Spin projections for even electron systems

A new method is presented for obtaining the spin eigenfunctions of 2n electron systems in the spin state S and M_S = 0. Using a modified Young operator the function for the state S, M_S ( = S) of the system is first projected out. The projected function is then symmetrized over the last n particles and the weight lowering operator ? is then applied to it, resulting in a projection of the state S, 0. To within a multiplicative factor, the resulting function is identical with the one resulting from the vector coupling methods.     

Entanglement friction and dynamics in blends of starlike and linear polymer molecules

We investigate relaxation dynamics in a series of six‐arm star/linear 1,4‐polybutadiene blends with mechanical rheometry measurements. Blend systems are formulated to systematically probe constraint release and arm relaxation dynamics. Zero shear viscosity and terminal relaxation times of star/linear polymer blends with fixed star arm molecular weights (M_a) and compositions (?_S) are found to follow nonmonotonic dependencies on the linear polymer molecular weight (M_L). At low values of ?_S, at least two scaling regimes are apparent from the data (ξ₀ ～ M and ξ₀ ～ M), where ξ₀ refers to the zero shear viscosity or terminal relaxation time of the blend. The two regimes are separated by a critical linear polymer molecular weight M^* that is more than 20 times larger than the critical molecular weight for entanglements. When the linear polymer contribution to blend properties is removed, a clear transition from dilution dynamics, ξ₀ ～ M, to Rouse‐like constraint‐release dynamics, ξ₀ ～ M, is apparent at low values of ?_S. At higher ?_S values, a new activated constraint‐release dynamic regime is evident in which ξ₀ ～ M and ξ₀ ～ ?, where α changes continuously from approximately 2 to 0.5 as ?_S increases and β varies from 2.0 to 1.0 as M_L increases. The experimental results are compared with theoretical predictions based on a drag coupling model for entangled polymer liquids. All features observed experimentally are captured by this model, including the value of M^* for the transition from dilution to Rouse constraint‐release dynamics. Predictions of the drag coupling model are also compared with published data for the zero shear viscosity and terminal relaxation time in bidisperse linear polymer blends and pure entangled starlike molecules. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2501–2518, 2001     

Structural analysis of aggregates formed by a thermoresponsive homopolymer in dilute aqueous solutions

The aqueous solution of a thermoresponsive polymer, poly[2‐(2‐ethoxy) ethoxyethyl vinyl ether] poly(EOEOVE), contains a tiny amount of large polymer aggregates at low polymer concentrations far below the lower critical solution temperature (～40 °C). The molar mass M_w,slow, radius of gyration 〈S²〉, and hydrodynamic radius R_H,slow of the aggregating component of poly(EOEOVE) were obtained by simultaneous static and dynamic light scattering as functions of the polymer concentration and temperature, while the weight fraction w_slow of the component was estimated by size‐exclusion chromatography. The M_w,slow dependencies of 〈S²〉 and R_H,slow, as well as the ratio 〈S²〉/R_H,slow, indicated that the poly(EOEOVE) aggregate takes a sparsely branched polymer‐like conformation. We have analyzed the structure of the aggregate, using the branched polymer model of random type. The M_w,slow dependence of 〈S²〉 obtained was favorably compared with this model with reasonable structural parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1179–1187, 2006     

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.     

Entropies and heat capacities of free radicals

Methods are presented for rapidly estimating the entropies and heat capacities of free radicals from the known S⁰ and C of structurally similar compounds. The methods consist of estimating the differences due to changes in mass, vibration frequencies, spin, symmetry, and changes in rotational barriers. Tables of contributions to S⁰ and C by different frequencies over the temperature range 300–1500°K are presented to facilitate the tabulation of the above differences. Conjugated radicals, such as benzyl and allyl, are included. It is shown that the greatest uncertainties in the estimates arise from uncertainties in the barriers to rotation in the radicals. The results are applied to kinetic data on the pyrolysis of branched hydrocarbons and the reverse reactions of radical recombination. Major discrepancies exist in these data which can be nearly reconciled by postulating improbably high rotational barriers of 8 kcal for CH₃ rotation in isopropyl and t-butyl radicals. It is shown that radical thermochemistry can be fitted into group schemes and tables of groups values are given for the rapid estimation of ΔH, S⁰, and C for different organic radicals, including those containing sulfur, oxygen, and nitrogen.     

