On the connectivity index of trees

The connectivity index χ₁(G) of a graph G is the sum of the weights d(u)d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u. Let T(n, r) be the set of trees on n vertices with diameter r. In this paper, we determine all trees in T(n, r) with the largest and the second largest connectivity index. Also, the trees in T(n, r) with the largest and the second largest connectivity index are characterized. Mei Lu is partially supported by NNSFC (No. 10571105).     

The molecular structure of gaseous tetrachloro-p-benzoquinone and tetrachloro-o-benzoquinone by electron diffraction

The structures of tetrachloro-p-benzoquinone and tetrachloro-o-benzoquinone (p- and o-chloranil) have been investigated by gas electron diffraction. The ring distances are slightly larger and the carbonyl bonds slightly smaller than in the corresponding unsubstituted quinones. The molecules are planar to within experimental error, but small deviations from planarity such as those found for the para compound in the crystal are completely compatible with the data. Values for the geometrical parameters (r_a distances and bond angles) and for some of the more important amplitudes (l) with parenthesized uncertainties of 2σ including estimated systematic error and correlation effects are as follows. Tetrachloro-p-benzoquinone: D_2h symmetry (assumed); r(CO) = 1.216 Å(4), r(CC) = 1.353 Å(6), r(C-C) = 1.492 Å(3), r(C-Cl) = 1.701 Å(3), ∠C-C-C = 117.1° (7), ∠CC-C1 = 122.7° (2), l(CO)= 0.037 Å(5), l(CC) = l(C-C) - 0.008 Å(assumed) = 0.049 Å(7), and l(C-Cl) = 0.054 Å(3). Tetrachloro-o-benzoquinone: C_2v symmetry (assumed); r(CO) = 1.205 Å(5), r(CC) = 1.354 Å(9), r(C_cl-C_cl) = 1.478 Å(28), r(Co-C_cl) = 1.483 Å(24), r(C_o-C_o) = 1.526 Å(2), r(C-Cl)= 1.705 Å(3), <C_o-CO = 121.0° (22), ∠C-C-C = 117.2° (9), ∠C_co, ClC-Cl = 118.9° (22), ∠C_ccl, ClC-Cl = 122.2°(12), l(CO) = 0.039 Å(5), and l(C_cl-C_cl) = l(C_o-C_cl) = l( Co-Co) = l(CC) + 0.060 Å(equalities assumed) = 0.055 Å(9). Vibrational'shortenings (shrinkages) of a few of the long non-bond distances have also been measured.     

Selective N-methylation of primary aliphatic amines with dimethyl carbonate in the presence of alkali cation exchanged Y-faujasites

The N-methylation of aliphatic amines [XC₆H₄(CH₂)_nNH₂; n=1, X=H (1a), o-MeO (1b), p-MeO (1c); n=2, X=H (2a), o-MeO (2b); 1d: PhCH(Me)NH₂] with dimethyl carbonate (DMC) is efficiently catalysed by NaY faujasite: on condition that CO₂ (a co-product of the reaction) is carefully removed, N-methyl- and N,N-dimethyl-amines (RNHMe and RNMe₂) are obtained in good overall yields (70-90%). Otherwise, in the presence of CO₂, carbamates (RNHCO₂Me) form competitively to a large extent. The reaction probably proceeds through a B_Al2 displacement of the amine on DMC.     

Why is ‘amount of substance’ so poorly understood? The mysterious Avogadro constant is the culprit!

The base quantity ‘amount of substance’ is poorly understood and the name and symbol usually avoided. This is because of its formal interpretation as the number of entities multiplied by the reciprocal of the mysterious Avogadro constant, N _A. If X signifies the kind of entities involved, the number of entities in a sample, N(X), is easily comprehended, and if m _av(X) is the sample-average entity mass, the total mass, m(X) = N(X)m _av(X)—an aggregate of N(X) average entity masses—is also conceptually straightforward. However, the corresponding amount of substance, n(X) = N(X)(1/N _A)—an aggregate of N(X) ‘reciprocal Avogadro constants’—is incomprehensible unless some physical meaning can be attached to 1/N _A. By contrast, the base unit, mole, is thought of by chemists as an aggregate of a particular number of entities: mol = \( {\mathcal N}_{\rm{Avo}} \) ent, where \( {\mathcal N}_{\rm{Avo}} \) is the Avogadro number (equal to g/Da) and ent represents one entity. It makes sense, therefore, to interpret amount of substance as an aggregate of a general number of entities: n(X) = N(X) ent—an easily grasped concept. A ‘reciprocal Avogadro constant’ is thus seen to actually be exactly one entity. One mole then corresponds to setting N(X) = \( {\mathcal N}_{\rm{Avo}} \), for which the total mass is the relative entity mass in grams—conforming to the original mole concept.     

