The structure and thermochemistry of 3:4,5:6-dibenzo-2-hydroxymethylene-cyclohepta-3,5-dienenone (1) and some related compounds

Condensed and gas phase enthalpies of formation of 3:4,5:6-dibenzo-2-hydroxymethylene-cyclohepta-3,5-dienenone (1, (−199.1 ± 16.4), (−70.5 ± 20.5) kJ mol⁻¹, respectively) and 3,4,6,7-dibenzobicyclo[3.2.1]nona-3,6-dien-2-one (2, (−79.7 ± 22.9), (20.1 ± 23.1) kJ mol⁻¹) are reported. Sublimation enthalpies at T=298.15 K for these compounds were evaluated by combining the fusion enthalpies at T = 298.15 K (1, (12.5 ± 1.8); 2, (5.3 ± 1.7) kJ mol⁻¹) adjusted from DSC measurements at the melting temperature (1, (T _fus, 357.7 K, 16.9 ± 1.3 kJ mol⁻¹)); 2, (T _fus, 383.3 K, 10.9 ± 0.1) kJ mol⁻¹) with the vaporization enthalpies at T = 298.15 K (1, (116.1 ± 12.1); 2, (94.5 ± 2.2) kJ mol⁻¹) measured by correlation-gas chromatography. The vaporization enthalpies of benzoin ((98.5 ± 12.5) kJ mol⁻¹) and 7-heptadecanone ((94.5 ± 1.8) kJ mol⁻¹) at T = 298.15 K and the fusion enthalpy of phenyl salicylate (T _fus, 312.7 K, 18.4 ± 0.5) kJ mol⁻¹) were also determined for the correlations. The crystal structure of 1 was determined by X-ray crystallography. Compound 1 exists entirely in the enol form and resembles the crystal structure found for benzoylacetone.     

On the interaction between mercury(II) salts and 3-methylpyrazoline-5-one. The first crystal structure of a cyclic organomercuric compound with a dimercurated methylenic carbon atom

Synthesis and characterization of two types of novel organomercury derivatives of 3-methylpyrazoline-5-one (MepzH₂-one), (XHg)₂(MepzH-one) (X = Cl⁻, Br⁻) and Hg(MepzH-one)₂ are described. The ¹H and ¹³C NMR data revealed existence of dimercurated compounds in the dimethylsulfoxide-d ₆ solution. NMR spectra confirmed that the mercuration took place at the C-4 atom of the pyrazole ring. X-ray crystal structure analysis of 4,4-bis(chloromercurio)-3-methylpyrazoline-5-one revealed almost linear coordination of both mercury atoms [Hg–C 2.099(6) and 2.104(5) ; Hg–Cl 2.330(2) and 2.338(2) ; C–Hg–Cl 171.1(2) and 174.4(2)°]. The slight deviation from linearity is caused by contacts with nitrogen or oxygen atoms from the neighbouring molecule [HgN 2.768(5) and HgO 2.748(5) ]. The molecules are interconnected by hydrogen bonds N–HCl of 3.286(5) .     

Synthesis and magneto-structural correlation of a new maleato bridged copper(II) coordination polymer

A one-dimensional (1-D) copper(II) coordination polymer [Cu(maleate)(2,2′-bipyridyl)] _n ·2H₂O has been synthesised. Single crystal X-ray diffraction study reveals that maleate ion bridges two adjacent copper(II) centres along the chain in a syn–anti fashion. A complete cryomagnetic investigation of the title complex correlates well with the distorted square pyramidal geometry of the central copper(II) ion and bridging nature of the maleate. A τ value of 0.26 indicates the distortion towards tbp coordination allowing the magnetic orbital to acquire some character leading to a weak antiferromagnetic interaction having J = −0.26 cm⁻¹. The complex has also been firmly established from several other instrumental techniques like Fourier transform infrared (FT-IR) and EPR spectroscopies.     

On the largest eigenvalues of trees with perfect matchings

Let λ₁ (G) and Δ (G), respectively, denote the largest eigenvalue and the maximum degree of a graph G. Let be the set of trees with perfect matchings on 2m vertices, and . Among the trees in , we characterize the tree which alone minimizes the largest eigenvalue, as well as the tree which alone maximizes the largest eigenvalue when . Furthermore, it is proved that, for two trees T ₁ and T ₂ in (m≥ 4), if and Δ (T ₁) > Δ (T ₂), then λ₁ (T ₁) > λ₁ (T ₂).     

