Study on the normalized Laplacian of a penta-graphene with applications

Let L _n denote a linear pentagonal chain with 2n pentagons. The penta-graphene (penta-C), denoted by R _n is the graph obtained from L _n by identifying the opposite lateral edges in an ordered way, whereas the pentagonal Möbius ring is the graph obtained from the L _n by identifying the opposite lateral edges in a reversed way. In this paper, through the decomposition theorem of the normalized Laplacian characteristic polynomial and the relationship between its roots and the coefficients, an explicit closed-form formula of the multiplicative degree-Kirchhoff index (resp. Kemeny's constant, the number of spanning trees) of R _n is obtained. Furthermore, it is interesting to see that the multiplicative degree-Kirchhoff index of R _n is approximately of its Gutman index. Based on our obtained results, all the corresponding results are obtained for .     

On the number of spanning trees and normalized Laplacian of linear octagonal-quadrilateral networks

The normalized Laplacian makes a great contribution on analyzing the structure properties of nonregular graphs. Let O_n be a linear octagonal-quadrilateral network. In this article, we first concern the normalized Laplacian spectrum of O_n based on the decomposition theorem for the corresponding matrices. Then we derive the closed-term formulas of the degree-Kirchhoff index and the number of spanning trees of linear octagonal-quadrilateral networks on the basis of the relations between the roots and coefficients, respectively.     

Synthesis,Crystal Structure,and Luminescence of Metal Iodide Cluster Compounds (nBu4N)2[M6I8(NCO)6] with M = Mo,W

Molybdenum and tungsten iodide clusters with the [M₆I₈] cluster core show versatile photophysical properties that strongly depend on the nature of six apical ligands (L) in [M₆I₈L₆]^2–. In course of our syntheses we report a new efficient preparation of Cs₂[Mo₆I₁₄] as precursor. Target compounds (ⁿBu₄N)₂[M₆I₈(NCO)₆] with M = Mo, W with cyanate ligands were synthesized and structurally characterized to study their photophysical properties. (ⁿBu₄N)₂[M₆I₈(NCO)₆] compounds appear as deep red (Mo) and light yellow (W) crystal powders showing strong phosphorescence. Compared to other cluster compounds of this type there is no significant concentration quenching obtained by the presence of molecular oxygen.     

On topological indices of carbon nanocones and nanotori

Let G be a graph with n vertices and d _i is the degree of its ith vertex (d _i is the degree of v _i). In this article, we compute the redefined first Zagreb index, redefined second Zagreb index, redefined third Zagreb index, augmented Zagreb index of graphs carbon nanocones CNC _k[n], and nanotori [C₄C₆C₈(p,q)]. Also, compute the multiplicative redefined first Zagreb index, multiplicative redefined second Zagreb index, multiplicative redefined third Zagreb index, multiplicative augmented Zagreb index of carbon nanocones CNC _k[n], and nanotori [C₄C₆C₈(p,q)].     

On the normalized Laplacian of Möbius phenylene chain and its applications

Let denote a molecular graph of linear [n] phenylene with n hexagons and n squares, and let the Möbius phenylene chain be the graph obtained from the by identifying the opposite lateral edges in reversed way. Utilizing the decomposition theorem of the normalized Laplacian characteristic polynomial, we study the normalized Laplacian spectrum of , which consists of the eigenvalues of two symmetric matrices ℒ _R and ℒ _Q of order 3n. By investigating the relationship between the roots and coefficients of the characteristic polynomials of the two matrices above, we obtain an explicit closed-form formula of the multiplicative degree-Kirchhoff index as well as the number of spanning trees of . Furthermore, we determine the limited value for the quotient of the multiplicative degree-Kirchhoff index and the Gutman index of .     