On the general transformation from molecular geometric parameters to cartesian coordinates

This article presents a general method and accurate algorithm for calculating the Cartesian coordinates (x_a, y_a, z_a) from an arbitrary triple of distances r(a,i), angles, θ(a,j,k), or dihedral angles ?(a,l,m,n), specifying the position of the nucleus a relative to nuclei i, ?, n with known Cartesian coordinates. There is a brief discussion of the requirements on the 3N-6 geometric parameters in order for them to determine the shape of an N-atomic molecule.     

Ab initio study of the O4 molecule

SCF-CI calculations were done on tetratomic oxygen complexes at various geometries. The results point to the existence of a metastable covalent molecule O₄ completely different from the van der Waals structure (O₂)₂ detected experimentally. At its equilibrium geometry, the O₄ molecule is a quasi-square (r(OO) ≈ 1.4 Å), slightly twisted out of plane, corresponding to the symmetry group D_2d. The activation energy of the reaction O₄(¹A_g) → 20₂(X ³Σ^?_g) is found to be ≈ 15 kcal/mole, that of the inverse reaction, ≈ 75 kcal/mole.     

Electronic transition moment of the AΠr-XΣ system of TiN

The A²Π_r-X²Σ⁺ transition of TiN was observed by the dispersed laser induced fluorescence (DLIF) spectroscopy. The relative intensities of the DLIF spectra were analyzed to determine the dependence of the electronic transition moment, R_e(r), on the internuclear distance, r, as R_e(r)∝{1−0.281(26)r} (1.380 Å≤r≤1.823 Å). This r-dependence was analyzed simultaneously with the reported values of the spin-orbit constants for A²Π_r and the hyperfine-coupling constants for X²Σ⁺ to evaluate the ionic character of the TiN bond, the 4s atomic character in the 9σ orbital of X²Σ⁺, and the 4p atomic character in the 4π orbital of A²Π_r. These characters were confirmed to be in accordance with the reported theoretical prediction. A strong r-dependence was indicated for the 3d-4p mixing in the A²Π_r state due to the configuration mixing of the Ti(3d⁴) and Ti(3d³4p) states at a large internuclear distance.     

The distance distribution of radical—paramagnetic ion pairs studied by the electron spin echo method. Spatial regularities of radical diffusion in glassy alcohols

Applications of the electron spin echo (ESE) technique to determine the distance distribution function for radical-ion pairs stabilized in solids are described. The ESE signal intensity depends on the ion spin-lattice relaxation time T₁, thus on temperature, as well as on the function n(r),n(r) can be determined up to a distance of 50 A. At r < 10 - 20 A it is possible to estimate the portion of radicals stabilized at these distances in the vicinity of a paramegnetic ion. The photochemical reaction Fe³⁺ + R₂CH(OH)→Fe²⁺ +_R₂C(OH) + H⁺ has been studied in glassy methanol and isopropanol. The pair distribution function n(r) has been obtained at 17 < r < 26 A. Its changes induced by radical diffusion have been studied. The portion of radicals stabilized at distance r < 17 A was about 80% for both alcohols.     

The molecular structure of selenonyl fluoride,SeO2F2, and sulfuryl fluoride,SO2F2, as determined by gas-phase electron diffraction

The molecular structure of selenonyl fluoride (SeO₂F₂) and sulfuryl fluoride (SO₂F₂) has been studied by gas-phase electron diffraction. The geometries of both molecules are consistent with predictions of VSEPR (valence-shell electron-pair repulsion) theory. The results for the more important distance (r_a), bond angle, and r.m.s. amplitude (l) parameters with estimated uncertainties estimated at 2σ are for SeO₂F₂r(Se = 0) = 1.575 Å (0.002), r(Se-F) = 1.685 Å (0.002), ∠OSeO = 126.2° (0.5), ∠FSeF = 94.1° (0.5), l(Se = 0) = 0.0440 Å (0.0046), l(Se-F) = 0.0472 Å (0.0042), and for SO₂F₂r(S = 0) = 1.397 Å (0.002), r(S-F) = 1.530 Å (0.002), ∠OSO = 122.6° (1.2), ∠FSF = 96.7° (1.1), l(S = 0) = 0.0331 Å (0.0015), l(S-F) = 0.0393 Å (0.0018).     

