Multiplication theorems for orthogonal polynomials

In this paper, a general method is presented that allows the derivation of the expansion coefficients of the product of two orthogonal functions provided the generating function is known. For the three classical orthogonal polynomials, the Laguerre, the Hermite, and the Legendre polynomials, the coefficients b_lmn with ?_m?_n = ∑_lb_lmn?_l are derived. © 1993 John Wiley & Sons, Inc.     

Ab initio spectroscopic study for the NaRb molecule in ground and excited states

A wide adiabatic study is performed for NaRb molecule, involving 15¹Σ⁺ electronic states including the ionic state Na^?Rb⁺, as well as 14³Σ⁺, 1–9^1,3Π, and 1–5^1,3Δ states. This investigation is performed using an ab initio approach which involves the effective core potential, the core polarization potential with l‐dependent cut‐off functions. The NaRb system has been treated as a two‐electron system and the full valence configuration interaction is easily achieved. The spectroscopic constants R_e, D_e, T_e, ω_e, ω_ex_e, B_e, and D₀ for all these states are derived. We have also computed the vibrational levels as well their spacing for different values of J. In addition, permanent and transition dipole moments are determined and analyzed. The Dunham coefficients have been used to perform experimental spacing to compare directly with our results. The present calculations on NaRb extend previous theoretical works to numerous electronic excited states in the various symmetries. © 2014 Wiley Periodicals, Inc.     

Linearly and circularly polarized raman spectra of the iron (II) bis[1-(2'-pyridylmethyleneamino)-2-aminoethane] ion evidence for asymmetric raman tensor

Raman spectra of solutions of iron(II)bis[1-(2'-pyridylmethyleneamino)-2-aminoethane] iodide in acetonitrile were recorded using both linearly and circularly polarized light for excitation. The tensor invariants 45$\text{}\text{?}$ga², 7γ_s² and 5γ_as² were determined for three prominent lines with 488.0, 514.5 and 528.7 nm excitation. With two of the lines, significant anti-symmetric anisotropies are found.     

A new expansion for r−212

A new expansion for r^?2₁₂ expressed in terms of Legendre polynomials is given. The explicit expression is . For the coefficients C′_l,k and C_l,k numerically stable formulas are derived.     

Vibrational force constants from generalized X-ray scattering factors

Generalized X-ray scattering factors have been extracted from an accurate one-electron density function of molecular hydrogen. With the approximation that the atomic densities perfectly follow the nuclei, vibrational force constants are given in terms of sum rules for the generalized X-ray scattering factors. Calculated (experimental) results for H₂ are k_e = 5.76 (5.73) mdyne Å^?1, l_e = -38.7 (~36.9) mdyne Å^?2 and m_e = 246 (235) mdyne Å^?3.     

Acetaldehyde photochemistry: Testing the additivity assumption and polarized basis set effects

Selected portions of the S₀ and T₁ potential energy surfaces of acetaldehyde surveyed in our earlier studies have been reexamined. The assumption of the additivity of basis-set polarization and of electron correlation effects used extensively in our earlier work on acetaldehyde has been tested through explicit polarized basis-set electron-correlation calculations. The “additivity assumption” introduces average absolute errors in energy differences of only 1.9 (MP3) to 3.4 (MP2) kcal mol^?1 in seven comparisons. The effects of using 6?31G^** SCF optimized geometries as opposed to single-point calculations on 3?21G SCF structures (6–31G^**//3–21G) as in our previous papers were examined. In six comparisons, the average absolute error in relative SCF energies introduced by the use of the 3–21G geometries rather than the fully consistent 6–31G^– ones was only 0.3 kcal mole^?1. After a uniform scaling procedure, comparisons of the 6–31G^** and 3–21G calculated vibrational frequencies with experiment for CH₃CHO (S₀), CH₄, and CO (20 comparisons) yielded absolute differences of 41 cm^?1 (6–31G^**) and 57 cm^?1 (3–21G). All these more elaborate calculations support for the specific case of acetaldehyde and various minima and transition states of relevance to its photochemistry, the commonly used and practically important approximations (e.g., additivity) made in our earlier studies.     