Crystal Structures and Chemical Properties of Dimesitylcadmium and Dimesitylmercury

Mesityllithium was used to synthesize dimesitylcadmium and dimesitylmercury from CdCl₂ and HgCl₂, respectively. X‐ray‐crystallographic data show that the group 12 metal compounds M[Mes]₂ (M = Zn, Cd, Hg) are isomorphous (monoclinic, P2₁/n). The asymmetric unit of M[Mes]₂ (M = Zn, Cd, Hg) consists of one mesityl group bonded to the metal atom, which is related to the second substituent by an inversion center. In addition we have investigated the reaction of BBr₃ with M[Mes]₂ (M = Cd, Hg) for our understanding of the reactivity of donor‐free group 12 mesityl compounds. The reaction of M[Mes]₂ (M = Cd, Hg) with an excess of BBr₃ produces MesBBr₂. UV‐induced conversion of Hg[Mes]₂ in benzene yielded quantitatively mesitylene and mercury whereas irradiation of a chloroform solution of Hg[Mes]₂ for 1290 min (λ_max = 510 nm) gave mesitylene, Hg[Mes]Cl, and HgCl₂ in a ratio of 6:4:1. Slow concentration of the reaction solution led to the deposition of X‐ray quality crystals of the addition compound of two Hg[Mes]Cl molecules and HgCl₂ (monoclinic space group P2₁/n).     

One—dimensional Anion—chain Containing [Mo2O6（pic）2]^2—Unit Connected by Unclassical Hydrogen Bond

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｒｉｎｇｔｈｅｐａｓｔｄｅｃａｄｅｓ ,ｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｔｈｅｃｏ ｏｒｄｉｎａｔｉｏｎｃｈｅｍｉｓｔｒｙｏｆｍｏｌｙｂｄｅｎｕｍ(ＶＩ)ｆｏｃｕｓｅｄｏｎｍｅｔ ａｌ ｏｘｙｇｅｎｃｌｕｓｔｅｒｓｃｈａｒａｃｔｅｒｉｚｅｄｂｙｆａｓｃｉｎａｔｉｎｇｓｔｒｕｃｔｕｒａｌ,ｅｌｅｃｔｒｏｃｈｅｍｉｃａｌ,ｃａｔａｌｙｔｉｃ ,ｍａｇｎｅｔｉｃ ,ｍｅｄｉｃｉｎａｌ,ａｎｄｐｈｏｔｏｐｈｙｓｉｃａｌｐｒｏｐｅｒｔｉｅｓ ,1ｗｈｉｃｈａｒｅｏｆｆｕｎｄａｍｅｎｔａｌａｎｄ…     

Cyanidosilicates—Synthesis and Structure

Starting from fluoridosilicate precursors in neat cyanotrimethylsilane, Me₃Si?CN, a series of different ammonium salts [R₃NMe]⁺ (R=Et, ⁿPr, ⁿBu) with the novel [SiF(CN)₅]^2? and [Si(CN)₆]^2? dianions was synthesized in facile, temperature controlled F^?/CN^? exchange reactions. Utilizing decomposable, non‐innocent cations, such as [R₃NH]⁺, it was possible to generate metal salts of the type M₂[Si(CN)₆] (M⁺=Li⁺, K⁺) via neutralization reactions with the corresponding metal hydroxides. The ionic liquid [BMIm]₂[Si(CN)₆] (m.p.=72 °C, BMIm=1‐butyl‐3‐methylimidazolium) was obtained by a salt metathesis reaction. All the synthesized salts could be isolated in good yields and were fully characterized.     

Polymerizations of methyl methacrylate and rac-lactide by zinc(II) precatalyst containing N-substituted 2-iminomethylpyridine and 2-iminomethylquinoline

