A multireference perturbation theory study on the vertical electronic spectrum of thiophene

The vertical electronic spectrum of the thiophene molecule is investigated by means of second and third order multireference perturbation theory (NEVPT). Single-state and quasi-degenerate NEVPT calculations of more than 25 singlet excited states have been performed. The study is addressed to the theoretical characterization of the four lowest-energy valence states, as well as the 3s, 3p and 3d Rydberg states. In addition, the excitation energies of two and valence states are also reported. For almost all the excited states, coupled cluster calculations (CCSD and CCSDR(3)) have been also carried out, using the same geometry and basis set used for the NEVPT ones, in order to make the comparison between the results of the two methods meaningful. A remarkable accordance between the NEVPT and CC excitation energies is found. The present results, over all, confirm the experimental assignments but, above all, represent an important contribution to the assignments of some low-energy states, valence and Rydberg, for which a firm interpretation is not available in the literature.     

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.     

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).     

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.      

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.     

Unified treatment of complete orthonormal sets for exponential type vector orbitals of particles with spin 1 in coordinate, momentum and four-dimensional spaces

The new formulas are obtained for complete orthonormal sets of exponential type vector orbitals of a particle with spin 1 in coordinate, momentum and four-dimensional spaces using the properties of spherical vectors and complete orthonormal scalar basis sets of -exponential type orbitals ( -ETO), -momentum space orbitals ( -MSO) and -hyperspherical harmonics ( -HSH) introduced by the author for particles with spin s = 0, where These vector orbitals are complete without the inclusion of the continuum and, therefore, their group of transformation is the four-dimensional rotation group of O(4). For overlap integrals over vector Slater orbitals with the same screening constant the analytical relations in coordinate space are also derived. It should be noted that the new idea presented in this study is the combination of spherical vectors with complete orthonormal scalar sets for radial parts of -orbitals.     

Cluster Oxalate Complexes [W3(μ3-Q)(μ2-Q)3 (C2O4)3(H2O)3]2? (Q=S, Se): Mechanochemical Synthesis and Crystal Structure

Mechanochemical reaction of cluster coordination polymers (Q=S, Se) with solid leads to the cluster core excision with the formation of anionic complexes . Extraction of the reaction mixture with water followed by crystallization gives crystalline (main product) and (1) (minor product). In the case of the Se cluster, the complex could not be isolated, and the treatment of the aqueous extract with PPh₃ gave (2) in a low yield. Alternatively, it was obtained from and in high yield. Both 1 and 2 were characterized by X-ray structure analysis. Dedicated to Academician I. I. Moiseev on the occasion of his 75th birthday and in recognition of his outstanding contribution to cluster chemistry.     

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.     

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

On the special values of monic polynomials of hypergeometric type

Special values of monic polynomials y _n (s), with leading coefficients of unity, satisfying the equation of hypergeometric type

The First Structurally Characterized Mn(III) Substituted Sandwich-type Polyoxotungstates

The new polyoxotungstates H₂O (1), · 28H₂O (2) and H₂O (3) were synthesized in aqueous solution and characterized by IR and Raman spectroscopy, energy dispersive X-ray fluorescence and single-crystal X-ray analysis. The anions in 1 and 2 are the first structurally characterized sandwich-type polyoxoanions which contain trivalent manganese atoms. The manganese atoms are coordinated by four oxygen atoms of two Keggin fragments and one water molecule, forming a square pyramid. The manganese(II) containing anions in 3 are linked via Mn–O–W-bonds, forming a two-dimensional network.Dedicated to Prof. M.T. Pope on the occasion of his retirement.     

Interaction of glycine with cationic, anionic, and nonionic surfactants at different temperatures: a volumetric, viscometric, refractive index, conductometric, and fluorescence probe study

A number of thermodynamic parameters viz. apparent molar volumes, ϕ _v , partial molar volumes, , transfer volumes, , Falkenhagen coefficients, A, Jones–Dole coefficients, B, free energies per mole of solute, , and per mole of solvent, , molar refraction, R _D , and limiting molar conductivity, , have been calculated by using the experimentally measured densities, ρ, viscosities, η, refractive indices, n _D , and specific conductivities, κ, data of glycine (0.02–0.10 m) in 0.01 m aqueous sodium dodecyl sulphate, cetyltrimethylammonium bromide, and triton X-100 (TX-100) solutions at 298.15, 303.15, 308.15, and 313.15 K. The above calculated parameters were found to be sensitive towards the interactions prevailing in the studied amino acid–surfactant–water systems. Moreover, fluorescence study using pyrene as a photophysical probe has also been carried out, the results of which support the conclusions obtained from other techniques.     

