Quantum wave packet and quasiclassical trajectory studies of the reaction H(2S) + CH(X2Π; v = 0, j = 1) → C(1D) + H2(X1 ): Coriolis coupling effects and stereodynamics

The quantum mechanics (QM) and quasiclassical trajectory (QCT) calculations have been carried out for the title reaction with the ground minimal allowed rotational state of CH (j = 1) on the 1 ¹A′ potential energy surface. For the reaction probability at total angular momentum J = 0, a similar trend of the QM and QCT calculations is observed, and the QM results are larger than the latter almost in the whole considered energy range (0.1–1.5 eV). The QCT integral cross sections are larger than the QM results with centrifugal sudden approximation, while smaller than those from QM method including Coriolis coupling for collision energies bigger than 0.25 eV. The quantum wave‐packet computations show that the Coriolis coupling effects get more and more pronounced with increasing of J. In addition to the scalar properties, the stereodynamical properties, such as the average rotational alignment factor <P₂( j′?k )>, the angular distributions P(θ_r), P(?_r), P(θ_r,?_r), and the polarization‐dependent generalized differential cross sections have been explored in detail by QCT approach. © 2013 Wiley Periodicals, Inc.     

Unusual finite size effects in the Monte Carlo simulation of microphase formation of block copolymer melts

Extensive Monte Carlo simulations are presented for the Fried-Binder model of block copolymer melts, where polymer chains are represented as self and mutually avoiding walks on a simple cubic lattice, and monomer units of different kind (A, B) repel each other if they are nearest neighbors (ε_AB > 0). Choosing a chain length N = 20, vacancy concentration Φ_v = 0,2, composition ƒ = 3/4, and a L × L × L geometry with periodic boundary conditions and 8 ≤ L ≤ 32, finite size effects on the collective structure factor S(q) and the gyration radii are investigated. It is shown that already above the microphase separation transition, namely when the correlation length ξ(T) of concentration fluctuations becomes comparable with L, a nonmonotonic variation of both S(q) and the radii with L sets in. This variation is due to the fact that the wavelength λ^*(T) of the ordering (defined from the wavenumber q^* where S(q) is maximal at λ^* = 2 π/q^*) in general is incommensurable with the box. The competition of two nontrivial lengths ξ(T), λ^* (T) with L makes the straigthforward application of finite size scaling techniques impossible, unlike the case of polymer blends. Since also the specific heat is found to have a broad rounded peak near the transition only, locating the transition accurately from Monte Carlo simulations remains an unsolved problem.     

Electron-pair radial density functions

We introduce and discuss a generalized electron-pair radial density function G(q; a) that represents the probability density for the electron-pair radius |r ₁+ar ₂| to be q, where a is a real-valued parameter. The density function G(q; a) is a projection of the two-electron radial density D ₂(r ₁, r ₂) along lines r ₁ + ar ₂ ± q = 0 in the r ₁ r ₂ plane onto a point in the qa plane, and connects three densities S(s), D(r), and T(t), defined independently in the literature, as a smooth function of a: For an N-electron (N ≥ 2) system, S(s) = G(s; + 1), D(r) = 2G(r; 0)/(N − 1), and T(t) = G(|t|;−1)/2, where S(s) and T(t) are the electron-pair radial sum and difference densities, respectively, and D(r) is the single-electron radial density. Simple illustrations are given for the helium atom in the ground 1s² and the first excited 1s2s ³S states.     

Compton profiles and momentum space inequalities

Rigorous upper and lower bounds to the atomic Compton profileJ(q) are obtained for any value of the momentum transferredq in terms of radial expectation values 〈p ⁿ 〉 of the atomic momentum density γ(p). In doing so, a procedure based on moment-theoretic techniques and Chebyshev inequalities has been used. This type of results can be employed to study the compatibility of diverse information obtained by using different models, techniques, numerical calculations or experimental data. The same method allows also to obtain approximations to the Compton profile and to bound other relevant characteristics ofJ(q). A comparison of the approximations with some previously known Maximum Entropy Approximations is done. In order to test the accuracy of the bounds, a numerical study of the results is carried out in a Hartree-Fock framework for atomic systems.     