The reaction of [ZnCl₂] with N-cyclopentyl-1-(quinolin-2-yl)methanimine (L_A), N-cyclohexyl-1-(quinolin-2-yl)methanimine (L_B), N-cyclohexyl-1-(pyridin-2-yl)methanimine (L_C), 2,6-diethyl-N-(pyridin-2-ylmethylene)aniline (L_D), N-cyclopentyl-1-(pyridin-2-yl)methanimine (L_E), and N-phenyl-(pyridin-2-yl)methanimine (L_F) in ethanol produced the bidentate [(NN′)ZnCl₂] complexes, [L_AZnCl₂], [L_BZnCl₂], [L_CZnCl₂], [L_DZnCl₂], [L_EZnCl₂] and [L_FZnCl₂], respectively. The molecular structures revealed that the zinc in [L_nZnCl₂] (L_n = L_A ? L_D) showed a distorted tetrahedral geometry involving two nitrogens of N,N’-bidentate ligands and two chloride ligands. Most of these initiators were effective for polymerization of methyl methacrylate (MMA) and polymerization of rac-lactide (rac-LA). [L_CZnCl₂] (with N-cyclohexyl substituted at imine-pyridine moiety) exhibited the highest catalytic activity for MMA polymerization in the presence of modified methylaluminoxane (MMAO) with an activity of 3.33 × 10⁴ g PMMA/mol·Zn·h at 60 °C, giving moderate syndiotactic poly methyl methacrylate (PMMA) with high molecular weight (9.62 × 10⁵ g/mol). The dimethyl derivatives [L_nZnMe₂] (L_n = L_A ? L_F), generated in situ, polymerized rac-LA with moderate activity and yielded a polylactide (PLA) with good number-average molecular weights and narrower polydispersity indices (PDIs). [L_AZnMe₂] effectively initiates the ring-opening polymerization (ROP) of rac-LA to attain heterotactic PLA (P_r = 0.91).     

Synthesis and reactions of cysteine‐based telechelic polymers

The radical polyaddition of N‐4‐vinylbenzoyl‐L ‐cysteine methyl ester (VCM) was carried out in the presence of 2,2′‐azobisisobutyronitrile (AIBN, 3 mol %) as an initiator in dimethyl formamide (DMF) with monomer concentrations of 0.5 and 1.0 M at 60 °C for 20 h under nitrogen atmosphere to afford the corresponding polymers [poly(VCM), PVCM] with number‐average molecular weights (M_n)'s of 5300 and 18,000 in 92 and 95% yields, respectively. The obtained polymers had a heterotelechelic structure with thiol and olefin end moieties. The radical polymerization of methyl methacrylate and trityl methacrylate was carried out in the presence of PVCM with AIBN (3 mol %) as an initiator in DMF at 60 °C for 20 h to afford the block copolymers with M_n values in the range of 13,000–26,800 in good yields. PVCM [M_n = 18,000; polydispersity (M_w/M_n) = 1.56] was treated with 4 equiv of NaOH aq. (1.0 M) to afford the polymer having carboxyl groups in the side chain with a M_n of 17,300 and M_w/M_n of 1.88 in 95% yield and was also oxidized to polysulfoxide and polysulfone with 4 equiv of H₂O₂ per sulfide unit in CH₂Cl₂ (1.0 M) for 20 h. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 23–31, 2001     

Pseudoelementverbindungen. IV. Modifizierung der Ionen Sulfit [SOY2]2−, Sulfat [SO4−nYn]2− und Sulfonat [RSO2Y]− durch Einführung der Pseudochalkogengruppen NCN und C(CN)2

Pseudoelement Compounds. IV. Modification of the Ions Sulfite [SO₂Y]^2?, Sulfate [SO_4?nY_n]^2?, and Sulfonate [RSO₂Y]^? by Introducing Pseudochalcogen Groups NCN and C(CN)₂ . Described is the synthesis of pseudochalcogen modified sulfites M₂[SOY₂], sulfates M₂[SO_4?nY_n] (Y = NCN), and arylsulfonates M[RSO₂Y] (Y = NCN, C(CN)₂). The ¹³C-NMR and IR spectra of the new compounds are discussed.     

Mass spectrometric determination of the configuration of 2-methyl-and 1,2-dimethyl-4-vinyl-ethinyl(n-butyl)-4-hydroxyperhydroquinolines

The configuration at C-2 and C-4 in the molecules of 2-methyl- and 1,2-dimethyl-4-vinylethinyl(n-butyl)-4-hydroxyperhydroquinolines was determined by mass spectrometry. The principal conclusions concerning the stereochemistry were made on the basis of differences in the values of the I_[M?15]⁺/I_[M]⁺·, I_[M?17]⁺/I_[M]⁺·, I[_M?43]⁺/I_[M]⁺· and I_[M?57]⁺/I_[M]⁺· ratios in the mass spectra of the epimeric vinylethinylic alcohols, and of the I_[M?15]⁺/I_[M]⁺· and I_[M?15]⁺/I_[M]⁺· ratios in the case of the n-butylic alcohols.     

