Absorption line shape of two coupled oscillators decaying in two different mediums

The linear response theory is used to study the line shape of two coupled oscillators, decaying in two different baths, when one of the oscillators is coupled to the radiation field. The baths are considered to be thermally excited. The analysis is based on the computation of the correlation functions 〈a (t)a_i (0)〉 and 〈a_i (t)a(0)〉 of each oscillator, taking the coefficients associated with the operators a and a_i in the Heisenbemg representation as the starting point of the calculation. The line shape in different cases is also discussed.     

Kinetics and mechanism of the cationic polymerization of tetrahydrofuran in solution: THF-CH3NO2 system

Polymerization of tetrahydrofuran (THF) in CH₃NO₂ solvent was initiated with 1,3-dioxolan-2-ylium cations with AsF and SbF anions, as well as with esters of FSO₃H and CF₃SO₃H acids. Polymerization shows in this solvent a living feature: values of k_p (determined directly from the semilogarithmic kinetic plots) were the same for all of the listed above initiators; thus k_p is the same for AsF, CF₃SO, FSO, and SbF anions. The identity of the k_p values for complex and noncomplex (ester-forming) anions comes from the fact that in CH₃NO₂ solvent equilibrium between macroesters and macroion pairs is shifted almost completely (K_e = 33.0 at 25°C and |THF|₀ = 7.0M) to the macroions side. Dissociation constants of the polytetrahydrofuranium ion pairs (CF₃SO and SbF anions) were measured (e.g., K_D = 2 × 10^?3 M at 25°C and |THF|₀ = 7.0M; i.e., at D = 22.8, ΔH_D = ?3.8 ± 6 kcal mole; ΔS_D = ?25 ± 2 eu). On the basis of the known values of K_D, and therefore dissociation degrees α, rate constants of propagation on the free and paired THF cations (k and k) were determined for a large range of degrees of dissociation (α from 0.15 to 0.52). The rate constants k and k were found to be the same within an experimental error of measurements (± 15% of the value of k_p). Apparently, the polytetrahydrofuranium cations are highly solvated or even separated from their anions by molecules of THF itself. At these conditions the reactivities of the solvated “free” and solvated (or separated) paired cations became undistinguishable.     

Variation of the polarizability of the hydrogen molecule ion and the hydrogen molecule with internuclear separation

The variation of the polarizability of H and H₂ with internuclear separation R = 1.6 – R = 2.4 a.u. for H and R = 1.0 – R = 2.0 a.u. for H₂ is determined using a variational method suggested by Das and Bersohn. From these data, values of 〈α〉_0,J for which nuclear motion due to zero point vibration and centrifugal stretching is taken into account, are calculated at 300°K. The relative percent increases of the motion averaged values compared to the equilibrium values are as follows: 10.50% for H and 6.52% for H₂.     

Dilute solution properties of a polybenzimidazole

Light scattering and viscometric studies have been carried out on dilute solutions of a polybenzimidazole in N,N-dimethylacetamide. The data, which span the molecular weight range 2.9 ≦ 10^?4M_w ≦ 23.3, and the temperature range 290 ≦ T/K ≦343, yield the dependence of the mean-square radius of gyration 〈s²〉_LS, the second virial coefficient A₂, and the intrinsic viscosity [η] on molecular weight M_w and temperature. The unperturbed mean-square radius 〈s〉_LS was calculated using experimental values of 〈s²〉_LS and A₂. It was found that excluded volume effects on 〈s²〉_LS are very small. The unperturbed hydrodynamic chain dimension 〈s〉_η was estimated by considering draining effects. A small value of the draining parameter was obtained. Analysis of the temperature dependence of A₂ and [eta;] leads to the conclusion that this system approaches a lower theta temperature with increasing temperature. The steric factor σ = 〈s〉/〈s〉f, based on the value of 〈s〉_f calculated for the polymer chain with free rotation, is nearly unity. Most of these properties can be interpreted in terms of long rotational units within the main chain.     

Die Kristallstruktur von NaBiO2

The crystal structure of NaBiO₂ NaBiO₂ crystallizes monoclinic in C with a = 7.39₄, b = 7.26₂, c = 5.88₆ Å, β = 127.7°; Z = 4. Parameters were refined by least-squares (555 hkl with |h?l| = 0 to 4; R = 10.9%). Angular groups [BiO₂] are twisted by 180°, forming chains [BiO_2/2O_2/2] along [001]. The MADELUNG part of lattice energy (MAPLE) is calculated and discussed.     

