Reorientational motions of substituted benzenes in the crystalline state. A consideration of the dielectric relaxation of appropriate site models having non-equivalent sites

A method is developed for solving the basic rate equations, and hence the dielectric behaviour, of C_N-type barrier systems. Both adjacent-jump (A–J) and multiple-jump (M-J) models are considered. It is shown that for certain six-fold barrier systems the active dielectric relaxation mode is characterized by a relaxatuion time τ which is, to a good approximation, inversely proportional to the transition probability κ₁₂ ≡ κ₁ = κ₀ exp(?W/κT) where W is the principal barriers height. The proportionality factor is either constant or is a slowly varying function of temperature when compared with that for κ₁.     

Configuration interaction study of H2 using a modified slater-type orbital

A non-standard 1s basis function, χ = (1 + ar²) exp(?ζr), is used to approximate the ground state of the hydrogen molecule in a configuration interaction framework and using numerical integration over MO's. Results are compared to the traditional 1s STO.     

A quadratically convergent reference state optimization procedure

A quadratically convergent procedure for the optimization of multiconfigurational reference states is presented and analyzed. The optimal reference state is determined from the energy variation principle by means of a sequence of unitary transformations of the form exp(i$\text{Λ}$exp(i$\text{k}$, where the hermitean operators $\text{Λ}$ and $\text{k}$ generate transformations of orbitals and correlation coefficients, respectively. Sample calculations are carried out within the Pariser—Parr—Pople model using a correlated reference state suggested by Clementi and Veillard. For the systems considered so far, convergence is achieved after 2–4 transformations.     

Note on the Hylleraas-Eckart split-shell description of the groundstate of atomic two-electron systems

When the space part of the wavefunction of the groundstate of atomic two-electron systems is taken to be Φ(1, 2)=u(1)v(2)+v(1)u(2), where u=exp(?ar) and v=exp(?br), the parameters a and b as well as the energy associated with Φ(1,2) can be determined in the form of power series involving the nuclear charge Z. For small values of Z the convergence of these series is rather slow. The quantities mentioned, however, may be determined to any degree of accuracy by a method of stepwise approximation.     

Study of thermal decomposition of poly(vinyl chloride) type polymers with the use of model substances—III: Gas phase pyrolysis of acetates

The decompositions of the following poly(vinylacetate) models were investigated in the gas phase: 2-acetoxypentane (in the range 323–380°), meso and racem. 2,4-diacetoxypentane (325–375°), 4-acetoxy-1-pentene (302–375°), 4-acetoxy-2-pentene (314–381°), 5-acetoxy-2-hexene (328–391°), and 7-acetoxy-3,5-nonadiene (299–361°). The decompositions are homogeneous unimolecular first-order reactions with rate constants of 1·04 × 10¹³ exp(?45·/RT, 1·63 × 10¹³ exp(?45·4/RT), 1·01 × 10¹³ exp(?44·5/RT), 5sd76 × 10¹² exp(?42·8/RT), 2·01 × 10¹³ exp(?45·5/RT), and 3·29 × 10¹² exp(?41·5/RT) sec^?1, respectively. The two 2,4-diacetoxypentane stereoisomers decompose at almost the same rate. From the course of decomposition of models in the gas phase, possible conclusions about decomposition of polymer are drawn. The role of configuration of sequences, double bonds, their number and geometric isomerism in the macromolecular chains are discussed in connection with elimination of acetic acid from poly(vinyl acetate).     

One-dimensional models of polymer dynamics. I. Dashpot-spring models applied to a single rotor

The proposion of Clark and Zimm that a dashpot and a spring can be used in place of a set of rotational barriers in polymer dynamics is studied. The simplest possible case is examined here, that of a single rotor. Reasons for altering the Clark–Zimm diffusion equation are presented and an alternative diffusion equation is proposed. The results of both diffusion equations for the correlation function 〈exp[?iθ(0)] exp[iθ(t)]〉 (θ is the angular position of the rotor) are compared with the correlation function for a rotor in an n-fold cosine potential. Although the two diffusion equations differ, both agree well with the n-fold cosine model for barriers above a few k_BT. This agreement is obtained in the absence of adjustable parameters, and motivates the application of these two diffusion equations to polymeric systems.     