Line-Pro le Analysis of Excitation Spectroscopy in the Even 3p5(2P1/2)nl'[K']J(l'=1,3) Autoionizing Resonances of Ar

The even-parity autoionizing resonance series 3p⁵np'[3/2]_1,2, 3p⁵np'[1/2]₁, and 3p⁵nf'[5/2]₃ of Ar have been investigated exciting from the two metastable states 3p⁵4s[3/2]₂ and 3p⁵4s'[1/2]₀ in the photon energy range of 32500-35600 cm^-1 with an experimental bandwidth of ~0.1 cm^-1. The excitation spectra of the even-parity autoionizing resonance series show typical asymmetric line shapes. New level energies, quantum defects, line profile index and resonance widths, resonance lifetime and reduced widths of the autoionizing resonances are derived by a Fano-type line-shape analysis. The line profile index q and the resonance widths Γ are shown to be approximately proportional to the effective principal quantum number n^*. The line separation of the 3p⁵np' autoionizing resonances is discussed.     

Kirchhoff index of linear hexagonal chains

The resistance distance r_ij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices. In this work, according to the decomposition theorem of Laplacian polynomial, we obtain that the Laplacian spectrum of linear hexagonal chain L_n consists of the Laplacian spectrum of path P_2n+1 and eigenvalues of a symmetric tridiagonal matrix of order 2n + 1. By applying the relationship between roots and coefficients of the characteristic polynomial of the above matrix, explicit closed‐form formula for Kirchhoff index of L_n is derived in terms of Laplacian spectrum. To our surprise, the Krichhoff index of L_n is approximately to one half of its Wiener index. Finally, we show that holds for all graphs G in a class of graphs including L_n. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Kinetic Study of the Bromine-Catalyzed Isomerization of Maleic Acid in Aqueous Ce(IV)-Br−-H2SO4 Medium

The presence of ceric and bromide ions catalyzes the isomerization of maleic acid (MA) to fumaric acid (FA) in aqueous sulfuric acid. A kinetic study of this bromine-catalyzed reaction was carried out. The reaction between ceric ion and maleic acid is first order with respect to Ce(IV). For [Ce(IV)]₀=5.0×10^?4 M, [H₂SO₄]₀=1.2 M, μ=2.0 M (adjusted by NaClO₄), and [MA]₀=(0.5–1.0)M, the observed pseudo-first-order rate constant (k₀₃) at 25° is k₀₃=7.622×10^?5 [MA]₀/(1+0.205[MA]₀). The reaction between ceric and bromide ions is first order with respect to Ce(IV). For [Ce(IV)]₀=5.0×10^?4 M, [H₂SO₄]₀=1.2 M, μ=2.0 M, and [Br^?]₀=(0.025–0.150)M, the pseudo-first-order rate constant (k₀₂) at 25° is k₀₂= (4.313±0.095)x10^?2[Br^?]²+(2.060±0.119)x10^?3[Br^?]. The reaction of Ce(IV) with maleic acid and bromide ion is also first order with respect to Ce(IV). For [Ce(IV)]₀=5.0×10^?4 M, [MA]₀=0.75 M, [H₂SO₄]₀=1.2 M, μ=2.0 M, and [Br^?]₀= (0.025–0.150)M, the pseudo-first-order rate constant (k₀₃) at 25° is k₀₃= (5.286±0.045)x10^?2[Br^?]²+(3.568±0.056)x10^?3[Br^?]. For [Ce(IV)]₀=5.0 × 10^?4 M, [Br^?]₀=0.050 M, [H₂SO₄]₀=1.2 M, μ=2.0 M, and [MA]₀=(0.15–1.0)M at 25°, k₀₃=(2.108×10^?4+2.127×10^?4[MA]₀)/(1+0.205[MA]₀). A mechanism is proposed to rationalize the results. The effect of temperature on the reaction rate was also studied. The energy barrier of Ce(IV)—Br^? reaction is much less than that of Ce(IV)—MA reaction. Maleic and fumaric acids have very different mass spectra. The mass spectrum of fumaric acid exhibits a strong metastable peak at m/e 66.5.     

