Multiple solutions of coupled-cluster doubles equations for the Pariser–Parr–Pople model of benzene

To gain some insight into the structure and physical significance of the multiple solutions to the coupled-cluster doubles (CCD) equations corresponding to the Pariser–Parr–Pople model of cyclic polyenes, complete solutions to the CCD equations for the ¹A _1g ^- states of benzene are obtained by means of the homotopy method. By varying the value of the resonance integral ß from –5.0 to –0.5 eV, we cover the so-called weakly, moderately, and strongly correlated regimes of the model. For each value of ß, 230 CCD solutions are obtained. It turned out, however, that only for a few solutions a correspondence with some physical states can be established. It has also been demonstrated that, unlike for the standard methods of solving CCD equations, some of the multiple solutions to the CCD equations can be attained by means of the iterative process based on Pulay's direct inversion in the iterative subspace approach.     

Quasispin symmetry for the derivation of coupled cluster equations for the Hubbard model of benzene

The concept of quasispin is applied to a special case of the Pariser–Parr–Pople (PPP ) model of the benzene molecule, namely, the Hubbard Hamiltonian. Added to the spin, space, and alternancy symmetries already taken into account in the PPP Hamiltonian, this new symmetry, called quasispin symmetry, has the effect of reducing the size of the CI matrix. Coupled cluster (CC ) equations are then obtained after applying the CC approach with doubles as well as its extension that accounts for triexcited clusters (CCSDT -1). The derivation of these equations following the use of quasispin to the Hubbard model of benzene constitutes the most simple nontrivial example of CC results. In addition, the CC equations can be written in explicit algebraic form using the symbolic computation language MAPLE.     

Potentiometric sensors based on new active components in the multisensor determination of homologues anionic surfactants

Potentiometric sensors are proposed on the basis of alkyl sulfates and cationic copper(II) complexes with organic reagents selective to anionic surfactants. Physical and chemical properties of the ionophores (composition, thermal stability, solubility) are determined in aqueous solutions and in the membrane phase. The studied compounds are poorly soluble (K _s = n × 10^–22–n × 10^–20) and thermally stable at 80?90°C. The main electroanalytical properties of sensors are estimated, i.e., analytical range in solutions of sodium alkyl sulfates 2 × 10^–7–1 × 10^–2 M; 46 <α < 66 mV/рc; LOD = 1 × 10^–7 M; response time 8–9 s in a solution of sodium dodecyl sulfate with the concentration not lower than 1 × 10^–4 M; potential drift 2–3 mV/day; and lifetime 12 months. The multisensor determination of homologues sodium alkyl sulfates in model mixtures and natural waters is performed using the proposed sensors.     

Correlation effects in the PPP model of alternant π-electronic systems: two-point Padé approximant approach

A general procedure, based on the two-point Padé approximant technique, is formulated, enabling an interpolation of the low-lying energy levels of the PPP (Pariser–Parr–Pople) Hamiltonian over the divergency gap separating the asymptotic perturbation expansions in both strongly and weakly correlated limits. The methods for the determination of the first few terms of the perturbation expansions in both limits are also briefly outlined. The procedure is applied to the five lowest singlet energy levels of the PPP model of the benzene molecule and the results are compared with the exact solutions for this model. The advantages as well as the shortcoming of this approach are pointed out and illustrated on the model calculation for benzene. The applicability of this technique to larger π-electronic systems is discussed and a feasible procedure for its implementation is formulated.     

Numerical evaluation of second and third virial coefficients of some inert gases via classical cluster expansion

In this project we evaluate second virial coefficient of some inert gases via classical cluster expansion, assuming each atomic pair interaction is of Lennard-Jones type. We also try to numerically evaluate the third virial coefficient of Argon gas based on bipolar-coordinate integration (Mas et?al. in J Chem Phys 10:6694, 1999), assuming the same Lennard-Jones potential as before. The second virial coefficient (Vega et?al. in Phys Chem Chem Phys 4:3000–3007, 2002) calculated from our model are compatible to the experimental data [19] The temperature at which B ₂(T) → 0 is called the Boyle’s temperature T _B (Vega et?al. in Phys Chem Chem Phys 4:3000–3007, 2002) for the Lennard-Jines (12-6) potential. For the second virial coefficient of He, we obtain the Boyle’s temperature as follow: T _B ?=?34.9312438964844 (K) B ₂(T) = 9.82958 × 10^?6 (cm³/mol).     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: XII. Calculation of the 13C NMR chemical shifts of fluoromethanes at the DFT level

Calculation was carried out of chemical shifts in ¹³C NMR spectra for a series of fluoromethanes CH _n F_4?n (n = 0–4) by the methods of the electron density functional theory GIAO-DFT taking in consideration the solvent effect in the framework of the polarizable continuum model Tomasi IEF-PCM. The best results were obtained at the use of Keal-Tozer KT3 functional combined with Pople standard basis sets 6-311G(d,p) and 6-311++G(d,p), and also with Jensen special set pcS-2 containing tight p-functions. The optimum reference in the calculation of chemical shifts in ¹³C NMR spectra for the fluoromethanes series is TMS.     