Densities and Volumetric Properties of Binary Mixtures of Formamide with 1-Butanol, 2-Butanol, 1,3-Butanediol and 1,4-Butanediol at Temperatures between 293.15 and 318.15 K

The densities of binary mixtures of formamide (FA) with 1-butanol, 2-butanol, 1,3-butanediol, and 1,4-butanediol, including those of the pure liquids, over the entire composition range were measured at temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure. From the experimental data, the excess molar volume, V _m ^E, partial molar volumes, and , at infinite dilution, and excess partial molar volumes, and , at infinite dilution were calculated. The variation of these parameters with composition and temperature of the mixtures are discussed in terms of molecular interactions in these mixtures. The partial molar expansivities, and , at infinite dilution and excess partial molar expansivities, and , at infinite dilution were also calculated. The V _m ^E values were found to be positive for all the mixtures at each temperature studied, except for FA + 1-butanol which exhibits a sigmoid trend wherein V _m ^E values change sign from positive to negative as the concentration of FA in the mixture is increased. The V _m ^E values for these mixtures follow the order: 1-butanol < 2-butanol < 1,3-butanediol < 1,4-butanediol. It is observed that the V _m ^E values depend upon the number and position of hydroxyl groups in these alkanol molecules.     

Thermal analysis of PVA/CNTs 2D membrane

The power–time curves of micellar formation of two anionic surfactants, sodium laurate (SLA) and sodium dodecyl sulfate (SDS), in N,N-dimethyl acetamide (DMA) in the presence of various long-chain alcohols (1-heptanol, 1-octanol, 1-nonanol and 1-decanol) were measured by titration microcalorimetry at 298 K. The critical micelle concentrations (CMCs) of SLA and SDS under various conditions at 298 K were obtained based on the power–time curves. Thermodynamic parameters (, and ) for micellar systems at 298 K were evaluated according to the power–time curves and the mass action model. The influences of the number of carbon-atom and the concentration of alcohol were investigated. Moreover, combined the thermodynamic parameters at 303, 308 and 313 K in our previous work and those of 298 K in the present work for SLA and SDS in DMA in the presence of long-chain alcohols, an enthalpy–entropy compensation effect was observed. The values of the enthalpy of micellization calculated by direct and indirect methods were made a comparison.     

Relationship between current response and time in ion transport problem including diffusion and convection. 1. An analytical approach

   The mathematical models of the ion transport problem in a potential field are anayzed. Ion transport is regarded as the superposition of diffusion and convection. In the case of pure diffusion model the classical Gottrell’s result is studied for a constant as well as for the time dependent Dirichlet data at the electrode. Comparative analysis of the current response and the classical Gottrellian is given on the obtained explicit formulas. The approach is extended to find out the current response corresponding to the diffusion-convection model. The relationship between the current response and Gottrellian is obtained in explicit form. This relationship permits one to compare pure diffusion and diffusion-convection models, including asymptotic behaviour of current response and an influence of the convection coefficient. The theoretical result are illustrated by numerical examples.      

Identifiability of chemical reaction networks

We consider the dynamics of chemical reaction networks under the assumption of mass-action kinetics. We show that there exist reaction networks for which the reaction rate constants are not uniquely identifiable, even if we are given complete information on the dynamics of concentrations for all chemical species of . Also, we show that there exist reaction networks such that their dynamics are identical under appropriate choices of reaction rate constants, and present theorems that characterize the properties of , , that make this possible. We use these facts to show how we can determine dynamical properties of some chemical networks by analyzing other chemical networks.     

On zeroth-order general Randić index of conjugated unicyclic graphs

Let G be a graph and d _v denote the degree of the vertex v in G. The zeroth-order general Randić index of a graph is defined as where α is an arbitrary real number. In this paper, we investigate the zeroth-order general Randić index of conjugated unicyclic graphs G (i.e., unicyclic graphs with a perfect matching) and sharp lower and upper bounds are obtained for depending on α in different intervals.     

Interaction of an isolated state with an infinite quantum system containing several one-parameter eigenvalue bands: II. time-dependent case

Time-dependent properties of a state that interacts with an infinite dimensional quantum system containing several one-parameter eigenvalue bands are considered. This is done by a new mathematical method that produces correct results, however strong the interaction between the state and the system . It is shown that in the case of the weak interaction one obtains standard results that are usually obtained within the formalism of the perturbation expansion method. In particular, if the eigenvalue E of the state is embedded inside the range of the unperturbed eigenvalues, time evolution of the state that is initially prepared in the state has typical exponential decay behavior. One also reproduces standard results concerning probabilities of the transition of the state at infinite time (t=∞) into various eigenvalue bands. However, if the interaction is strong, one finds much more complex and much more complicated behavior.     

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.     

Mechanism of the catalyzed by cysteine electroreduction of the insoluble in water cobalt(II) salt as a component of carbon paste electrode

The mechanism of the Co(II) catalytic electroreduction of water insoluble CoR₂ salt in the presence of cysteine was developed. CoR₂ = cobalt(II) cyclohexylbutyrate is the component of a carbon paste electrode. Electrode surface consecutive reactions are: (a) fast (equilibrium) reaction of the complex formation, (b) rate-determining reversible reaction of the promoting process of CoR(Ac⁺) complex formation, (c) rate-determining irreversible reaction of the electroactive complex formation with ligand-induced adsorption, and (d) fast irreversible reaction of the electroreduction. Reactions (a,b) connected with CoR₂ dissolution and reactions (c,d) connected with CoR₂ electroreduction are catalyzed by . Regeneration of (reactions “b,d”) and accumulation of atomic Co(0) (reaction “d”) take place. Experimental data [Sugawara et al., Bioelectrochem Bioenergetics 26:469, 1991]: i _a vs E (i _a is anodic peak, E is cathodic accumulation potential), i _a vs , and i _a vs pH have been quantitatively explained.