Reactivity Studies of η5‐ Indenyl and η5‐Cp* Ruthenium(II) Complexes towards some Polypyridyl Ligands

The reaction of [(η⁵‐L³)Ru(PPh₃)₂Cl], where; L³ = C₉H₇ ( 1 ), C₅Me₅ (Cp*) ( 2 ) with acetonitrile in the presence of [NH₄][PF₆] yielded cationic complexes [(η⁵‐L³)Ru(PPh₃)₂(CH₃CN)][PF₆]; L³= C₉H₇ ([3]PF₆) and L³ = C₅Me₅ ([4]PF₆), respectively. Complexes [3]PF₆ and [4]PF₆ reacts with some polypyridyl ligands viz, 2,3‐bis (α‐pyridyl) pyrazine (bpp), 2,3‐bis (α‐pyridyl) quinoxaline (bpq) yielding the complexes of the formulation [(η⁵‐L³)Ru(PPh₃)(L²)]PF₆ where; L³ = C₉H₇, L² = bpp, ([5]PF₆), L³ = C₉H₇, L² = bpq, ([6]PF₆); L³ = C₅Me₅, L² = bpp, ([7]PF₆) and bpq, ([8]PF₆), respectively. However reaction of [(η⁵‐C₉H₇)Ru(PPh₃)₂(CH₃CN)][PF₆] ([3]PF₆) with the sterically demanding polypyridyl ligands, viz. 2,4,6‐tris(2‐pyridyl)‐1,3,5‐triazine (tptz) or tetra‐2‐pyridyl‐1,4‐pyrazine (tppz) leads to the formation of unexpected complexes [Ru(PPh₃)₂(L²)(CH₃CN)][PF₆]₂; L² = tppz ([9](PF₆)₂), tptz ([11](PF₆)₂) and [Ru(PPh₃)₂(L²)Cl][PF₆]; L² = tppz ([10]PF₆), tptz ([12]PF₆). The complexes were isolated as their hexafluorophosphate salts. They have been characterized on the basis of micro analytical and spectroscopic data. The crystal structures of the representative complexes were established by X‐ray crystallography.     

Structure of uranyl complexes with acetylenedicarboxylic acid, K(H5O2)[UO2(OOCC≡CCOO)2 · H2O] · 2H2O and Cs2[UO2(OOCC≡CCOO)2 · H2O] · 2H2O

Uranyl complexes with acetylenedicarboxylic acid, K(H₅O₂)[UO₂L₂H₂O] · 2H₂O (I) and Cs₂[UO₂L₂H₂O] · 2H₂O (II), L²⁻ = C₄O ₄ ²⁻ were prepared for the first time. The composition and structure of the complexes were determined by X-ray diffraction. The crystal data are as follows: a = 16.254(12) ?, b = 13.508(8) ?, c = 7.683(6) ?, β = 90.91(7)°, space group C2/c, V = 1687(2) ?³ (I); a = 7.0745(10), b = 18.4246(10), c = 13.1383(10) ?, space group Abm2, V = 1712.5(3) ?³ (II). The structures of I and II are based on [UO₂L₂H₂O] _n ²⁻ anionic chains stretched along the [101] direction (I) or [010] direction (II). In I and II, the uranium coordination polyhedron is a pentagonal bipyramid in which the equatorial environment of the uranyl ions is formed by the oxygen atoms of the four L²⁻ anions and the water molecule. The L²⁻ anions in I and II are bidentate bridging ligands connecting two uranium atoms that are next to each other in the anionic chain; their coordination capacity is equal to 2. In I, the K⁺ and H₅O ₂ ⁺ cations are outer-sphere species. The latter form hydrogen bonds combining the anionic chains shifted by translation b with respect to each other. The [UO₂L₂H₂O] _n ²⁻ chains in I are surrounded by the potassium and oxonium cations; in II, these are combined by hydrogen bonds into anionic layers between which Cs⁺ cations are arranged. The IR spectrum of compound II was measured and interpreted. Original Russian Text ? I.A. Charushnikova, A.M. Fedoseev, N.A. Budantseva, I.N. Polyakova, Ph. Moisy, 2007, published in Koordinatsionnaya Khimiya, 2007, Vol. 33, No. 1, pp. 63–69.     