Molecular structure of ErCl<Subscript>3</Subscript> and YbCl<Subscript>3</Subscript> according to the data of the simultaneous electron diffraction and mass spectrometric experiment

The saturated vapors of ErCl₃ and YbCl₃ were studied in a simultaneous electron diffraction and mass spectrometric experiment at 1165 K and 1170 K, respectively. In the vapors of these compounds, we found up to 3 mol.% dimers along with the monomers. The parameters of the r _g effective configuration of the monomer molecules were determined. For ErCl₃ and YbCl₃, the internuclear distances r _g(Ln-Cl) were 2.436(5) Å and 2.416(5) Å, and the bond angles ∠_g(Cl-Ln-Cl) were 117.0(10)° and 117.2(10)°, respectively. The equilibrium configurations and vibration frequencies of the monomer and dimer molecules were calculated by the HF, B3LYP, and MP2 methods using the combination of the ECP_D energy-consistent quasirelativistic core potential, including 4f electrons [Kr4d ¹⁰4f ⁿ ], and the contracted [5s4p3d] valence basis set for Er and Yb atoms and the MIDIX [4s3p1d] basis set for Cl atoms. The parameters of the effective r _g configuration of the monomer molecules corresponding to the temperature of the experiment were calculated. The difference between the calculated equilibrium r _e(Ln-Cl) and temperature-averaged r _g(Ln-Cl) distances was found to be 0.001–0.002 Å and did not exceed the error of the r _g(Ln-Cl) parameter determined in the electron diffraction experiment. The experimental parameters of the r _g structure were shown to be consistent with the idea about the planar equilibrium geometrical configuration of ErCl₃ and YbCl₃ molecules.     

Hosoya index of unicyclic graphs with prescribed pendent vertices

The Hosoya index z(G) of a (molecular) graph G is defined as the total number of subsets of the edge set, in which any two edges are mutually independent, i.e., the total number of independent-edge sets of G. By G(n, l, k) we denote the set of unicyclic graphs on n vertices with girth and pendent vertices being resp. l and k. Let be the graph obtained by identifying the center of the star S _n-l+1 with any vertex of C _l . By we denote the graph obtained by identifying one pendent vertex of the path P _n-l-k+1 with one pendent vertex of . In this paper, we show that is the unique unicyclic graph with minimal Hosoya index among all graphs in G(n, l, k).      

Molecular structure and microwave spectra of isotopic chloro-, bromo-, and iodocyanoacetylene

The microwave spectra of the halogeno-cyanoacetylenes, X-CC-CN (X = ¹²⁷I, ⁸¹Br, ⁷⁹Br, ³⁷Cl, ³⁵Cl), have been investigated. The molecules were found to be linear. The vibration-rotation constants of the three bending vibrations and the lower stretching vibration were determined. Lines belonging to the monosubstituted ¹³C and ¹⁵N species in their natural abundances were measured and the rotational constants obtained. The bond distances based on the substitution coordinates were: for I-CC-CN r(I-C) = 1.984₆ Å, r(CC) = 1.207_o Å, r(C-C) = 1.370₂ Å, r(CN) = l.l60₄ Å; for Br-CC-CN, r(Br-C) = 1.785₈ Å, r(CC) = 1.204₁ Å, r(C-C) = 1.369₉ Å, r(CN) = 1.159₃ Å; and for C1-CC-CN, r(Cl-C) = 1.624₅ Å, r(CC) = 1.209_o Å, r(C-C) = 1.369_o Å, r(CN) = 1.160₂ Å.     

Zur Berechnung von Bindungsabständen aus Valenzkraftkonstanten (SIEBERT-BADGER-JENSOVSKY-Iteration)

On the Evaluation of Bond Distances from Valence Force Constants (Siebert-Badger-Jensovsky Iteration) For the evaluation of bond distances r_XY,N (Å) from valence force constants f_XY,N (mdyn/Å) an iteration cycle is reported. For X ions with the electronic configuration d¹⁰ the Jensovsky relation has to be modified.     

