Subduction coefficients for 〈2N/2–S, 12S〉 ↓ 〈2, 1〉 ⊗ 〈2, 1〉 of U(n) ↓ U(n1) ⊗ U(n2)

The determination of the subduction coefficients for states of the unitary group U(n) under the restrictions U(n) ↓ U(n₁) ? U(n₂) have been considered for the spin free states of many electron systems. Using the transformation properties of the tensor basis spanning the irreducible representation 〈2^N/2–S, 1^2S〉 of U(n) under the permutations of electron coordinates, a simple programmable procedure has been developed for the determination of these coefficients. The procedure has been illustrated using a simple example.     

Synthesis and properties of phosphorus-containing polyesters derived from 2-(6-oxido-6H-dibenz〈c,e〉〈1,2〉oxaphosphorin-6-yl)-1,4- hydroxyethoxy phenylene

A series of phosphorous-containing aliphatic polyesters were synthesized by high-temperature solution condensation of 2-(6-oxido-6H-dibenz〈c,e〉〈1,2〉oxaphosphorin-6-yl)-1,4-hydroxyethoxy phenylene (III) with various aromatic acid chlorides in o-dichlorobenzene. All polyesters are amorphous and readily soluble in many organic solvents such as DMAc, NMP, DMSO, and o-dichlorobenzene at room temperature or upon heating. These polyesters are thermally quite stable. The glass transition temperatures of these aliphatic polyesters ranged from 126.6 to 162.2°C. The degradation temperatures (T_d onset) in nitrogen ranged from 424 to 448°C, and the char yields at 700°C are 20–32%. The activation energies of degradation ranged from 160.9 to 226.0 kJ/mol. The LOIs of these polyesters ranged from 36 to 43. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 3051–3061, 1998     

Synthesis and properties of phosphorus containing polyester‐amides derived from 1,4‐bis(3‐aminobenzoyloxy)‐2‐(6‐oxido‐6H‐dibenz〈c,e〉〈1,2〉oxaphosphorin‐6‐yl) phenylene

A series of polyester‐amides that contain phosphorus were synthesized by low temperature solution condensation of 1,4‐bis(3‐aminobenzoyloxy)‐2‐(6‐oxido‐6H‐dibenz〈c,e〉〈1,2〉oxaphosphorin‐6‐yl) phenylene (III) with various aromatic acid chlorides in N‐methyl pyrrolidone (NMP). All polyester‐amides are amorphous and readily soluble in many organic solvents such as dimethylacetamide (DMAc), NMP, dimethylsulfoxide, and dimethylformamide at room temperature or on heating. Light yellow and flexible films of these polyester‐amides could be cast from the DMAc solutions. The polymers with an inherent viscosity of 0.26–0.72 dL/g were obtained in quantitative yields. These polyester‐amides have good mechanical properties (G′ of ∼ 10⁹ Pa up to 200°C) and good thermal and flame retardant properties. The glass transition temperatures of these polyester‐amides ranged from 250 to 273°C. The degradation temperatures (T_d 5%) in nitrogen ranged from 466 to 478°C and the char yields at 800°C were 59.6–65.2%. The limiting oxygen indexes of these polyester‐amides ranged from 35 to 43. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 891–899, 1999     

On the evaluation of the integral 〈pu|∂/∂ν|s〉 occurring in covalency reduction factor

Explicit expressions for integrals of the form 〈p_u|?/?ν|s〉 occurring in expression of covalence reduction factors, introduced by Stevens and Tinkham, have been derived for various types of atomic functions. Numerical values of the integral for some common ligands are given. Misconceptions regarding the sign and the magnitude of this integral existing in the literature have been clarified.     

Additionen von SF5Cl und TeF5Cl an 〈CC〉 Doppelbindungen

Addition of SF₅Cl and TeF₅Cl on 〈C?C〉 double bonds Addition of SF₅Cl on 〈C?C〉 double bonds is investigated in a few examples. The results indicate a radical mechanism, in which the SF₅· free radical attacks the double bonds first. This is in agreement with many earlier findings. The direction of the addition is not changed by sterical influences. Sterically strained derivatives such as (SF₅)₂CH? CF₂Cl and SF₅(CF₃)₂C? CH₂Cl are obtained. In a single case the addition of TeF₅Cl on CH₂?CF₂ was possible, but the analogous reaction with SeF₅Cl was unsuccessful.     