Synthesis,crystal structure and catalytic performance of bis (imino)pyridyl nickel complexes

Two new Ni(II) complexes of 2,6-bis[1-(2,6-diethylphenylimino)ethyl]pyridine (L¹), 2,6-bis[1-(4-methylphenylimino)ethyl]pyridine (L² ) have been synthesized and structurally characterized. Complex Ni(L¹)Cl₂?·?CH₃CN (1), exhibits a distorted trigonal bipyramidal geometry, whereas complex Ni(L¹)(CH₃CN)Cl₂ (2), is six-coordinate with a geometry that can best be described as distorted octahedral. The catalytic activities of complexes 1, 2, Ni{2,6-bis[1-(2,6-diisopropyl-phenylimino)ethyl]pyridine} Cl₂?·?CH₃CN (3), and Ni{2,6-bis[1-(2,6-dimethylphenylimino) ethyl]pyridine}Cl₂?·?CH₃CN (4), for ethylene polymerization were studied under activation with MAO.     

Kristallstrukturen,Schwingungsspektren und Normalkoordinatenanalyse von (n‐Bu4N)2[Os(NCS)6] und (n‐Bu4N)3[Os(NCS)6]

Crystal Structure, Vibrational Spectra, and Normal Coordinate Analysis of ( n ‐Bu₄N)₂[Os(NCS)₆] and ( n ‐Bu₄N)₃[Os(NCS)₆] By tempering the solid mixture of the linkage isomers (n‐Bu₄N)₃[Os(NCS)_n(SCN)_6–n] n = 0–5 for a longer time at temperatures increasing from 60 to 140 °C the homoleptic (n‐Bu₄N)₃[Os(NCS)₆] is formed, which on oxidation with (NH₄)₂[Ce(NO₃)₆] in acetone yields the corresponding Os^IV complex (n‐Bu₄N)₂[Os(NCS)₆]. X‐ray structure determinations on single crystals of (n‐Bu₄N)₂[Os(NCS)₆] (1) (triclinic, space group P 1, a = 12.596(5), b = 12.666(5), c = 16.026(5) Å, α = 88.063(5), β = 80.439(5), γ = 88.637(5)°, Z = 2) and (n‐Bu₄N)₃[Os(NCS)₆] ( 2 ) (cubic, space group Pa 3, a = 24.349(4) Å, Z = 8) have been performed. The nearly linear thiocyanate groups are coordinated with Os–N–C angles of 172.3–177.7°. Based on the molecular parameters of the X‐ray determinations the IR and Raman spectra are assigned by normal coordinate analysis. The valence force constant f_d(OsN) is 2.3 ( 1 ) and 2.10 mdyn/Å ( 2 ).     

Syntheses,characterizations, and antimicrobial activities of binuclear ruthenium(III) complexes containing 2-substituted benzimidazole derivatives

Binuclear ruthenium(III) complexes [RuX₃L]₂?·?nH₂O (X?=?Cl, L?=?L¹, L², L³; n?=?1, L⁴ and L⁵, X?=?Br; L?=?L³), [RuX₃L_1.5]₂?·?nH₂O (X?=?Br, L?=?L¹; n?=?0, L⁴; n?=?6 and L⁵; n?=?10), and [RuX₃L₂]₂ (X?=?Br, L?=?L²) have been isolated by treatment of hydrated RuX₃ (X?=?Cl/Br) in acetone with 2-(2′-aminophenylbenzimidazole) (L¹), 2-(3′-aminophenylbenzimidazole) (L²), 2-[(3′-N-salicylidinephenyl)benzimidazole] (L³), 2-(3′-pyridylbenzimidazole) (L⁴), and 2-(4′-pyridylbenzimidazole) (L⁵) in acetone. The complexes were characterized by elemental analysis, conductivity and magnetic susceptibility measurements, IR, electronic, EPR, and mass spectral studies. The complexes were dimeric; based on analytical and spectral studies, an octahedral geometry was proposed for the complexes. The synthesized complexes were screened against Gram-positive and Gram-negative bacteria and fungi.