Variational RRKM theory calculation of thermal rate constant for carbon—hydrogen bond fission reaction of nitro benzene

The present work provides quantitative results for the rate of unimolecular carbon-hydrogen bond fission reaction of benzene and nitro benzene at elevated temperatures up to 2000 K. The potential energy surface for each C-H (in the ortho, meta, and para sites) bond fission reaction of nitro benzene was investigated by ab initio calculations. The geometry and vibrational frequencies of the species involved in this process were optimized at the MP2 level of theory, using the cc-pvdz basis set. Since C-H bond fission channel is barrier less reaction, we have used variational RRKM theory to predict rate constants. By means of calculated rate constant at the different temperatures, the activation energy and exponential factor were determined. The Arrhenius expression for C-H bond fission reaction of nitro benzene on the ortho, meta and para sites are k(T) = 2.1 × 10¹⁷exp(?56575.98/T), k(T) = 2.1 × 10¹⁷exp(?57587.45/T), and k(T) = 3.3 × 10¹⁶exp(?57594.79/T) respectively. The Arrhenius expression for C-H bond fission reaction of benzene is k(T) = 2 × 10¹⁸exp(?59343.48.18/T). The effect of NO₂ group, location of hydrogen atoms on the substituted benzene ring, reaction degeneracy, benzene ring resonance and tunneling effect on the rate expression have been discussed.     

Theory of the expansion of wave functions in a gaussian basis

The convergence properties of the expansions of (a) the function 1/r and (b) the function exp(-αr) in an even-tempered basis of Gaussians are studied analytically. The starting points are the Gaussian integral representations of 1/r and exp(?αr). One arrives at an expansion in a finite number of Gaussians in three steps: (1) a restriction of the integration domain, (2) a variable transformation, and (3) discretization of the integral. The cutoff error goes in both cases essentially as exp(?ah), and the discretization error, as exp(?b/h). The minimum overall error is reached for the β-parameter of an even-tempered basis β ∽ exp(c/√n), where n is the dimension of the basis, and the error itself decreases as ? ∽ exp(?d√n). Different optimum basis parameters are obtained depending on which quantity one wants to minimize, e.g., the error of the energy expectation value, the distance in Hilbert space, the variance of the energy, or the density at the nucleus. © 1994 John Wiley & Sons, Inc.     

The determination of the redox state of a dissolved depolariser by cyclic voltammetry in the case of electrochemically reversible systems

In the case of electrochemically reversible systems, it is possible to determine the redox state of the dissolved depolariser with the help of cyclic voltammetry. This can be done by measuring the currents at the lower and upper limits of the potential range, i.e., the cathodic and anodic currents i_λ,c and i_λ,a. The difference I=|i_λ,a|−|i_λ,c| is a reliable parameter for distinguishing solutions of the reduced and oxidised forms of the depolariser. When background currents are of appreciable size, the value of I has to be compared with that of a solution without the depolariser. When the solution simultaneously contains the oxidised and reduced forms of the depolariser, I is a linear function of their molar ratio. Hence, it is possible to follow a coulometric titration using cyclic voltammetry.     

Chromatographic properties of mesoporous silica gel modified with acetylacetonates of europium and copper

New mesoporous materials prepared from tetraethoxysilane, i.e., sorbents obtained with the use of surfactants, are synthesized. Their chromatographic polarity is assessed quantitatively. Their Kovats retention indices and Rohrschneider polarity coefficients are calculated. Based on physicohemical data, it is demonstrated that modifying supports with metal chelates changes the structure and properties of the initial sorbents: the differential molar Gibbs free energies rise considerably for sorbent modified with copper acetylacetonate with respect to ethanol (?ΔG′ _i = 7.09 kJ/mol) and nitromethane (?ΔG′ _i = 6.75 kJ/mol), relative to the initial silica gel (5.43 and 4.15 kJ/mol, respectively).     

The connection between Young's rule for apparent molar volumes and a Young's rule for density

It is shown that the Young's rule approximation for apparent molar volumes is equivalent to a Young's rule approximation for density, provided that volumetric concentrations are used. If the densities of the constituent binary solutions are evaluated at the molar ionic strength S of the ternary solution, for example, then $$d(S) = y_1 d_1 (S) + y_2 d_2 (S)$$ where the y _i are ionic strength fractions. However, if the binary solution densities d _i are evaluated at the same total equivalent concentration E of the ternary solution, then the coefficients of d_i become equivalent fractions, etc. A small correction term can be included to improve agreement with experiment, and the results are easily extended to multicomponent systems. This form of the density rule does not follow from Young's rule if the various quantities are in molality or other mass units. Relations among various types of apparent volumes are clarified. Three binary evaluation strategies are considered for both volume and mass units, based on evaluating binary solution densities at constant molarity, constant equivalents, and constant ionic strength. Some binary approximation examples are given for aqueous solutions.     

On some problems in quantum pharmacology I. The partition functions

We performed an analysis of the drug-receptor equilibrium constant, K_i = {Q_DiRQ_Di^?1Q_R^?1} exp (?Δ_εi/kT). It is shown that, for a group of nonrotating molecules we may consider the product of the partition functions as constant if log(mass) = constant for all the molecules.     