Comparison of theory and experiment for excited singlet states of the H2 molecule

This paper presents a survey of published and unpublished ab initio calculations of the vibrational structures of the ten lowest electronic singlet states of the hydrogen molecule up to the H(n = 1) + H(n = 2) dissociation limit. The data are based on adiabatic potential functions (clamped-nuclei electronic energies and nuclear-mass-dependent diagonal corrections). Nonadiabatic coupling has been treated ab initio within the five states. of ¹Λ symmetry (X,EF, GK, HH?) and ¹Σ I.¹Π_g. The accuracies of the theoretical energies are determined by comparisons with experimental data for H₂, HD, and D₂. The level shifts and predissociation probabilities of the excited ¹Σ states, generated by nonadiabatic coupling with the discrete and continuous vibrational structure of the ground state, and radiative properties have also been calculated.     

Leading‐order behavior of the correlation energy in the uniform electron gas

We show that, in the high‐density limit, restricted Møller‐Plesset (RMP) perturbation theory yields E = π^?2(1 ? ln 2) ln r_s + O(r) for the correlation energy per electron in the uniform electron gas, where r_s is the Seitz radius. This contradicts an earlier derivation which yielded E = O(ln|ln r_s|). The reason for the discrepancy is explained. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Magnesium chloride-supported high-mileage catalysts for olefin polymerization XI. Determinations of poly(decene-1) molecular weight chain dimension and thermal transitions

Decene-1 was polymerized with the CW catalyst and fractionated by precipitation technique. Light-scattering and viscometric measurements on these fractions established the relationship [η] = 5.19 × 10^?3 M . The unperturbed mean square end-to-end distance is (〈R〉/M)^1/2 = (6.17 ± 0.34) × 10^?9. Light-scattering data is consistent with a relatively stiff molecule with length of L = 1.75 × 10^?5 cm for poly(decene-1) with MW = 397,000. Its mean square radius of gyration 〈R〉 is 2.79 × 10^?11 cm.² The ratio of L²/〈R〉 = 11 is close to the theoretical ratio of 12 for this kind of macromolecule.     

Simulation studies of branched polymer molecules

Monte Carlo simulation results are presented for lattice models of uniform stars (one branch point of functionality f = 3), combs (two branch points, ? = 3,3) and brushes (two branch points ? = 3,4 and ? = 3,5). We estimate the critical exponent γ(?), the ratio g(?) = 〈S(?)〉/〈S(1)〉 (where 〈S(?)〉 is the mean-square radius of gyration of a structure having ? branches and N monomers), and the meansquare end-to-end branch lengths, as a function of the number and arrangement of branches. Comparisons with theoretical predictions and experimental data are made where possible, leading to a test of some predictions, and a suggestion concerning future experiments.     

Small- and intermediate-angle neutron scattering from amorphous and semicrystalline polyethylene terephthalate

Small- and intermediate-angle (0.006 < Q < 0.25 Å) neutron scattering experiments have been performed on polyethylene terephthalate (PET). Amorphous and semicrystalline samples with deuterated PET molecular weights of 24,200 and 40,500 were prepared. The average value of R/M determined in the small-angle region for the amorphous samples is 0.406, in close agreement with the experimental θ-solvent (0.398–0.420) and theoretical (0.394) values for unperturbed dimensions. The intermediate-angle results for the amorphous sample are consistent with the random coil prediction to Q = 0.08 Å, but beyond this Q value there is some deviation from Gaussian behavior. The semicrystalline samples show a decrease in the radius of gyration as measured in the small-angle region and an increase in intensity (when compared to the amorphous data) in the intermediate-angle region, especially for the low-molecular-weight material. These results suggest that crystallization in PET is accompanied by greater molecular reorganization than has previously been observed in most bulk polymers.     