Vibrational isotope effect by the low rank perturbation method

Mathematical formalism of the Low Rank Perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation with a standard assumption that force field does not change under isotopic substitutions. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at ρ atomic sites is considered. In the LRP approach vibrational frequencies ω _k and normal modes of the isotopomer B are expressed in terms of the vibrational frequencies ν _i and normal modes of the parent molecule A. In those relations complete specification of the normal modes is not required. Only amplitudes at sites τ affected by the isotopic substitutions and in the coordinate direction s (s = x, y, z) are needed. Out-of-plane vibrations of the (H,D)-benzene isotopomers are considered. Standard error of the LRP frequencies with respect to the DFT frequencies is on average . This error is due to the uncertainty of the input data (± 0.5 cm⁻¹) and in the absence of those uncertainties and in the harmonic approximation it should disappear. In comparing with experiment, one finds that LRP frequencies reproduces experimental frequencies of (H,D)-benzene isotopomers better () than scaled DFT frequencies () which are designed to minimize (by frequency scaling technique) this error. In addition, LRP is conceptually and numerically simple and it also provides a new insight in the vibrational isotope effect in the harmonic approximation.     

Direct and exchange contributions to inner and outer radii in many-electron atoms

Within the Hartree-Fock framework, the spinless two-electron density function Γ (r ₁, r ₂) consists of direct Γ_di (r ₁, r ₂) and exchange Γ_ex (r ₁, r ₂) parts. Accordingly, the inner and outer radii in many-electron systems are rigorously separated into the direct and exchange contributions, i.e., and . It is generally shown that and , where is the usual average radius of an electron. Numerical examinations of the direct and exchange contributions for the 102 atoms from He to Lr in their ground states find that the electron exchange works to decrease and increase . However, the exchange parts are very small and the direct parts essentially govern the inner and outer radii.     

Synthesis, crystal structure and density functional theoretical studies on phenyl-thiocarbamic acid-O-pyridin-4-ylmethyl ester

The title compound of phenyl-thiocarbamic acid-O-pyridin-4-ylmethyl ester has been synthesized and characterized by elemental analysis, IR, electronic spectroscopy and X-ray single crystal diffraction. Density functional theory (DFT) method calculations of the structure, atomic charge distributions and the thermodynamic properties at different temperatures have been performed. Calculated results show that DFT method at B3LYP/6-311G^** level can well reproduce the structure of the title compound. The predicted vibrational frequencies are compared with the experimental ones and they support each other on the whole. The atoms of sulfur, oxygen and the atom of nitrogen from pyridine ring all have bigger negative charges, which make the title compound become a multidentate organic ligand. The correlation equations of the thermodynamic properties of and with temperature are also obtained.     

Interaction of a finite quantum system with an infinite quantum system that contains a single one-parameter eigenvalue band

Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied, however strong the interaction between those two systems. This provides a strong verification of the suggested method.     

Kinetics and Equilibria for Complex Formation between Palladium(II) and Chloroacetate

Kinetics and equilibria for the formation of a 1:1 complex between palladium(II) and chloroacetate were studied by spectrophotometric measurements in 1.00 mol HClO₄ at 298.2 K. The equilibrium constant, K, of the reaction

New hexamethine–hemicyanine dyes for the development of integrated optochemical sensors

New far-visible absorbing anilino-cyanine dyes have been synthesised for future application as chromoionophores in integrated waveguide absorbance optodes based on bulk optodes. The effect of the heterocycle, of the substitution of the heterocyclic nitrogen and of the type of heptamethine central ring on the pK _a values (4.3–8.2 in ethanol–water solutions and 9.5–11.0 in plasticised PVC membranes), on the spectroscopic characteristics of the dye and on photostability is discussed. pH-selective bulk optodes have been formulated as a first approach to develop ion-selective optodes, and sensitivity, repeatability, lifetime and response time have been determined. The dyes show good analytical behaviour for use as chromoionophores for the development of ion-selective optodes. Reversible (80–87%), fast (tr_90% = 0.94–2.28 min) and pH-sensitive membranes (slopes of 0.09–0.23 ΔAbs·pHdec^–1, absorbance range 0.19–0.53) have been obtained. Moreover, they exhibit good spectroscopic features for employment with integrated optochemical sensors: absorption maxima of the acidic species in plasticised PVC membranes matched those of 650–670-nm LEDs, high molar absorption coefficients ( L mol^–1 cm^–1 and L mol⁻¹ cm⁻¹) and fluorescence. Absorption spectra of the acidic and basic structures of one of the synthesised chromoionophores at different pKa values. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Determination of norfloxacin in human urine by capillary electrophoresis with electrochemiluminescence detection