Scaling in the S and P states of the helium isoelectronic sequence

Mean values of r ₁ ^r and r _r ¹² for the ground and several excited states of the helium isoelectronic sequence are used to demonstrate that a simple scaling which superimposes the distribution function f(r ₁₂) as a function of the atomic number leads to a similar result for the electron density distribution D(r₁). On the basis of a screening interpretation of the scaling parameter , it is concluded that screening is greater in the singlet than the triplet state of a particular configuration, that screening is greater in the P states than the corresponding S states, and that the screening approaches the limiting value of 1 for the highly excited states. The perturbation expansions of Scherr and Knight are used to determine the limiting value of when Z and the relationship between the scaling parameter and the scale factor, chosen so that a trial wave function satisfies the virial theorem, is discussed. A brief discussion of the scaling of the Coulomb hole is presented.     

Critical point,singularities and extrapolations in the helium iso-electronic sequence

The Z-expansion of two-electron systems is analyzed with the Padé technique with emphasis on establishing analytical properties of the function E(Z) formally associated with the power series expansion. The concept of critical point in this connection is stressed. For this sequence it occurs at Z_c = 0.911246 with E(Z_c) = ?0.415184. The structure of E(Z) for Z < Z_c is investigated. The use of Padé approximants to extrapolate values of electron affinities is emphasized.     

Calculations on the helium isoelectronic sequence using Coulomb Green's function variables

Calculations on the ground states of the helium isoelectronic series are carried out using variational wavefunctions of the form ψ (x,y), in which x and y are the combinations r₁ + r₂ ± r₁₂ occurring in the Coulomb Green's function. The results for helium are the most accurate to date using a two-variable wavefunction accounting for 71.5% of the correlation energy.     

One-Parameter double-zeta atomic functions for the hartree–fock energies of helium isoelectronic sequence

The double-zeta atomic functions are characterized by the nuclear charge z of the two-electron atomic system. The Hartree–Fock total energies and the corresponding orbital energies are calculated using various atomic wave functions for the helium isoelectronic sequence. The expectation values rⁿ of various wave functions are also examined. It is found that the accuracy of our one-parameter double-zeta functions corresponds to the accuracy of the usual five-parameter double-zeta functions.     

Fermi and Coulomb correlations in the 21 S state of the helium isoelectronic sequence

The Fermi and Coulomb holes of the 2¹ S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 2³ S state are pointed out and discussed.     

The Coulomb hole in the 23S state of the helium isoelectronic sequence

The pair distribution functions evaluated for the 2³S state of the helium isoelectronic sequence from the Hart and Herzberg correlated wave functions and those corresponding to the Hartree-Fock approximation are used to determine the shape of the corresponding Coulomb holes. As a consequence of a discontinuity in the Hartree-Fock solution between He and Li⁺, the Coulomb hole has a different shape for He than for Li⁺ and the other isoelectronic ions.     

Polydispersity of ethylene sequence length in metallocene ethylene/α‐olefin copolymers. II. Influence on crystallization and melting behavior

In this work, crystallization and melting behavior of metallocene ethylene/α‐olefin copolymers were investigated by differential scanning calorimetry (DSC) and atomic force microscopy (AFM). The results indicated that the crystallization and melting temperatures for all the samples were directly related to the long ethylene sequences instead of the average sequence length (ASL), whereas the crystallization enthalpy and crystallinity were directly related to ASL, that is, both parameters decreased with a decreasing ASL. Multiple melting peaks were analyzed by thermal analysis. Three phenomena contributed to the multiple melting behaviors after isothermal crystallization, that is, the melting of crystals formed during quenching, the melting‐recrystallization process, and the coexistence of different crystal morphologies. Two types of crystal morphologies could coexist in samples having a high comonomer content after isothermal crystallization. They were the chain‐folded lamellae formed by long ethylene sequences and the bundlelike crystals formed by short ethylene sequences. The coexistence phenomenon was further proved by the AFM morphological observation. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 822–830, 2002     

Synthesis and crystallization behavior of rigid copolyesters with biphenyl‐4,4′‐dicarboxylate and 2,6‐naphthalenedicarboxylate in the main chain

Structurally rigid copolyester thermoplastics were synthesized from 1,4‐cyclohexanedimethanol and the diesters dimethyl biphenyl‐4,4′‐dicarboxylate and dimethyl 2,6‐naphthalenedicarboxylate (DMN) via conventional melt transesterification. Conventional differential scanning calorimetry (CDSC) showed all compositions to exhibit multiple endotherms upon heating. Wide‐angle X‐ray diffraction analysis showed copolyester compositions to exhibit the crystalline structure of either the homopolyester Poly(1,4‐cyclohexylenedimethylene 2,6‐naphthalate) (PCN) or the homopolyester Poly(1,4‐cyclohexylenedimethylene 4,4′‐bibenzoate) (PCB), but not both simultaneously. Further thermal analysis using CDSC and fast DSC investigated the origin of the multiple endotherm behavior. While three endotherms are observed for low heating rates, the upper two endotherms appear to merge at heating rates about 1–5 °C s^?1 and a single endotherm remains above heating rates about 10–50 °C s^?1. While the behavior of the upper two endotherms is undeniably consistent with the mechanism of melting–recrystallization–remelting (MRR), we suggest that the low endotherm is likely associated with the melting of constrained secondary crystals, although MRR effects cannot be ruled out. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 973–980     