A molecular approach to chain entanglement in linear polymers

The phenomenon of chain entanglement in undiluted linear amorphous polymers is treated by calculating the probability of forming closed intramolecular loops. Adoption of the rotational isomeric state model of polymer chains permits an appropriate accounting of the detailed molecular structure to be made through the configurational characteristics of the polymer. The second (〈r〉₀) and fourth (〈r〉₀) moments of the vector r_hk connecting groups h and k in the isolated polymer chain and averaged over all chain conformations are calculated and used to evaluate the probability W_x(0) that r_hk is 0, or that an intramolecular loop of x = k ? h bonds is formed. Several linear polymers with widely differing molecular structures are treated. An attempt is made to correlate the degree of chain entanglement they manifest in the bulk with their ability to fold back upon themselves to form closed intramolecular loops.     

Darstellung,Schwingungsspektrum und Kristallstruktur von (n‐Bu4N)2[(W6Cl)F] · 2 CH2Cl2 und 19F‐NMR‐spektroskopischer Nachweis der gemischten Clusteranionen [(W6Cl)FCl]2–, n = 1–6

Synthesis, Vibrational Spectra, and Crystal Structure of ( n ‐Bu₄N)₂[(W₆Cl )F ] · 2 CH₂Cl₂ and ¹⁹F NMR Spectroscopic Evidence of the Mixed Cluster Anions [(W₆Cl )F Cl ]^2–, n = 1–6 The reaction of (n‐Bu₄N)₂[(W₆Cl)Cl] with CF₃COOH in dichloromethane gives intermediately a mixture of the cluster anions [(W₆Cl)(CF₃COO)Cl]^2–, n = 1–6. By treatment with NH₄F the outer sphere coordinated trifluoracetato ligands are easily substituted and the components of the series [(W₆Cl)FCl], n = 1–6 are formed and characterized by their distinct ¹⁹F NMR chemical shifts. An X‐ray structure determination has been performed on a single crystal of (n‐Bu₄N)₂[(W₆Cl)F] · 2 CH₂Cl₂ (orthorhombic, space group Pbca, a = 15.628(4), b = 17.656(3), c = 20.687(4) Å, Z = 4). The low temperatur IR (60 K) and Raman (20 K) spectra are assigned by normal coordinate analysis based on the molecular parameters of the X‐ray determination. The valence force constants are f_d(WW) = 1.89, f_d(WF) = 2.43 and f_d(WCl) = 0.93 mdyn/Å.     

Variable-Temperature and Variable-Pressure Kinetic and Equilibrium studies of formation and dissociation of [V(H2O)5NCS]2+

The kinetics of formation and dissociation of [V(H₂O)₅NCS]²⁺ have been studied, as a function of excess metal-ion concentration, temperature, and pressure, by the stopped-flow technique. The thermodynamic stability of the complex was also determined spectrophotometrically. The kinetic and equilibrium data were submitted to a combined analysis. The rate constants and activation parameters for the formation (f) and dissociation (r) of the complex are: k/M ^?1 · S^?1 = 126.4, k/s^?1 = 0.82; ΔH /kJ · mol^?1 = 49.1, ΔH/kJ · mol^?1 = 60.6; ΔS/ J·K^?1·mol^?1= ?39.8, ΔSJ·K^?1·mol^?1 = ?43.4; ΔV/cm³·mol^?1 = ?9.4, and ΔV/cm³ · mol^?1 =?17.9. The equilibrium constant for the formation of the monoisothiocynato complex is K²⁹⁸/M ^?1 = 152.9, and the enthalpy and entropy of reaction are ΔH⁰/kJ · mol^?1 = ? 11.4 and ΔS⁰/J. K^?1mol^?1 = +3.6. The reaction volume is ΔV⁰/cm³· mol^?1 = +8.5. The activation parameters for the complex-formation step are similar to those for the water exchange on [V(H₂O)₆]³⁺ obtained previously by NMR techniques. The activation volumes for the two processes are consistent with an associative interchange, I_a, mechanism.     

Characteristic operators and unitarily invariant decomposition of hermitian operators

A set of characteristic operators {F} is proposed for performing the decomposition of p-particle Hermitian operators {D^p} to constitute irreducible components {D} of the unitary group D = FD^p, q = 0,1,2,…,p. For a deeper expolration of the properties of the characteristic operators, a few theorems are presented. As an illustration, the expected values for symmetric p-particle Hermitian operators are obtained as a number of terms having invariant group-theoretical meaning.     