A fast and sensitive approach that can be used to detect norfloxacin in human urine using capillary electrophoresis with end-column electrochemiluminescence (ECL) detection of is described. The separation column was a 75-μm i.d. capillary. The running buffer was 15 mmol L⁻¹ sodium phosphate (pH 8.2). The solution in the detection cell was 50 mmol L⁻¹ sodium phosphate (pH 8.0) and 5 mmol L⁻¹ The ECL intensity varied linearly with norfloxacin concentration from 0.05 to 10 μmol L⁻¹. The detection limit (S/N=3) was 0.0048 μmol L⁻¹, and the relative standard deviations of the ECL intensity and the migration time for eleven consecutive injections of 1.0 μmol L⁻¹ norfloxacin (n=11) were 2.6% and 0.8%, respectively. The method was successfully applied to the determination of norfloxacin spiked in human urine without sample pretreatment. The recoveries were 92.7–97.9%.      

Estimation of partial linear error-in-variables models for ρ<Superscript>−</Superscript>-mixing dependence data

Consider the partly linear regression model Y = xβ + g(t) + e where the explanatory x is erroneously measured, and both t and the response Y are measured exactly, the random error e is ρ⁻-mixing. Let be a surrogate variable observed instead of the true x in the primary survey data. Assume that in addition to the primary data set containing N observations of , which is ρ⁻-mixing data sets, an independent validation data containing n observations of is available. The exact observations on x may be obtained by some expensive or diffcult procedures for only a small subset of subjects enrolled in the study. In this paper, inspired by Berberan-Santos et al. [J. Math. Chem. 37 (2005)101], a semiparametric method with the primary data is employed to obtain the estimators of β and g(·) based on the least squares criterion with the help of validata. The proposed estimators are proved to be strongly consistent.      

Doubly Bridged Dinuclear Cadmium(II)azido Schiff Base Complexes: Synthesis, X-Ray Structure and Luminescence Properties of [Cd(L)(N3)]2(Y)2 [L = Schiff Bases, Y = ClO4 −, PF6 −]

Three new Schiff bases, -(bis(pyridin-2-yl)alkylidene)butane-1,4-diamine [(py)(R)C=N-(CH)N=C(R)(py), L: py = pyridine; R = H, -(bis(pyridin-2-yl)formylidene)butane-1,4-diamine (bpfd); R = Me, -(bis(pyridin-2-yl)methylidene)butane-1,4-diamine (bpmd); R = C, -(bis(pyridin-2-yl)bezylidene)butane-1,4-diamine (bpbd)] were prepared and used to synthesize six dinuclear cadmium(II)azido complexes of type [Cd(L)(N)](Y) [L = bpfd, Y = ClO (1a); L = bpfd, Y = PF (1b); L = bpmd, Y = ClO (2a); L = bpmd, Y = PF (2b); L = bpbd, Y = ClO (3a); and L = bpbd, Y = PF (3b)]. Two representative members of the series, 3a and 3b, have been characterized by single crystal X-ray diffraction measurements. Structural study reveals that each cadmium center in both dinuclear compounds is located in a distorted octahedral coordination environment surrounded by six nitrogen atoms—four (N1, N2, N3, N4) from tetradentate ligand, and the fifth and sixth positions occupied by nitrogen atoms (N5, N5^*) of doubly end-on bridging azides. The complexes display intraligand ¹ fluorescence and intraligand ³ phosphorescence in glassy solutions (MeOH at 77 K).     

Interfacial behavior of sulforhodamine 101 at the polarized water/1,2-dichloroethane interface studied by spectroelectrochemical techniques

The transfer mechanism of an amphoteric rhodamine, sulforhodamine 101 (SR101), across the polarized water/1,2-dichloroethane (DCE) interface was investigated using cyclic voltammetry, differential voltfluorometry and potential-modulated fluorescence (PMF) spectroscopy. The voltammetric response for the ion transfer of SR101 monoanion from water to DCE was observed as the diffusion-controlled transfer process. An unusual voltammetric response was found at 0.15 V more negative than the formal transfer potential of SR101⁻ in the cyclic voltammogram and voltfluorogram. The frequency dependence of the PMF responses confirmed the presence of the adsorption processes at negative potentials. In addition, a further transient adsorption step was uncovered at The interfacial mechanism of SR101 is discussed by comparing the results obtained from each technique.     