Dipole moment and conformational properties of poly(methacrylic acid) in solvents with hydrogen bonding

Dielectric polarization of solutions of un-ionized linear poly(methacrylic acid) in polar associated liquids is studied in the temperature range 20–50°C. The solutions are in methanol, with the molar fraction of polymer units x ₂ = (3 × 10^?3)?(1.5 × 10^?2), and in water, with x ₂ = (4 × 10^?5)?(4 × 10^?3). The permittivity ε₁₂ of the polyacid solutions in methanol is shown to be lower than the permittivity of the pure solvent ε₁; the permittivity of the polyacid solutions in water exceeds ε₁ of water in the concentration range x ₂ = (4 × 10^?5)?(2.13 × 10^?4) and becomes lower than ε₁ as the polymer concentration in the solution increases further. A procedure for estimating the dipole moment μ₂ per monomer unit of the polymer macromolecule in solution is proposed. The estimation is based on Buckingham’s statistical polarization theory for a two-component mixture of polar molecules under the conditions of infinite dilution. The μ₂ values amount to 2.76–2.14 D (x ₂ < 1.5 × 10^?2) in methanol at 20–50°C and to 11.4?3.8 D (x ₂ < 2.13 × 10^?4) in water at 20–40°C. The difference in the dipole moments of the polyacid and in the patterns of their temperature dependences in methanol and in water is due to the effects of the polyacid-solvent hydrogen bonding, to intramacromolecular hydrogen bonds, and to specificity of the local structure of the solvent. It is shown that the μ₂ value corresponds to the dipole moment of the solvates and decreases with temperature owing to changes in the stoichiometry of the solvates, to the formation of cyclic associates in the macromolecule, and to conformational changes in the chain.     

Anodic overoxidation of poly-p-phenylene in aqueous electrolytes

Poly-p-phenylene (PPP), synthesized chemically by the Kovacič method, was mixed with 7.5% carbon black and used as a pressed thin-layer electrode (100 μm) on Pt mesh. Its overoxidation as an anode in aqueous acid electrolytes (8–18 M H₂SO₄, 8–11.3 M HClO₄, 8 M HBF₄) was investigated systematically.Slow cyclic voltammetry reveals that the reversible redox peak 1, leading to an insertion compound up to 1 F per mole (C₆H₄)₆, is following by a large second peak 2 at more positive potentials, corresponding to about 15 F with respect to the unit mentioned above. Peak separation increases with increasing acid concentration due to a negative shift of the insertion potential (peak 1) by 60 mV mol⁻¹ dm³, but normal Nernst behaviour is observed in the case of peak 2. The strong decay of the current efficiency for reversible cycling of PPP at concentrations below 10 M can be understood readily from these findings. The overoxidation starts with the formation of the polymer radical cation, which is oxidized further to the quinone, then to the product of ring opening and finally to the product of cleavage of the polymer chain. The final product seems to be a derivative of maleic acid. The p-quinone path is preferred over the o-quinone path, quite contrary to the case with graphite. The practical consequences with respect to battery application are discussed in detail.     

Calculation of the nmr relaxation time of dilute 129 Xe gas

The spin-lattice relaxation time T₁ of ¹²⁹ Xe gas is calculated with the kinetic theory due to Chem and Snider. A Lennard-Jones (12,6) potential functions is employed as a model for the spherical potential while the transient spin-rotation interaction is assumed to be responsible for the relaxation of the nuclei. Cross sections for spin transitions on collisions are calculated either quantum mechanically or semiclassically depending on the relative energy. The temperature dependence of T₁ is determined in the range 200–450 K. The calculated value of T₁ at 298 K and 1 amagat is 2.8 x 0⁵ s while the value measured by Hund and Carr is (2.0 ± 0.2) x 10⁵s.     

Osmotic coefficient data for NaOH–NaCl–NaAl(OH)4–H2O system measured by an isopiestic method and modeled using Pitzer's model at 298.15 K

Osmotic coefficient data were obtained for the aqueous solutions of NaOH–NaCl–NaAl(OH)₄. The solutions were prepared by dissolving AlCl₃·6H₂O in aqueous NaOH solutions. The osmotic coefficients of the solutions were measured by an isopiestic method at 25°C. The osmotic coefficient data were used to evaluate the unknown binary and mixing parameters of Pitzer's model for the aqueous NaOH–NaCl–NaAl(OH)₄–H₂O system. The binary Pitzer's parameters, β⁽⁰⁾, β⁽¹⁾, and C^φ, for NaAl(OH)₄ were found to be −0.0083, 0.0710, and 0.00184 respectively. These binary parameters were obtained from the data on the ternary system. This was necessary since it was not possible to prepare a single (NaAl(OH)₄) solution. The mixing parameters, Θ_{OH⁻Al(OH)⁻4}, Θ_{Cl⁻Al(OH)⁻4}, Ψ_{Na⁺OH⁻Al(OH)⁻4}, and Ψ_{Na⁺Cl⁻Al(OH)⁻4} were found to be −0.2255, −0.2430, −0.0388, and 0.2377 respectively. The experimental osmotic coefficient data were correlated well with Pitzer's model using the parameters obtained.     