Magnesium chloride supported high mileage catalysts for olefin polymerization. XII. Polymerization of ethylene

Polymerizations of ethylene by the MgCl₂/ethylbenzoate/p-cresol/AlEt₃ TiCl₄-AlEt₃/methyl-p-toluate (CW-catalyst) have been studied. The initially formed active site concentration, [Ti] has a maximum value of 50% of total titanium at 50°C and lower values at other temperatures. The Ti decays rapidly to Ti sites with conc. ca. 10 mol %/mol Ti. The rate constants for four chain transfer processes have been obtained at 50°C: for transfer with AlEt₃, k = 2.1 × 10^?4 s^?1 and k = 4.8 × 10^?4 s^?1; for transfer with monomer, k = 3.6 × 10^?3 (M s)^?1 and K = 8.3 × 10^?3 (M s)^?1; for β-hydride transfer, k = 7.2 × 10^?4 s^?1 and k = 4.9 × 10^?4 s^?1; and transfer with hydrogen, k = 4.0 × 10^?3 torr^1/2 s^? and k = 5.1 × 10^?3 torr^1/2 s^?1. The rate constants for the termination assisted by hydrogen is k = 1.7 (M^1/2 torr^1/2 S)^?1. If monomer is assisting termination as was observed for propylene polymerization, then k = 7.8 (M^3/2 s)^?1. Values of all the rate constants can be higher or lower at other temperatures. Detailed comparisons were made with the results of propylene polymerizations. There are more than four times as many Ti active sites for ethylene polymerization than there are for stereospecific polymerization of propylene; the difference is more than a factor of two for the Ti sites. Certain rate constants are nearly the same for both monomers while others are markedly different. Some of the differences can be explained by stereoelectronic effects.     

Darstellung und Kristallstruktur von trans-(Ph4As)2[OsCl2(NCS)(SCN)], Schwingungsspektren und Normalkoordinatenanalyse

Preparation and Crystal Structure of trans-(Ph₄As)₂[OsCl₂(NCS) (SCN) ], Vibrational Spectra and Normal Coordinate Analysis By treatment of trans-[OsCl₂I₄]^2? with (SCN)₂ in dichloromethane a mixture of different linkage isomers is formed, from which trans-[OsCl₂(NCS)(SCN)]^2? has been isolated by ion exchange chromatography on diethylaminoethyl cellulose. The X-Ray structure determination on a single crystal of trans-(Ph₄As)₂[OsCl₂(NCS)(SCN)] (triclinic, space group P 1 , a = 12.505(5), b = 12.056(5), c = 19.833(5) Å, α = 108.047(5)°, β = 91.964(5)°, γ = 117.048(5)°, Z = 2) reveals that two cis-positioned Thiocyanate(N) groups are coordinated with Os? N? C angles of 172.1° and 173.0° and two cis-positioned Thiocyanate(S) groups are coordinated with Os? S? C angles of 106.9° and 108.7°. Using the molecular parameters of the X-Ray determination the low temperature (10 K) IR and Raman spectra of the (n-Bu₄N) salt of the linkage isomer are assigned by a normal coordinate analysis based on a modified valence force field. The valence force constants are f_d(OsN) = 1.63 and f_d(OsS) = 1.30 mdyn/Å. Taking into account the trans influence a good agreement between observed and calculated frequencies is achieved.     

The formation of highly excited H in the reaction H2+(v) + H2 → H + H

A quasiclassical trajectory surface hopping method has been used to study H(v) + H₂ → H + H for v = 0, 3, 7, 10, 13, and 17 with an emphasis on determining the H internal energy and angular momentum distributions for high v. For v = 13 and 17, significant cross sections are found for producing H at energies above its dissociation energy. An average metastable H lifetime of 11.5 ps for v = 13 and 4.7 ps for v = 17 is found, but there is also a much longer lived component to the lifetime distributions that is more important for v = 13 than for v = 17. Some of the longer lived metastables correspond to high angular momentum orbiting states of H, but other sources of metastability are also present.     