Über das Auftreten von Polysulfan-diphosphonaten bei der Umsetzung von Monothiophosphat mit Disulfan-diphosphonat

On the Formation of Polysulphane Diphosphonates by the Reaction of Monothiophosphonate with Disulphane Diphosphonate In acid solution SPO reacts with S₂P₂O forming higher polysulphane diphosphonates. The formation of S₃P₂O and S₄P₂O is proved by evaluation of the double labelling with ³⁵S? ³²P after high paper electrophoresis.     

Thallium(I)-thiometallate(II,IV) vom Typ TI2MeMeIVS6

Thallium(I) Thiometallates(II, IV), Tl₂MeMe^IVS₆ The preparation and some properties of the compounds Tl₂MeMe^IVS₆ are reported, where Me^II = Pt, Pd, Ni; Me^IV = Pt, Zr, Sn, Ta. Their structure is discussed in relation to the structure of the alkali compounds A₂MeMe^IVS₆.     

Nitridsulfidchloride der Lanthanide: II. Der Formeltyp M6N3S4Cl (M = La?Nd)

Nitride Sulfide Chlorides of the Lanthanides. II. The Composition M₆N₃S₄Cl (M = La? Nd) The oxidation of the “light” lanthanides (M = La? Nd) with sulfur and NaN₃ in the presence of the chlorides MCl₃ yields chlorine-poor nitride sulfide chlorides with the composition M₆N₃S₄Cl when appropriate molar ratios of the reactants are used. Additional NaCl as a flux secures complete and fast reactions (7 d) at 850°C in evacuated silica vessels as well as single-crystalline products (red-brown needles). The crystal structure was determined from X-ray single crystal data for the limiting representatives La₆N₃S₄Cl (orthorhombic, Pnma (no. 62), Z = 4, a = 1159.7(4), b = 410.95(7), c = 2756.8(9)pm, R = 0.030, R_w = 0.027) and Nd₆N₃S₄Cl (a = 1137.1(3), b = 399.34(6), c = 2687.6(9)pm, R = 0.034, R_w = 0.033). Guinier powder data revealed the cerium and praseodymium analogues to be isotypic. The crystal structure exhibits two different chains of connected [NM₄] tetrahedra which are commensurate in translation. Six crystallographically different M³⁺ are present, two of them (M1 and M2) build up the chain [(N1)(M1) · (M2)]³⁺ together with (N1)^3? by cis-edge connection of tetrahedra. The four remainders (M3? M6) arrange as pairs [N₂M₆] of edge-shared [NM₄] tetrahedra with (N2)^3? and (N3)^3? which are further connected via four vertices to form the [(M5)(N-2){(M3)_(1+1)/(1+1)(M4)_(1+1)/(1+1))}^e(N3)(M6)]⁶⁺ double chain. Bundled along [010] like a closest packing of rods, both types of chains are held together by five crystallographically different but by X-ray diffraction indistinguishable anions S^2? (S1? S4) and Cl^? adjusting the charge balance in a molar ratio of 4:1.     

Fractionation and characterization of a protein–polysaccharide complex from Pleurotus tuberregium sclerotia

A water‐soluble sample (TM4b), extracted from sclerotia of Pleurotus tuberregium, was analyzed using elemental analysis, one‐ and two‐dimensional ¹H and ¹³C NMR. The results indicated that TM4b was protein–polysaccharide complex, and the polysaccharide moiety was hyperbranched β‐D ‐glucan with residuals branched at C3, C2, C4, and C6 positions. A preparative size‐exclusion chromatography (SEC) column combined with nonsolvent addition method was used to fractionate TM4b, and nine fractions were obtained. Solution properties of TM4b in 0.15 M aqueous NaCl were studied using static laser light scattering and viscometry at 25 °C. The dependences of intrinsic viscosity ([η]) and radius of gyration (〈S²〉) on weight–average molecular weight (M_w) for TM4b in the M_w range from 1.89 × 10⁴ to 2.58 × 10⁶ were found to be [η] = 0.21M and 〈S²〉 = 3.63M. It indicated that TM4b existed as compact sphere conformation in the aqueous solution. Atomic force microscopy image further confirmed that the TM4b molecules exhibited globular shape in the solution. This work gave valuable information on fractionation and chain conformation characterization of the globular protein–polysaccharide complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2546–2554, 2007     

The kinetics of the interaction of peroxy radicals. I. The Tertiary Peroxy Radicals