Trace fluoride determination with specific ion electrode

A method is described for determining 10^-5–10^-4M fluoride in a variety of solutions potentiometrically with a fluoridc-specific electrode, by a standard addition method. Any change of ionic strength or the nature of the solution that might alter activity coefficients or junction potentials is minimized. The relationship between potential and fluoride concentration thus follows the Nernst equation, and the unknown concentration can be calculated. Experimental data are given for solutions of sodium choride, sodium nitrate, acidified sodium silicate and sodium hydroxide, lithium chloride, and phosphoric acid. Metal ions (e.g., Al³⁺, UO₂²⁺, Fe³⁺, Th⁴⁺) that interfere by forming complexes with fluoride can be precomplexed with phosphoric acid. The relative error is estimated at 10%, and the relative standard deviation is less than 5% over the concentration range 10^-5–10^-4M fluoride.     

Application of the many-body perturbation theory by using localized orbitals

Diagrammatic formulation of the many-body perturbation theory is investigated when both the occupied orbitals and the virtual ones are localized, i.e., they are unitary transforms of the canonical Hartree–Fock orbitals. All diagrams representing ground state correlation energy can be generated through fifth order. For cyclic polyenes C₆H₆ and C₁₀H₁₀ as model systems, the energy corrections are calculated in the Pariser–Parr–Pople approximation for a wide range of the coupling constant β^?1, through fourth order including some fifth order terms. The results are compared to those obtained by other methods: perturbation theory by using canonical orbitals and full CI. The effect of neglecting contributions from orbitals localized into neighboring sites is also studied.     

Magnetic circular dichroism and absorption spectra of the mononegative and dinegative ions of [16] annulene

The magnetic circular dichroism (MCD) and absorption spectra of the mononegative and dinegative ions of [16] annulene have been measured in the 16000–30000 cm^?1 region. The results are interpreted using a PPP molecular orbital calculation. It is found that the D_4h symmetry, using Slater type atomic orbitals excellent agreement between experiment and calculations is obtained. The excited ²E_g and ¹E_u states of the mono- and dinegative ions have experimental averaged angular monomenta of 1.0 h and 2.3 h respectively and we conclude to planar ring structures for the ions. Variations in the parameters for the PPP calculations, i.e. B, do not influence the MCD values to any great extent.In addition, from temperature dependent measurements between 20°C and ?150°C, the thermodynamic parameters ΔH and ΔS for the equilibrium observed between molecule and ions in solution have been determined.     

Diagrammatic valence-bond theory for finite model Hamiltonians

Valence bond (VB ) diagrams form a complete basis for model Hamiltonians that conserve total spin, S, and have one valence state, ?_p, per site. Hubbard and Pariser–Parr–Pople (PPP ) models illustrate ionic problems, with zero, one, or two electrons in each ?_p, while isotropic Heisenberg models illustrate spin problems, with only purely covalent VB diagrams. The difficulty of nonorthogonal VB diagrams is by-passed by exploiting the finite dimensionality of the complete basis and working with unsymmetric sparse matrices. We introduce efficient bit manipulations for generating, storing, and handling VB diagrams as integers and describe a new coordinate relaxation method for the ground and lowest excited states of unsymmetric sparse matrices. Antiferromagnetic spin-½ Heisenberg rings and chains of N ? 20 spins, or 2^N spin functions, are solved in C₂ symmetry as illustrative examples. The lowest S = 1 and 0 excitations are related to domain walls, or spin solitons, and studied for alternations corresponding to polyacetylene. VB diagrams with arbitrary S and nonneighbor interactions are constructed for both spin and ionic problems, thus extending diagrammatic VB theory to other topologies.     