Excess molar quantities of (a halogenated n-alkane + an n-alkane) A comparative study of mixtures containing either 1-chlorobutane or 1,4-dichlorobutane

Excess molar volumes V_m^E at 298.15 K were obtained, as a function of mole fraction x, for series I: {x1-C₄H₉Cl + (1 ? x)n-C_lH_{2l + 2}}, and II: {x1,4-C₄H₈Cl₂ + (1 ? x)n-C_lH_{2l + 2}}, for l = 7, 10, and 14. 10, and 14. The instrument used was a vibrating-tube densimeter. For the same mixtures at the same temperature, a Picker flow calorimeter was used to measure excess molar heat capacities C_{p, m}^E at constant pressure. V_m^E is positive for all mixtures in series I: at x = 0.5, V_m^E/(cm³ · mol^?1) is 0.277 for l = 7, 0.388 for l = 10, and 0.411 for l = 14. For series II, V_m^E of {x1,4-C₄H₈Cl₂ + (1 ? x)n-C₇H₁₆} is small and S-shaped, the maximum being situated at x_max = 0.178 with V_m^E(x_max)/(cm³ · mvl^?1) = 0.095, and the minimum is at x_min = 0.772 with V_m^E(x_min)/(cm³ · mol^?1) = ?0.087. The excess volumes of the other mixtures are all positive and fairly large: at x = 0.5, V_m^E/(cm³ · mol^?1) is 0.458 for l = 10, and 0.771 for l = 14. The C_{p, m}^Es of series I are all negative and |C_{p, m}^E| increases with increasing l: at x = 0.5, C_{p, m}^E/(J · K^?1 · mol^?1) is ?0.56 for l = 7, ?1.39 for l = 10, and ?3.12 for l = 14. Two minima are observed for C_{p, m}^E of {x1,4-C₄H₈Cl₂ + (1 ? x)n-C₇H₁₆}. The more prominent minimum is situated at x′_min = 0.184 with C_{p, m}^E(x′_min)/(J · K^?1 · mol^?1) = ?0.62, and the less prominent at x″_min = 0.703 with C_{p, m}^E(x″_min)/(J · K^?1 · mol^?1) = ?0.29. Each of the remaining two mixtures (l = 10 and 14) has a pronounced minimum at low mole fraction (x_min = 0.222 and 0.312, respectively) and a broad shoulder around x = 0.7.     

X‐ray diffraction study of the thermal expansion behavior of cellulose triacetate I

Highly crystalline samples of cellulose triacetate I (CTA I) were prepared from highly crystalline algal cellulose by heterogeneous acetylation. X‐ray diffraction of the prepared samples was carried out in a helium atmosphere at temperatures ranging from 20 to 250 °C. Changes in seven d‐spacings were observed with increasing temperature due to thermal expansion of the CTA I crystals. Unit cell parameters at specific temperatures were determined from these d‐spacings by the least squares method, and then thermal expansion coefficients (TECs) were calculated. The linear TECs of the a, b, and c axes were α_a = 19.3 × 10^?5 °C^?1, α_b = 0.3 × 10^?5 °C^?1 (T < 130 °C), α_b = ?2.5 × 10^?5 °C^?1 (T > 130 °C), and α_c = ?1.9 × 10^?5 °C^?1, respectively. The volume TEC was β = 15.6 × 10^?5 °C^?1, which is about 1.4 and 2.2 times greater than that of cellulose I_β and cellulose III_I, respectively. This large thermal expansion could occur because no hydrogen bonding exists in CTA I. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 517–523, 2009     

Electrocapillary Activity and Adsorptive Accumulation of U(VI)‐Cupferron and U(VI)‐Chloranilic Acid Complexes on Mercury Electrode

Interfacial activity of uranium(VI)‐cupferron and uranium(VI)‐chloranilic acid (CAA) complexes (in 0.1 M acetate buffer pH 4.6 or 0.1 M NaClO₄ respectively) on polarized mercury electrode at 110 mV, 10 mV or ?240 mV respectively vs. saturated calomel electrode (SCE), and under conditions of the application of adsorptive stripping voltammetric techniques was studied. It revealed a competitive effect of interfacial activity of the mentioned complexes consisting in a nonmonotonous effect of the bulk concentration of U(VI) on the adsorption of the mentioned complexing reagents at their constant concentrations. At concentrations lower than 5×10^?5 mol L^?1 the complexes U(VI)‐cupferron or U(VI)‐CAA exhibited a relatively strong electrosorption providing the adsorption coefficients β of the order 10⁴ L mol^?1, the maximum surface excess Γ_m ≈ 5 to 10 μmol m^?2 and average Frumkin interaction coefficients reaching their absolute values 2 to 2.6.     