Existing data on the self-reactions of tertiary peroxy radicals RO₂ has been reanalyzed and corrected to deduce Arrhenius parameters for both termination and nontermination paths. For R = t-Butyl, these are logk_t(M^?1sec^?1) = 7.1 - (7.0/θ) and logk_nt(M^?1sec^?1) = 9.4 - (9.0/θ), respectively, different from those recommended by other authors. The higher magnitudes observed for termination processes of tertiary peroxy radicals like those of cumyl and 1,1-diphenylethyl have been discussed in terms of a much greater cage recombination of cumyloxy radicals as contrasted with t-butoxy radicals. It is shown that for benzyl peroxy radicals, the R—O bond dissociation energy is sufficiently low (18–20 kcal) that reversible dissociation into R^˙ + O₂ opens a competing second-order path to fast recombination R^˙ + RO → ROOR. This path is probably not important for cumyl peroxy radicals under usual experimental conditions but can become important for 1,1-diphenyl ethyl peroxy radicals at (O₂) < 10^?3M. At very low RO concentrations (<10^?5M), in the absence of added O₂, an apparent first-order disappearance of RO can occur reflecting the rate determining breaking of the cumyl—O bond followed by the second step above. The thermochemistry of RO is used to show that the reaction of R₂O₄ → 2RO + O₂ must be concerted and cannot proceed via RO which is too unstable and cannot form even from RO^˙ + O₂.     

Herstellung von Fluorophosphaten,Difluorophosphaten, Fluorophsophonaten und Fluorophosphiten in fluoridhaltigen Harnstoffschmelzen

Preparation of Fluorophosphates, Difluorophosphates, Fluorophosphonates, and Fluorophosphites in Fluoride-containing Urea Melts Phosphoric acid, phosphonic acid, and organylphosphonic acid react on heating in fluoride-containing urea melts in high yields to fluorophosphates, MPHO₂F, organylfluorophosphonates, M¹RPO₂F, organylpolyfluorophosphonates, MR¹CX(PO₂F)₂, MN(CH₂PO₂F)₃, and phosphonoorganylfluorophosphonates, MR¹CX(PO₃)PO₂F (M¹ = K, NH₄; R = organic substituent; R¹ = H, organic substituent; X = OH, NH₂, NR₂). The reaction mechanism of the formation of fluorophosphate ions in fluoride containing urea melts is discussed.     

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.     

Hartree Fock instabilities of sulfur-nitrogen ring systems: S2N2

The Hartree-Fock instablities of S₂N₂ are reported and compared with those of S₃N and S₄N. These unsaturated sulfur nitrogen planar rings are π electron rich and although the symmetry adapted HF solutions are singlet stable at the experimental bond lengths they become unstable with only a very modest increase in bond length. The broken symmetry solutions for S₂N₃, S₃N, and S₄N are of planar C_2v type with one of the nitrogens stripped of its π electrons, producing a π hole.     

Dipole,quadrupole, octupole,and dipole–dipole–quandrupole polarizabilities and second hyperpolarizabilities at real and imaginary frequencies for helium in the 23S state: Dispersion-energy coefficients for interactions between He(23S) and H(12S), He(11S), He(23S), or H2(X1∑g+)

We have determined the dynamic dipole (α₁), quadrupole (α₂), octupole (α₃), and dipole–dipole–quadrupole (B) polarizabilities and the second hyperpolarizability tensor (γ) for the helium atom in its lowest triplet state (2³S). We have done so for both real and imaginary frequencies: in the former case, for a range of frequencies (ω) between zero and the first electronic-transition frequency, and in the latter case for a 32-point Gauss–Legendre grid running from zero to ?ω = 20 E_h. We have also determined the dispersion-energy coefficients C₆, C₈, and C₁₀ for the systems H(1²S)? He(2³S), He(1¹S)? He(2³S), and He(2³S)? He(2³S) and the C, C, C, C, and C coefficients for the interaction He(2³S)? H₂(X¹∑). Our values of the higher-order multipolar polarizabilities and of γ for the 2³S state of helium are, we believe, the first to be published. © 1993 John Wiley & Sons, Inc.     

Kinetics of acid catalyzed and Ag(I) catalyzed decomposition of peroxodisulfate in aqueous medium

The mechanism of acid catalyzed decomposition of peroxodisulfate, (S₂O) in aqueous perchlorate medium involves the hydrolysis of the species H₂S₂O₈ and HS₂O and the homolysis of the species H₂S₂O₈, HS₂O and S₂O at the O? O bond. The overall rate law when 1.4M > [HClO₄] > 0.1M is The constants k′ and k″ contain the hydrolysis and homolysis rate constants of HS₂O₈^? and H₂S₂O₈, respectively. With added Ag(I), the acid catalyzed and Ag(I) catalyzed reactions take place independently. Ag(I) catalyzed decomposition appears to involve the species AgS₂O (aq).     