Hypervirial theorem and ladder operators. Recurrence relations for harmonic oscillator integrals

A second-quantization formalism combined with a hypervirial theorem is used to derive new recurrence relations for one-dimensional harmonic oscillator matrix elements. The most general case of 〈m|f(â, â⁺)|n〉 is considered, and the recurrence relations forf(â, â) = X^k, exp(?βX), and exp(?X²) are given as examples. The relations obtained are considerably simpler than those derived by using only the hypervirial theorem; comparatively, the recurrence relations presented here have the advantage of avoiding the use of the quantum mechanical sum-rules when determining initial matrix elements. The proposed procedure can be used to determine the recurrence relations for other potentials as well as to evaluate the two-center integrals.     

Reactions of CFBr studied by laser-induced fluorescence

Laser-induced fluorescence has been used to study reactions of CFBr radicals in a discharge-flow system. Arrhenius expressions of (1.9 ± 0.6) ξ 10^?12 exp(?762± 92/T) and (1.4 ± 0.3) ξ 10^?12 exp(?533 ± 62/T) cm³ molecule ^?1s^?1 for their reactions with Cl₂ and Br₂ respectively. Upper limits were obtained for the rate of reaction of CFBr with O₂ and F₂CCFBr.     

Oxidation of cyanogen. II. The mechanism of the oxidation

A detailed investigation of the mechanism of cyanogen oxidation is presented. Recent induction time measurements of ignition in cyanogen–oxygen–argon mixtures behind reflected shocks are computer modeled to obtain an agreement between the experimental and calculated values. A 15-step reaction scheme is suggested to reproduce the parameters E and β_i in the experimental parametric relation: τ = 10^αexp(E/RT)IIC_i^βi. An explanation is offered to the very strong dependence of the induction time on the cyanogen concentration and the very weak dependence on the oxygen concentration. The sensitivity spectrum shows that the induction time is highly dependent on the O + C₂N₂ → NCO + CN and NCO + M → N + CO + M reactions (shortened) and the O + NCO → CO + NO and N + NCO → N₂ + CO reactions (increased).     

Counterion influence on the N–I–N halogen bond

A detailed investigation of the influence of counterions on the [N–I–N]⁺ halogen bond in solution, in the solid state and in silico is presented. Translational diffusion coefficients indicate close attachment of counterions to the cationic, three-center halogen bond in dichloromethane solution. Isotopic perturbation of equilibrium NMR studies performed on isotopologue mixtures of regioselectively deuterated and nondeuterated analogues of the model system showed that the counterion is incapable of altering the symmetry of the [N–I–N]⁺ halogen bond. This symmetry remains even in the presence of an unfavorable geometric restraint. A high preference for the symmetric geometry was found also in the solid state by single crystal X-ray crystallography. Molecular systems encompassing weakly coordinating counterions behave similarly to the corresponding silver(i) centered coordination complexes. In contrast, systems possessing moderately or strongly coordinating anions show a distinctly different behavior. Such silver(i) complexes are converted into multi-coordinate geometries with strong Ag–O bonds, whereas the iodine centered systems remain linear and lack direct charge transfer interaction with the counterion, as verified by ¹⁵N NMR and DFT computation. This suggests that the [N–I–N]⁺ halogen bond may not be satisfactorily described in terms of a pure coordination bond typical of transition metal complexes, but as a secondary bond with a substantial charge-transfer character.     

Radiation induced transformation of CO in cyclohexane

The radiation induced incorporation of CO in cyclohexane leads to formation of: bicyclohexylketone (G_i = 2.40), α, α-bicyclohexyldiketone (G_i = 0.90), cyclohexanone (G_i = 0.24), cyclohexanol (G_i = 0.20), cyclohexanecarboxylic acid (G_i = 0.10), in addition to bicyclohexyl (G_i = 1.30) and polymers. The G_i-values are strongly dependent on the CO-concentration in the solution. Probable reaction mechanisms are presented.     

CH and C-atom time histories in dilute hydrocarbon pyrolysis: Measurements and kinetics calculations

CH and C-atom concentration-time histories were measured during pyrolysis of highly dilute mixtures (6 to 100 ppm) of ethane or methane in argon behind reflected shock waves over the temperature range 2500 to 3800 K and pressure range 0.5 to 1.3 atm. CH was detected using narrow-linewidth laser absorption at 431 nm. C-atom concentrations were measured using atomic resonance absorption spectroscopy (ARAS) at 156.1 nm. These data allow improved understanding of dilute hydrocarbon pyrolysis. A pyrolysis reaction mechanism was developed which fits essential characteristics of the CH and C-atom profiles (time to peak, peak concentration, and 50% decay time) within ±25%. Critical reactions for which rate coefficient data were not previously available are: Best-fit rate coefficients, valid over the range 2500 to 3800 K, are: k₄ = 5.0 × 10¹⁵ exp(?42800 K/T), k₅ = 4.0 × 10¹⁵ exp(?41800 K/T), k₆ = 1.3 × 10¹⁴ exp(?29700 K/T), and k₇ = 1.9 × 10¹⁴ exp(?33700 K/T) cm³ mol^?1 s^?1