Local Raman tensors in adenosine triphosphoric acid

A polarized laser (488.0 nm) Raman spectroscopic measurement has been made on a single crystal of a disodium salt of adenosine triphosphoric acid (Na₂ATP·3H₂O) by the use of a Raman microscope. The crystal belongs to an orthorhombic system of the space group P2₁2₁2₁, and has dimensions of 10, 100 and 100 μm along the crystallographic axes a, b and c, respectively. For each Raman band in the 300–1800 cm⁻¹ range, the scattering intensity ratio I _bb/I _cc of the bb and cc polarization components has been determined. For a few bands, the relative intensities of the bc components were also estimated. To augment the data, the depolarization ratio of each Raman band of ATP has also been determined for its acidic (pH = 2.42) H₂O and D₂O solutions. From these experimental results, the shapes and orientations of the Raman scattering tensors which are considered to be localized in the adenine-H⁺ portion and in the phosphate portion of the molecule have been derived.     

The Nonreversibility of Adsorption-Desorption of Dieldrin and Lindane on Chitin in Seawater

Abstract

Adsorption and desorption of dieldrin and lindane on chitin were investigated in seawater batch tests as a function of chitin concentration, temperature, pH and salinity. For chitin concentrations ranging from 0.5 g l^?1 to 12.5 g l^?1, the pesticide concentrations were varied from 4 μgl^?1 to 65 μg^?1 for dieldrin and from 40 μl^?1 to 680 μg l^?1 for lindane. Both dieldrin and lindane show adsorption-desorption hysteresis at low chitin concentration. At high chitin concentrations (m > 6.25 g l^?1 for dieldrin and m > 10 gl^?1 for lindane) both pesticides exhibit reversible behaviour. However, only lindane adsorption is affected by chitin concentration. These types of behaviour remain fixed in prewashed chitin. However, an increase in the temperature and a decrease in the salinity made the process become reversible. A resistant-reversible two component model has been applied to account for these types of behaviour and provides a way to explain most of the observed effects by defining mass independent distribution coefficients.     

Time‐Resolved Assembly of Cluster‐in‐Cluster {Ag12}‐in‐{W76} Polyoxometalates under Supramolecular Control

We report the time‐resolved supramolecular assembly of a series of nanoscale polyoxometalate clusters (from the same one‐pot reaction) of the form: [H_(10+m)Ag₁₈Cl(Te₃W₃₈O₁₃₄)₂]_n, where n=1 and m=0 for compound 1 (after 4 days), n=2 and m=3 for compound 2 (after 10 days), and n=∞ and m=5 for compound 3 (after 14 days). The reaction is based upon the self‐organization of two {Te₃W₃₈} units around a single chloride template and the formation of a {Ag₁₂} cluster, giving a {Ag₁₂}‐in‐{W₇₆} cluster‐in‐cluster in compound 1 , which further aggregates to cluster compounds 2 and 3 by supramolecular Ag‐POM interactions. The proposed mechanism for the formation of the clusters has been studied by ESI‐MS. Further, control experiments demonstrate the crucial role that TeO₃^2?, Cl^?, and Ag⁺ play in the self‐assembly of compounds 1 – 3 .     

A Study of picosecond dehalogenation of chlorobenzene anions in liquids by positronium inhibition measurements

Radiation chemistry and results of Ps yields indicate that the following processes occur in the positron spur in solution of halogen-substituted hydrocarbons, RX_n: e⁺ + e^? → Ps, e^? + RX _n → (RX_n)^? → RX_n?1 + X^?, e⁺ + (RX_n)^? → Ps + RX_n, e⁺ + X^? → [X^?, e⁺]. Hence the trapped electron can form Ps only if (RX _n)^? is stable or has a lifetime that is longer than o comparable to the Ps formation time. Previous studies have shown that some of the strongly chlorinated benzenes (n = 4.5 give reasonable inhibition in benzene but not in linear hydrocarbons. The reason is very probably that the dechlorination time is much shorter in benzene than in saturated hydrocarbons because Cl^? is more strongly solvated in benzene than in non-aromatic hydrocarbons. To test those ideas further we have begun detailed studies of solutions of the possible “intermediate” inhibitors, viz. 1,2,3,5- and 1,2,4,5-C₆H₂Cl₄, in mixtures of C₆H₆/C₆H₁₄ different methyl-substituted benzene aniline, anisole, dioxane and ethylbenzene. The results are discussed and interpreted in terms of the spur model. The Ps inhibition efficiency of the two isomeric forms of tetrachlorobenzene studied, appears most probably to depend on intramolecular electron transfer with subsequent dehalogenation of the molecular anion on a picosecond timescale. The divergence in inhibitor efficiency obtained for the chlorobenzenes when dissolved in aromatic solvents compared to the same solutes when dissolved in a saturated alkane appears most probably to be caused by complex formation between the initially formed chlorobenzene anion and benzene molecules, which permits a rapid relaxation of the molecular anion with subsequent bond stretching and expulsion of the chloride anion.     