Tetrameric aggregate of 1,c‐3‐diphenyltetran‐r‐1‐ol via an R44(8) homodromic ring

The compound 1,c‐3‐diphenyltetran‐r‐1‐ol (systematic name: 1,c‐3‐diphenyl‐1,2,3,4‐tetrahydro‐r‐1‐naphthol), C₂₂H₂₀O, which possesses the tetrahydronaphthalene core that is found in a large number of natural products, crystallizes with Z′ = 4 and with the four molecules forming a hydrogen‐bonded cyclic aggregate. The aliphatic six‐membered rings are present with two different conformations in the molecules of the asymmetric unit. A comparison with similar fragments reveals their conformational flexibility. In addition, the structure demonstrates the relative stereochemistries of the chiral centers, which are important since the title compound is used in the stereoselective synthesis of compounds with therapeutic activity.     

Voltammetric Behavior of Sodium 7-Methoxyl-4＇-hydroxylisoflavone-3＇-sulfonate and Its Application

Voltammetric behavior of sodium 7‐methoxyl‐4′‐hydroxylisoflavone‐3′‐sulfonate (SMHS) in the aqueous solution from pH 1 to 5 was studied by linear sweep voltammetry, cyclic voltammetry and normal pulse voltammetry. Experimental results showed that in 0.2 mol*L^?1 sodium citrate‐hydrochloric acid buffer solution (pH=4.65), SMHS caused only one reduction wave at ?1.34 V (vs. saturated calomel electrode, SCE), which was an h‐reversible adsorptive wave of SMHS protonized involving one electron and one proton. The peak current of SMHS on linear sweep voltammogram was proportional to its concentration in the range of 8.0 × 10 ?8.0·10 mol*L^?1 (r = 0.995). and the detection limit was 5.0·10^?‐⁶mol*L^?1. The method was applied to determination of SMHS, in synthetic samples. In addition, its scavenging effect on superoxide anion radical was studied by the auto‐oxidation of pyrogallol in HCI‐tris buffer solution (pH = 8.2) in order to explain its peculiar biological effects. The experimental results proved that SMHS has antioxidant quality, and it is an efficient free radical scavenger of superoxide anion radical.     

Limiting behavior of target fragmentation in the reactions of lanthanide nuclei induced by heavy projectiles

Nuclear reactions of¹⁶⁵Ho induced by 1.0 GeV¹⁵N or 1.8 GeV¹⁴N ions and those of¹⁴¹Pr induced by 2.3 GeV or 3.8 GeV⁴⁰Ar ions have been studied by off-line -ray spectrometry. Mass distributions of the products were confirmed to reveal a limiting characteristics at projectile energies beyond 2 GeV. Longitudinal momentum transfer was measured with a thick-target-thick-catcher technique. The results demonstrated that a provisional limiting of the recoil velocity appears in the energy range of 2–10 GeV, besides the ultimate limiting condition already pointed out. The coincidence in the onset energy of the limiting behavior was interpreted as the result of the existence of the limit heating of nucleus.     

Proton NMR determination of the 2,4–/2,6–isomer ratio in commercial toluene di-isocyanates

The CH₃-proton resonances for the 2,4- and 2,6-isomers of toluene di-isocyanate separate when hexafluorobenzene is used as a solvent. Integration of these absorptions over an expanded sweep scale gives the isomer ratio with an accuracy of ±0.5% over the range normally encountered with commercial samples.     

Polymerization behavior of 2,5‐bis(dicyanomethylene)‐ 2,5‐dihydrofuran

2,5‐Bis(dicyanomethylene)‐2,5‐dihydrofuran (TCNF) is not homopolymerizable with any initiators, but copolymerizable with styrene (St) in an alternating fashion. Reactivity of TCNF was compared with that of 2,5‐bis(dicyanomethylene)‐2,5‐dihydrothiophene (TCNT) on the basis of the terpolymerization of the TCNT‐TCNF‐St system and the rates of addition reactions of AIBN with TCNT and with TCNF. TCNF was found to be lower in reactivity than TCNT. The relative reactivity was explained with the energy difference between quinonoid structure and benzenoid one. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1285–1292, 1999