The acetyl radicals CH3CO· and CD3CO· studied by flash photolysis and kinetic spectroscopy

Ultraviolet absorption spectra have been characterized for the acetyl-h₃ and acetyl-d₃ radicals, which were generated by the flash photolysis of the corresponding acetones. The spectra are broad and intense, with values of the extinction coefficient at the respective maxima estimated as: ?CH₃CO(215) = (1.0 ± 0.1) × 10⁴ L/mol·cm and ?CD₃CO(207.5) = (1.0 ± 0.05) × 10⁴ L/mol·cm. Rate constants for the reactions of mutual interaction were estimated as: k = 3.5 × 10¹⁰ L/mol·s and k = 3.4 × 10¹⁰ L/mol·s. Rate constants for the reactions of cross interaction were estimated as: k = 8.6 × 10¹⁰ L/mol·s and k = 5.2 × 10¹⁰ L/mol·s. The related values of the cross interaction ratios k/(kk)^1/2 = 2.6 and k/(kk)^1/2 = 1.6 do not differ significantly from the statistical value of 2. The participation of the radical displacement reactions was estimated in terms of the fractions k/k = 0.38 and k/k = 0.47. Corroborative spectra were obtained from the flash photolysis of methyl ethyl ketone and biacetyl, and the relative rates of the competing primary processes were estimated from the relative peak heights of the acetyl and methyl radicals in each system.     

Laser ablation of AgSbS2 and cluster analysis by time‐of‐flight mass spectrometry

Thin films of AgSbS₂ are important for phase‐change memory applications. This solid is deposited by various techniques, such as metal organic chemical vapour deposition or laser ablation deposition, and the structure of AgSbS₂(s), as either amorphous or crystalline, is already well characterized. The pulsed laser ablation deposition (PLD) of solid AgSbS₂ is also used as a manufacturing process. However, the processes in plasma have not been well studied. We have studied the laser ablation of synthesized AgSbS₂(s) using a nitrogen laser of 337 nm and the clusters formed in the laser plume were identified. The ablation leads to the formation of various single charged ternary Ag_pSb_qS_r clusters. Negatively charged AgSbS, AgSb₂S, AgSb₂S, AgSb₂S and positively charged ternary AgSbS⁺, AgSb₂S⁺, AgSb₂S, AgSb₂S clusters were identified. The formation of several singly charged Ag⁺, Ag, Ag, Sb, Sb, S ions and binary Ag_pS_r clusters such as AgSb, Ag₃S^?, SbS (r = 1–5), Sb₂S^?, Sb₂S, Sb₃S (r = 1–4) and AgS, SbS⁺, SbS, Sb₂S⁺, Sb₂S, Sb₃S (r = 1–4), AgSb was also observed. The stoichiometry of the clusters was determined via isotopic envelope analysis and computer modeling. The relation of the composition of the clusters to the crystal structure of AgSbS₂ is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Aromaticity of ionic structures: Investigation and application of NICS value and 4n + 2 rule

At DFT/B3LYP/6‐31G** theoretical level, C₆H and C (n = 0, ?2, and +2), C₆H and C (n = 0, ±2, ±4, and ±6), C₆H (n = 0–6), as well as C₆H₆‐A and C₆‐A (A = Be, B, N, O, Mg, Al, Si, S, and Fe) structures were investigated. Comparing NICS values of C₆H and C (n = 0, ?2, and +2), we discovered that C₆H, C₆H were antiaromatic, and C₆H₆, C₆, C, C had aromaticity with negative NICS values. According to research of C₆H and C (n = 0, ±2, ±4, ±6), C₆H (n = 0–6), we sustained that their σ and π orbit were different and the locations of electrons were difficult to confirm in ionic structures. Thus, neither 4n + 2 rule nor NICS values can precisely estimate the aromaticity of ionic structures. Besides, through WBI (NBO) research of C₆H₆‐A and C₆‐A (A = Be, B, N, O, Mg, Al, Si, S, and Fe) structures, we found that C₆H₆ was easy to accept electrons, contrarily, C₆ was prone to bestowing electrons. Moreover, C₆H₆ took the symmetrical carbon atoms form feeble interaction or bond, and C₆ used all carbon atoms to impact with other atom. C₆H₆ generated two contrapuntal single bonds with oxygen, sulfur, and nitrogen atoms, whereas C₆ molecule formed double bond with oxygen and nitrogen atoms, two conjoint single bonds with sulfur atom. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010