Structure and conformation of 1,3-dithlane: an electron diffraction study

A gas-phase electron diffraction study of 1,3-dithiane, carried out at 100° C, has found no statistically significant evidence for the presence of any conformer in the vapor other than the chair, within an estimated uncertainty of 10%. An index of the degree of ring puckering in 1,3-dithiane is the average torsional angle which was found to be 61.3°, appreciably greater than that in cyclohexane, but somewhat less than that in 1,4-dithiane and 1,3,5-trithianc. The C-C-C, C-C-S and S-C-S valency angles, 113.6(33)°, 114.9(4)° and 115.0(3)° respectively, were all larger than the C-C-C valency angles in cyclohexane. The C-S-C valency angle, 98.1(7)°, was slightly smaller than that of dimethyl sulfide. Observed bond lengths were r_g(C-H) = 1.116(10) Å, r_g(C-H) = 1.533(5)Å, and r_g(C-S) = 1. 812(3)Å and mean amplitudes of vibration were l_g(C-H) = 0.081(12)Å, l_g(C-C) = 0.052(6)Å and l_g(C-S) = 0.052(4) Å (parenthesized quantities correspond to 3σ). Curiously, nonbonded distances between the axial hydrogen atoms in 1,3-dithiane are virtually identical to those in cyclohexane, even though these molecules have greatly different bond lengths, valency angles, and torsional angles.     

Synthese und Reaktivität von Silicium-übergangsmetall-Komplexen: XXI. Ferrio-azidosilane and Ferriosilyl-iminophosphorane

Reaction of the ferriochlorosilanes R₅C₅(CO)₂FeSiR′_3-nCl_n (1a–1f) with sodium azide in tetrahydrofuran yields the ferrio- (mono-, bis-, and tris-azido)silanes R₅C₅(CO)₂FeSiR′_3-n(N₃)_n (R = H, Me; R′ = Me, H; n = 1–3) (2a–2f). CCl₄ converts Cp(CO)₂FeSiMe(H)N₃ (2a) into the ferrioazido(chloro)silane Cp(CO)₂-FeSiMe(Cl)N₃ (3). Treatment of 2d, 2f with Me₃P results in the formation of the ferriosilyl-iminophosphoranes Cp(CO)₂FeSi(N₃)(R)NPMe₃ (R = Me, N₃), (4a, 4b) by N₂ elimination.     

Molecular structure of nickel(II) and copper(II) N,N′-ethylene-bis(acetylacetoneiminates) MO2N2C12H18 according to gas-phase electron diffraction data and quantum-chemical calculations

The molecular structure of nickel(II) and copper(II) N,N′-ethylene-bis(acetylacetoneiminates), NiO₂N₂C₁₂H₁₈ and CuO₂N₂C₁₂H₁₈, at 442(5) K and 425(5)K, respectively. Both molecules have C ₂ symmetry with a nearly planar MN₂O₂ coordination site and internuclear distances r _h1(M-O) = 1.862(10)/1.923(17) Å and r _h1(M-N) = 1.879(10)/1.947(18) Å for Ni(acacen) and Cu(acacen), respectively. The structure of free molecules is close to the structure of molecules in crystal. The DFT/3LYP quantum-chemical calculations (CEP-31G and 6-31G* basis sets) gave a molecular structure that agreed satisfactorily with the one found in experiment. The low-spin ¹ A and high-spin ³ A states of the Ni(acacen) molecule were considered. It was found that a change in multiplicity caused significant changes in the geometrical and electronic structure of the MN₂O₂ coordination site. As shown by experiment and calculations for the NiO₂N₂C₁₂H₁₈ molecule, the low-spin ¹ A state is the ground state. The internal rotation of CH₃(CN) and CH₃(CO) methyl groups was studied by the 3LYP/CEP-31G method. It was shown that steric hindrances led to a high rotation barrier of the CH₃(CN) group.     