Molecular mechanism of the viscosity of aqueous glucose solutions

Experimental relations are obtained for the viscosity of aqueous glucose solutions in the temperature range of 10–80°C and concentration range 0.01–2.5%. It is found that the concentration dependence of fluidity is linear when the concentration is higher than a certain value and varies at different temperatures. The existence of such a dependence indicates that the mobilities of solvent and solute molecules are independent of the concentration of solutions. This assumption is used to construct a theoretical model, in which the structure of an aqueous glucose solution is presented as a combination of two weakly interacting networks formed by hydrogen bonds between water molecules and between glucose molecules. Theoretical relations are obtained using this model of network solution structure for the concentration and temperature dependence of solution viscosity. Experimental data are used to calculate the activation energies for water (U _w = 3.0 × 10^–20 J) and glucose molecules (U _g = 2.8 × 10^–20 J). It is shown that the viscosity of a solution in such a network structure is governed by the Brownian motion of solitons along the chains of hydrogen bonds. The weak interaction between networks results in the contributions to solution fluidity made by the motion of solitons in both of them being almost independent.     

Density of states of alternant cyclic polyenes (CH)N by a direct Lanczos method

A direct full configuration interaction approach, previously used for studying individual low-lying eigenvalues, is combined with iterative Lanczos calculations, in order to obtain global properties of large Hermitean Hamiltonian matrices. To this effect systematic generation of random start vectors is used to compute statistical approximations to the density of states (DOS). Applications for cyclic polyenes in order to illustrate the viability of the scheme modeled by correlated, high-binding Pariser-Parr-Pople (PPP) Hamiltonians of increasing complexity are presented. The degree of correlation in the solutions is controlled by the parameter β. Convergence properties of the DOS for N = 10 and N = 14 are studied varying the extent of correlation. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 719–728, 1997     

The effect of sulfide ion chemisorption on the kinetics of gold dissolution in cyanide solutions

The effect of sodium sulfide additions (from 5 × 10^?6 to 2 × 10^?5 M) on the kinetics of gold dissolution in cyanide solutions of the following composition, M: 0.1 KCN, 0.02 KAu(CN)₂, 0.5 K₂SO₄, pH 10–13 is studied. Hydrosulfide ions are shown to exert a strong catalytic effect on the dissolution kinetics of this metal in a potential range where their adsorption is accompanied by the formation of polysulfides (?0.2 < E < 0.4 V). The reaction acceleration depend on the potential and is 100-fold for E ? 0.1 V. The effect becomes more pronounced as the concentration of hydrosulfide ions increases to 10^?4 M and is almost pH-independent in the pH range from 10 to 13. An attempt to explain the found relationships is undertaken.     

BaxC60 fullerides: π Electronic peculiarities of the C60 molecule and their consequences for the solid state

The electronic structure of Ba_xC₆₀ fullerides was studied theoretically under special consideration of π electronic effects in the C₆₀ molecule. Band structure data were derived by an intermediate neglect of differential overlap (INDO) crystal orbital (CO) approach. Different electronic configuration were evaluated in the Ba-doped C₆₀ fullerides. Ba_xC₆₀ solids with x=0, 3, 4, 6 are insulators. For a Ba₅C₆₀ model extrapolated from the crystal structure of Ba₆C₆₀, a finite band gap is also predicted. For a Ca₅C₆₀-like structure of Ba₅C₆₀, a quasi-degeneracy between a metallic configuration and an insulating Mott-like state was found. With an increasing Ba-to-C₆₀ charge transfer (CT), sizable changes in the π system of C₆₀ occur. In the neural molecule and for not too high an electron count, the π electrons form more or less electronically isolated hexagon–hexagon (6–6) “double” bonds with only minor hexagon–pentagon (6–5) “double-bond” admixtures. In the vicinity of C₆₀¹²⁻, the 6–6 bonds have lost most of their double-bond character while it is enhanced for the 6–5 bonds. In highly charged anions, the π electron system of the soccer ball approaches a configuration with 12 decoupled 6π electron pentagons. For electron numbers between C₆₀ and C₆₀¹²⁻, the net π bonding is not weakened. The INDO CO results of the Ba_xC₆₀ solids are supplemented by INDO MO and ab initio (3-21 G* split-valence basis) calculations of molecular C₆₀ and some highly charged anions. Ab initio geometry optimizations show that the bond alternation of C₆₀ with short 6–6 and long 6–5 bonds is inverted in C¹²⁻₆₀. The high acceptor capability of C₆₀ is explained microscopically on the basis of quantum statistical arguments. In the π electron configurations of C₆₀ and C₆₀¹²⁻, the influence of the Pauli antisymmetry principle (PAP) is minimized. The quantum statistics of (π) electron ensembles with a deactivated PAP is of the so-called hard-core bosonic (hcb) type. In these ensembles, the on-site interaction is fermionic while the intersite interaction is bosonic. Energetic consequences of the quantum statistical peculiarities of π systems are explained with the aid of simple model systems; we selected annulenes and polyenes. Computational tools in this step are Green's function quantum Monte Carlo (GF QMC) and full configuration interaction (CI) calculations for the π electrons of the model systems. These many-body techniques were combined with a Pariser–Parr–Pople (PPP) Hamiltonian. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 333–373, 1997