Pd(PBu 3 t ) Adducts of Os3(CO)12. Synthesis and Structures of Pd2Os3(CO)12(PBu 3 t )2 and Pd3Os3(CO)12 (PBu 3 t )3

Two new compounds Pd₂Os₃(CO)₁₂ , 13 and Pd₃Os₃(CO)₁₂ , 14 have been obtained from the reaction of with Os₃(CO)₁₂ at room temperature. The products were formed by the addition of two and three groups to the Os–Os bonds of Os₃(CO)₁₂. Compounds 13 and 14 interconvert between themselves by intermolecular exchange of the groups in solution. Compounds 13 and 14 have been characterized by single crystal X-ray diffraction analyses.Dedicated to Professor Brian F. G. Johnson on the occasion of his retirement – 2005.     

Unified treatment of complete orthonormal sets of nonrelativistic,quasirelativistic and relativistic sets of spinor wave functions,and Slater spinor orbitals in coordinate,momentum and four-dimensional spaces

Using the properties of tensor spherical harmonics introduced by the author in previous paper (Guseinov, Phys Lett A 372:44, 2007) and complete orthonormal scalar basis sets of nonrelativistic -exponential type orbitals ( -ETO), - momentum space orbitals ( -MSO) and z ^α-hyperspherical harmonics (z ^α-HSH) for particles with spin s = 0 the new analytical relations for the quasirelativistic and relativistic spinor wave functions and Slater spinor orbitals in coordinate, momentum and four-dimensional spaces are derived, where α = 1, 0, −1, −2,.... The 2-component quasirelativistic and 4-component relativistic spinor wave functions obtained are complete without the inclusion of the continuum. The relativistic spinor wave function sets and Slater spinor orbitals are expressed through the corresponding quasirelativistic spinor wave functions and Slater spinor orbitals, respectively. The analytical formulas for overlap integrals over quasirelativistic and relativistic Slater spinor orbitals with the same screening constants in coordinate space are also derived.     

Recurrence and Differential Relations for Spherical Spinors

We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) Ω_{κ μ}(n) used in relativistic atomic, molecular, and solid state physics, as well as in relativistic quantum chemistry. First, we list finite expansions in the spherical spinor basis of the expressions A·B Ω_κμ(n) and A·(B×C) Ω_κμ(n), where A, B, and C are either of the following vectors or vector operators: n=r/r (the radial unit vector), e ₀, e _±1 (the spherical, or cyclic, versors), (the 2×2 Pauli matrix vector), (the dimensionless orbital angular momentum operator; I is the 2×2 unit matrix), (the dimensionless total angular momentum operator). Then, we list finite expansions in the spherical spinor basis of the expressions A·B F(r)Ω_κμ(n) and A·(B×C) F(r)Ω_κμ(n), where at least one of the objects A, B, C is the nabla operator , while the remaining ones are chosen from the set .     

Unicyclic Graphs Possessing Kekulé Structures with Minimal Energy

Unicyclic graphs possessing Kekulé structures with minimal energy are considered. Let n and l be the numbers of vertices of graph and cycle C _l contained in the graph, respectively; r and j positive integers. It is mathematically verified that for and l = 2r + 1 or has the minimal energy in the graphs exclusive of , where is a graph obtained by attaching one pendant edge to each of any two adjacent vertices of C ₄ and then by attaching n/2 − 3 paths of length 2 to one of the two vertices; is a graph obtained by attaching one pendant edge and n/2 − 2 paths of length 2 to one vertex of C ₃. In addition, we claim that for has the minimal energy among all the graphs considered while for has the minimal energy.      

Theoretical study of deactivation and isomerization pathways of 1,2-dithiete in excited electronic states

The potential energy surface crossings for 1,2-dithiete have been investigated using the complete active space self-consistent field(CASSCF) method and simple group theory.Using the full Pauli-Breit spin-orbit coupling(SOC) operator(■) SO) which consists of the one-electron(■) SO1) and two-electron(■) SO2) terms,we estimate the strengths of the SOC(198.37 cm-1 when symmetry is imposed,and 211.35 cm-1 with no symmetry constraints),which plays an essential role in the spin transitions between different spin s...     

Formation of Aromatic and Other Unsaturated End Groups in Carboxymethyl Cellulose During Hot Alkaline Treatment

Carboxymethyl cellulose (CMC, DS 0.58) was treated in solutions of sodium hydroxide (0.001–1 M) at 95 °C. The treated (1–12 h) CMC samples were purified by dialysis and analyzed by UV spectroscopy and by UV resonance Raman spectroscopy (UVRRS) with excitation at 244 nm. A UV absorption maximum at 265 nm and a UVRR signal at 1650 cm⁻¹ were indicative of formation of -conjugated aldehyde end groups in CMC through -elimination. Another strong UVRR band at 1610 cm⁻¹ gave evidence on conversion of some of the -conjugated aldehyde end groups to alkali stable aromatic structures.