 43.46(7)^∘. The central thiazine ring is in a boat conformation. The phenyl substituent is unexpectedly in an axial location with respect to the thiazine ring with the C–N⋅ < eqid1 > ⋅S angle of 114.0(1)^∘ and it is perpendicular to the bisecting plane of the pentacyclic ring system.     

Removable edges in a 5-connected graph and a construction method of 5-connected graphs

An edge e of a k-connected graph G is said to be a removable edge if G?e is still k-connected. A k-connected graph G is said to be a quasi (k+1)-connected if G has no nontrivial k-separator. The existence of removable edges of 3-connected and 4-connected graphs and some properties of quasi k-connected graphs have been investigated [D.A. Holton, B. Jackson, A. Saito, N.C. Wormale, Removable edges in 3-connected graphs, J. Graph Theory 14(4) (1990) 465-473; H. Jiang, J. Su, Minimum degree of minimally quasi (k+1)-connected graphs, J. Math. Study 35 (2002) 187-193; T. Politof, A. Satyanarayana, Minors of quasi 4-connected graphs, Discrete Math. 126 (1994) 245-256; T. Politof, A. Satyanarayana, The structure of quasi 4-connected graphs, Discrete Math. 161 (1996) 217-228; J. Su, The number of removable edges in 3-connected graphs, J. Combin. Theory Ser. B 75(1) (1999) 74-87; J. Yin, Removable edges and constructions of 4-connected graphs, J. Systems Sci. Math. Sci. 19(4) (1999) 434-438]. In this paper, we first investigate the relation between quasi connectivity and removable edges. Based on the relation, the existence of removable edges in k-connected graphs (k?5) is investigated. It is proved that a 5-connected graph has no removable edge if and only if it is isomorphic to K₆. For a k-connected graph G such that end vertices of any edge of G have at most k-3 common adjacent vertices, it is also proved that G has a removable edge. Consequently, a recursive construction method of 5-connected graphs is established, that is, any 5-connected graph can be obtained from K₆ by a number of θ⁺-operations. We conjecture that, if k is even, a k-connected graph G without removable edge is isomorphic to either K_k+1 or the graph H_k/2+1 obtained from K_k+2 by removing k/2+1 disjoint edges, and, if k is odd, G is isomorphic to K_k+1.     

Path bundles on n-cubes

A path bundle is a set of 2^a paths in an n-cube, denoted Q_n, such that every path has the same length, the paths partition the vertices of Q_n, the endpoints of the paths induce two subcubes of Q_n, and the endpoints of each path are complements. This paper shows that a path bundle exists if and only if n>0 is odd and 0?a?n-⌈log₂(n+1)⌉.     

Polynomials satisfied by two linked matrices

Polynomials in two variables, evaluated at A and with A being a square complex matrix and being its transform belonging to the set {A⁼, A^†, A^∗}, in which A⁼, A^†, and A^∗ denote, respectively, any reflexive generalized inverse, the Moore-Penrose inverse, and the conjugate transpose of A, are considered. An essential role, in characterizing when such polynomials are satisfied by two matrices linked as above, is played by the condition that the column space of A is the column space of . The results given unify a number of prior, isolated results.     

Scattering in a Forked-Shaped Waveguide

We consider wave scattering in a forked-shaped waveguide which consists of two finite and one half-infinite intervals having one common vertex. We describe the spectrum of the direct scattering problem and introduce an analogue of the Jost function. In case of the potential which is identically equal to zero on the half-infinite interval, the problem is reduced to a problem of the Regge type. For this case, using Hermite-Biehler classes, we give sharp results on the asymptotic behavior of resonances, that is, the corresponding eigenvalues of the Regge-type problem. For the inverse problem, we obtain sufficient conditions for a function to be the S-function of the scattering problem on the forked-shaped graph with zero potential on the half-infinite edge, and present an algorithm that allows to recover potentials on the finite edges from the corresponding Jost function. It is shown that the solution of the inverse problem is not unique. Some related general results in the spectral theory of operator pencils are also given. This work was supported by the grant UM1-2567-OD-03 from the Civil Research and Development Foundation (CRDF). YL was partially supported by the NSF grants 0338743, 0354339 and 0754705, by the Research Board and Research Council of the University of Missouri, and by the EU Marie Curie “Transfer of Knowledge” program.     

Two new dammarane-type triterpene sapogenins from Chinese red ginseng

Two new dammarane-type triterpene sapogenins were isolated from the Chinese red ginseng. The new sapogenins were named as 24,26-dihydroxy-panaxdiol (1) and 24-hydroxy-panaxdiol (2). Their structures were elucidated by the combined analysis of NMR and mass spectrometry as 20(S),25(R)-epoxydammarane-3β,12β,24β,26-tetraol (1) and 20(S),25-epoxydammarane-3β,12β,24α-triol (2). The complete signal assignments of the two compounds were carried out by 2D NMR spectral and NOE differential spectroscopy analysis.