Novel hydridotris(pyrazolyl)borate ruthenium(II) complexes containing the water-soluble phosphane 1,3,5-triaza-7-phosphaadamantane: Synthesis and evaluation of DNA binding properties

A series of half-sandwich ruthenium(II) complexes containing κ³(N,N,N)-hydridotris(pyrazolyl)borate (κ³(N,N,N)-Tp) and the water-soluble phosphane 1,3,5-triaza-7-phosphaadamantane (PTA) [RuX{κ³(N,N,N)-Tp}(PPh₃)_2−n(PTA)_n] (n = 2, X = Cl (1), n = 1, X = Cl (2), I (3), NCS (4), H (5)) and [Ru{κ³(N,N,N)-Tp}(PPh₃)(PTA)L][PF₆] (L = NCMe (6), PTA (7)) have been synthesized. Complexes containing 1-methyl-3,5-diaza-1-azonia-7-phosphaadamantane(m-PTA) triflate [RuCl{κ³(N,N,N)-Tp}(m-PTA)₂][CF₃SO₃]₂ (8) and [RuX{κ³(N,N,N)-Tp}(PPh₃)(m-PTA)][CF₃SO₃] (X = Cl (9), H (10)) have been obtained by treatment, respectively, of complexes 1, 2 and 5 with methyl triflate. Single crystal X-ray diffraction analysis for complexes 1, 2 and 4 have been carried out. DNA binding properties by using a mobility shift assay and antimicrobial activity of selected complexes have been evaluated.     

Preferential energy transfer from N2(A) to specific energy levels of Cu atoms

Emission spectra resulting from reaction of “clean” N₂(A³ Σ_u⁺) with copper atoms were studied using a flowing afterglow apparatus. The population distribution of the Cu states was calculated from the spectrum; it indicates that Cu atoms are excited by nearly resonant energy transfer processes. N₂(A,v') + Cu(²S_{$\text{1}\text{2}$}) → N₂(X, v) + Cu^* , and that the transfer is most efficient for N₂(A,v') → N₂(X,v) transitions with large Franck-Condon factors. The preferential energy transfer results in population inversion between some of the Cu states.     

Stereo‐dynamics of the F + HCl → HF + Cl reaction

We present a quasi‐classical trajectory (QCT) study on product polarization for the reaction F(²P) + HCl(v = 0, j = 0) → HF + Cl(²P) on a recently computed 1² A′ ground‐state surface reported by Deskevich et al. J Chem Phys, 2006, 124, 224303. Four polarization dependent generalized differential cross‐sections (2π/σ)(dσ₀₀/dω_t), (2π/σ)(dσ₂₀/dω_t), (2π/σ)(dσ₂₂₊/dω_t), and (2π/σ)(dσ_21?/dω_t) were calculated in the center‐of‐mass frame at four different collision energies. The obtained P(θ_r), P(?_r), and P(θ_r, ?_r), which denote respectively the distribution of angles between k and j′, the distribution of dihedral angle denoting k‐k′‐j′ correlation and the angular distribution of product rotational vectors in the form of polar plots, indicate that the degree of rotational alignment of the product HF molecule is strong and the degree of the rotational alignment decreases as collision energy increases. The product rotational angular momentum vector j′ is not only aligned, but also oriented along the y‐axis, and the molecular rotation of the product prefers an in‐plane reaction mechanism rather than the out‐of‐plane mechanism. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Photochemical reactions of chromium hexacarbonyl with tetraalkyldiphosphine disulfides

New complexes [Cr(CO)₄(R₂P(S)P(S)R₂)] and [Cr₂(CO)₁₀(-R₂P(S)P(S)R₂)] (R = Me, Et, Pr ⁿ , Bu ⁿ ), (1a)–(1d) and (2a)–(2d) [(1a), R = Me; (1b), R = Et; (1c), R = Pr ⁿ ; (1d), R = Bu ⁿ ; (2a), R = Me; (2b), R = Et; (2c), R = Pr ⁿ ; (2d), R = Bu ⁿ ] have been prepared by the photochemical reaction of Cr(CO)₆ with R₂P(S)P(S)R₂ (R = Me, Et, Pr ⁿ and Bu ⁿ ) and characterized by elemental analyses, FT-i.r., ³¹P-[¹H]-n.m.r. spectroscopy and FAB-mass spectrometry. The spectroscopic data suggest cis-chelate bidentate coordination of the ligand in [Cr(CO)₄(R₂P(S)P(S)R₂)] and cis-bridging bidentate coordination of the ligand between two metals in [Cr₂(CO)₁₀(-R₂P(S)P(S)R₂)] (R = Me, Et, Pr ⁿ and Bu ⁿ ).