Measurements of light scattering changes induced by a strong optical field in solutions of tRNA

Changes in light scattering induced by a strong laser beam, as predicted theoretically by Kielich, were measured for unfractionated yeast transfer ribonucleic acid (tRNA) solutions. The vertically polarized electric field of a strong laser pulse (λ = 1060nm) amounted to 4.5 × 10³ esu cgs; its duration was 10 nsec. A weak incident laser beam (λ = 630nm) was also polarized vertically and the vertical and horizontal intensity components of the light scattered through 90° at the latter wavelength were measured. These measurements together with previous results from measurements of Rayleigh light scattering and light scattering in a magnetic field permitted evaluation of the tensor of third-order polarizability (c = 3 × 10^?30 esu cgs, c = ?373 × 10^?30 esu cgs) and the anisotropy of the third-order polarizability components with its sign (δ_c = +56 × 10^?2, δ_c = +0.25 × 10^?2 for tRNA monomer and aggregate, respectively). The new method described may be useful for studies of macromolecules and macromolecular complexes of biological importance.     

Coordination Chemistry of Diiodine and Implications for the Oxidation Capacity of the Synergistic Ag+/X2 (X=Cl,Br, I) System

The synergistic Ag⁺/X₂ system (X=Cl, Br, I) is a very strong, but ill‐defined oxidant—more powerful than X₂ or Ag⁺ alone. Intermediates for its action may include [Ag_m(X₂)_n]^m+ complexes. Here, we report on an unexpectedly variable coordination chemistry of diiodine towards this direction: ( A )Ag‐I₂‐Ag( A ), [Ag₂(I₂)₄]²⁺( A ^?)₂ and [Ag₂(I₂)₆]²⁺( A ^?)₂?(I₂)_x≈0.65 form by reaction of Ag( A ) ( A =Al(OR^F)₄; R^F=C(CF₃)₃) with diiodine (single crystal/powder XRD, Raman spectra and quantum‐mechanical calculations). The molecular ( A )Ag‐I₂‐Ag( A ) is ideally set up to act as a 2 e^? oxidant with stoichiometric formation of 2 AgI and 2 A ^?. Preliminary reactivity tests proved this ( A )Ag‐I₂‐Ag( A ) starting material to oxidize n‐C₅H₁₂, C₃H₈, CH₂Cl₂, P₄ or S₈ at room temperature. A rough estimate of its electron affinity places it amongst very strong oxidizers like MF₆ (M=4d metals). This suggests that ( A )Ag‐I₂‐Ag( A ) will serve as an easily in bulk accessible, well‐defined, and very potent oxidant with multiple applications.     

Identifying the Crystalline Orientation of Black Phosphorus Using Angle‐Resolved Polarized Raman Spectroscopy

An optical anisotropic nature of black phosphorus (BP) is revealed by angle‐resolved polarized Raman spectroscopy (ARPRS), and for the first time, an all‐optical method was realized to identify the crystal orientation of BP sheets, that is, the zigzag and armchair directions. We found that Raman intensities of A_g¹, B_2g, and A_g² modes of BP not only depend on the polarization angle α, but also relate to the sample rotation angle θ. Furthermore, their intensities reach the local maximum or minimum values when the crystalline orientation is along with the polarization direction of scattered light (e_s). Combining with the angle‐resolved conductance, it is confirmed that A_g² mode intensity achieves a relative larger (or smaller) local maximum under parallel polarization configuration when armchair (or zigzag) direction is parallel to e_s. Therefore, ARPRS can be used as a rapid, precise, and nondestructive method to identify the crystalline orientation of BP layers.     