On the Sanibel coefficients in the expansion of spin-projected slater determinants

Every Slater determinant D may be uniquely analyzed in terms of spin components D_l = O_lD which are pure spin eigenfunctions, so that S²D_l = l(l+1)D. Every component D_l = O_lD may in turn be written as a sum of symmetric combinations of Slater determinants, T_k = [α^μ?kβ^k‖α^kβ^ν?k], and the coefficients c in the expansion O_lD = ∑_k c T_k are known as the “Sanibel coefficients.” By using the relation S²D_l = l(l+1)D, a recursion formula for the coefficients c is derived, which is then explicitly solved in the special case when S_z has the pure quantum number m = 0.     

Studies on the composition and kinetics of chromium(III)-alanine system

Kinetics of the complex formation of chromium(III) with alanine in aqueous medium has been studied at 45, 50, and 55°C, pH 3.3–4.4, and μ = 1 M (KNO₃). Under pseudo first-order conditions the observed rate constant (k_obs) was found to follow the rate equation: Values of the rate parameters (k_an, k, K_IP, and K) were calculated. Activation parameters for anation rate constants, ΔH^≠(k_an) = 25 ± 1 kJ mol^?1, ΔH^≠(k) = 91 ± 3 kJ mol^?1, and ΔS^≠(k_an) = ?244 ± 3 JK^?1 mol^?1, ΔS^≠(k) = ?30 ± 10 JK^?1 mol^?1 are indicative of an (I_a) mechanism for k_an and (I_d) mechanism for k routes (‥substrate Cr(H₂O) is involved in the k route whereas Cr(H₂O)₅OH²⁺ is involved in k′ route). Thermodynamic parameters for ion-pair formation constants are found to be ΔH°(K_IP) = 12 ± 1 kJ mol^?1, ΔH°(K) = ?13 ± 3 kJ mol^?1 and ΔS°(K_IP) = 47 ± 2 JK^?1 mol^?1, and ΔS°(K) = 20 ± 9 JK^?1 mol^?1.     

The kinetics and thermochemistry of S2F10 pyrolysis

Data on the kinetics of S₂F₁₀ pyrolysis, which gives SF₄ + SF₆, have been reinterpreted to give a value for the equilibrium constant of S₂F₁₀ ? SF₄ + SF₆. This, together with statistical estimates of the entropy and heat capacity of S₂F₁₀, can be used to give for this reaction values of ΔH = 19.7 ± 1.0 kcal/mole and ΔS = 47.6 ± 2 gibbs/mole. ΔH(S₂F₁₀) = –494 kcal/mole. A compatible mechanism is shown to be S₂F₁₀ ? 2SF₅ (fast); 2SF₅ ? SF₆ + SF₄ (slow) with step 2 rate-determining. The overall, best first order rate constant is proposed as k_meas = 10^{17.42–43.0/θ} sec^?1 = K₁k₂, where θ = 2.303RT in kcal/mole. Independent measurements of δH and S° for the SF₅ radical, permits the evaluation of the equilibrium constant K₁ = 10^{8.92–(27.1 ± 6)/θ} l./mole-sec and yields k₂ = 10^{8.50–15.9/θ} l./mole-sec. The observed homogeneous catalysis by NO and CHCl ? CHCl can be explained in terms of a direct abstraction of F from S₂F₁₀ : C + S₂F₁₀ → CF + S₂F₉, followed by S₂F₉ → SF₅ + SF₄ and SF₅ + CF ? SF₆ + C (C ? NO or C₂H₂Cl₂).     

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.     

Correlated n1,3S states for coulomb three‐body systems

n^1,3S (n = 1 ? 4) states for atomic three‐body systems are studied with the Angular Correlated Configuration Interaction method. A recently proposed angularly correlated basis set is used to construct, simultaneously and with a single diagonalization, ground and excited states wave functions which: (i) satisfy exactly Kato cusp conditions at the two‐body coalescence points; (ii) involve only linear parameters; (iii) show a fast convergency rate for the energy; and (iv) form an orthogonal set. The efficiency of the method is illustrated by the study a variety of three‐body atomic systems [m m m] with two negatively charged light particles, with diverse masses m and m, and a heavy positively charged nucleus m. The calculated ground 1¹S and excited n^1,3S (n = 2 ? 4) state energies are compared with those given in the literature, when available. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011