Structure of the iodine columns in iodinated nylon-6

A study of iodine-complexed nylon 6 films by polarized resonance Raman spectra shows the presence of both I ₃^? and I ₅^? species, the latter most likely in the form of an I ₂/ I ₃^? complex. Polarization characteristics of the Raman spectra show that the I ₂/ I ₃ units are orinted along the polymer chain and the I ₃^? ions are perpendicular to the chain axis. The I ₂/ I ₃^? units are in a more stable moiety than the I ₃^? species. These Raman results are consistent with the x-ray diffraction data.     

二元无机物标准熵 So298的拓扑研究

为了预测二元无机物的标准熵,基于分子图的连接矩阵和离子参数gi、qi,提出了一种新的连接性指数mQ, mG及其逆指数mQ’, mG’。 qi、gi定义为：qi=(1.1+Zi1.1) /(1.7+ni), gi=(1.4+Zi) /(0.9+ri+ri-1),其中Zi 、ni和 ri分别代表离子i的电荷数、最外层主量子数和半径。从0Q, 0Q’, 1G,和1G’,利用多元线性回归分析方法和人工神经网络方法,可以构建优良的QSPR模型。对371个二元无机物,其多元线性模型及神经网络模型的相关系数、标准偏差和平均绝对偏差分别是：0.9905, 8.29 J.K-1.mol-1, 6.48 J. K-1.mol-1, 0.9960, 5.37 J.K-1.mol-1 和 3.90 J.K-1.mol-1。留一法交叉验证表明,其多元线性模型具有良好的稳定性。两个模型对187个未进入模型的二元无机物的标准熵的预测值和实验值之间的相关系数、标准偏差和平均绝对偏差分别是：0.9897, 8.64 J. K-1.mol-1, 6.84 J. K-1.mol-1, 0.9957, 5.63 J.K-1.mol-1, 和 4.18 J.K-1.mol-1。研究表明,本文方法在预测二元无机物标准熵时比文献方法更有效,两种模型均能较精确的预测二元无机物的标准熵,且神经网络模型的预测结果更精确。     

MRCI study on spectroscopic parameters and molecular constants of the ground state of AsP(X1Σ+) molecule

The potential energy curve (PEC) for the ground state of AsP(X¹Σ⁺) has been investigated by the highly accurate valence internally contracted multireference configuration interaction method in the Molpro2008 program package with the correlation consistent basis set. The PEC is fitted to the analytic Murrrell–Sorbie function (M–S function) from which the spectroscopic constants are determined. The present D_e, B_e, α_e, ω_eχ_e, R_e, and ω_e values are of 4.2823 eV, 0.188622 cm^?1, 0.000749 cm^?1, 1.984427 cm^?1, 2.0194 Å, and 598.60 cm^?1, respectively. In addition, by numerically solving the radial Schrödinger equation of nuclear motion in the adiabatic approximation, the total of 96 vibration states is predicted when the rotational quantum number J = 0. The complete vibration levels, classical turning points, inertial rotation, and centrifugal distortion constants are reproduced. Comparison has been made with recent theoretical and experimental data. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Sequential segregation of Sn and Sb in a Cu(111) single crystal

The sequential segregation of Sn and Sb to the surface of a Cu(111) single crystal was measured in the temperature range 400–1100 K by Auger electron spectroscopy. It was found that Sn with the higher diffusion coefficient first segregates to the surface and then is replaced by the slower‐segregating Sb. The results were fitted by a ternary segregation model yielding segregation energies (ΔG_Sn = 76.3 kJ mol^?1, ΔG_Sb = 95.9 kJ mol^?1), interaction parameters (Ω_SnCu = 3.8 kJ mol^?1, Ω_SbCu = 16.2 kJ mol^?1, Ω_SnSb = ?5.3 kJ mol^?1) and diffusion coefficients (D_0(Sn) = 1.8 × 10^?5 m² s^?1, E_Sn = 173 kJ mol^?1, D_0(Sb) = 6.0 × 10^?5 m² s^?1, E_Sb = 205 kJ mol^?1) for both species. The validity of the interaction coefficients and segregation energies was verified using the Guttman equations for equilibrium segregation in ternary systems. Copyright © 2003 John Wiley & Sons, Ltd.