Molecular orientational motion in discotic liquid crystals

Abstract

The spectral densities of motion for the aromatic and chain deuterons of the discotic mesogen hexahexyoxytriphenylene (THE6) have been reported in the literature for a frequency of 46 MHz. Most spectral densities J_p (pω₀, 90°) have been obtained from samples consisting of a planar distribution of domains in which the directors were perpendicular to the magnetic field Limited data J_p (pω₀) have also been available from single-domain samples with the director aligned parallel to the magnetic field. We have applied the small-step rotational diffusion model of Nordio et al. to the data from the aromatic deuterons of THE6-ard in its uniaxial columnar D_ho phase, to describe the spinning (D _∥, rotational diffusion constant about the planar normal to the disc) and the tumbling (D?, rotational diffusion constant of the planar normal) motions of the molecular core. Although this model has been successfully used for rod-like nematic liquid crystals, its use has not been attempted for discotic liquid crystals. The model seems to indicate that molecular reorientation has slowed down in the D_ho phase, giving frequency dependence to the spectral densities. This can be explained by the high orientational order of the molecules. We are able to account for the four spectral densities J ₁ (ω₀), J ₁ (ω₀, 90°), J ₂ (2ω₀) and J ₂(2ω₀, 90°) with a calculated ratio D∥/D? of about 1. This is quite different from that of rodlike liquid crystals.     

Homogeneous Fermi liquid with ‘artificial’ repulsive inverse square law interparticle potential energy

A good deal is known by now on the so-called jellium model of the homogeneous electron liquid. However, much of the quantitative progress at experimentally realizable densities has come from quantal computer simulation. Therefore, we here consider a homogeneous Fermion liquid with ‘artificial’ repulsive interaction λ/(r_ij )² between Fermions i and j at separation r_ij . We discuss first of all the way the static structure function S(q), essentially the Fourier transform of the pair correlation function, is changed because of non-zero λ from the ‘Fermi hole’ form due entirely to Pauli principle effects between parallel spin Fermions. Unlike jellium with e ²/r_ij repulsive interactions, S(q) is proportional to q at long wavelengths, whereas the plasmon in jellium annulls the q term and S(q) is quadratic in q as q tends to zero. However for λ/(r_ij )² interactions, the coefficient of q appearing in the Fermi hole structure factor, is renormalized by particle repulsions. Then some discussion is given of Fermion quasiparticle lifetimes τ as the Fermi surface is approached. Arguments are presented that τ^?1 is proportional to |E???E _F| as E tends to the Fermi energy. This is already interesting, in fact, in connection with the jellium model and therefore an approximate analytic form of τ is finally derived.     

Expansion coefficients and moments of electron momentum densities for singly charged ions

Numerical Hartree–Fock calculations of the first three coefficients of the MacLaurin expansion and the leading coefficient of the large-p asymptotic expansion of the electron momentum densities Π(p) are reported for 54 singly charged atomic cations from He⁺ (atomic number Z = 2) to Cs⁺ (Z = 55) and 43 anions from H⁻ (Z = 1) to I⁻ (Z = 53) in their experimental ground states. We also report all the finite moments <p ^k > (−2≤k≤+4) of the momentum densities Π(p) for the above-mentioned 97 ionic species. The results are compared with the previous ones for neutral atoms [Koga and Thakkar (1996) J Phys B 29: 2973], and the dependence of the expansion coefficients and moments on nuclear charge is discussed among isoelectronic species. Received: 20 November 1998 / Accepted: 15 January 1999 / Published online: 7 June 1999     

Hydrolysis of methyltin(IV) trichloride in aqueous NaCl and NaNO3 solutions at different ionic strengths and temperatures

The hydrolysis of methyltin(IV) trichloride (CH₃SnCl₃) has been studied in aqueous NaCl and NaNO₃ solutions (0 < I/mol dm⁻³ ≤ 1), at different temperatures (15 ≤ T/°C ≤ 45) by­potentiometric measurements (H⁺‐glass electrode). By considering the generic hydrolytic <?tw=97.2%>reaction pCH₃Sn³⁺ + qH₂O = (CH₃Sn)_p(OH)_q^3p−q<?tw>­+ qH⁺ (logβ_pq), we have the formation of five species and logβ₁₂ = −3.36, logβ₁₃ = −8.99, logβ₁₄ = −20.27 and logβ₂₅ = −7.61. The first hydrolysis step is measurable only at very low pH values and was not determined: a rough estimate of the hydrolysis constant is logβ₁₁ = −1.5 (± 0.5). The dependence on ionic strength of logβ_pq is quite different in NaNO₃ and NaCl solutions, and the formation at low pH values of the species CH₃Sn(OH)Cl⁺ has been found with logβ = −1.40. Hydrolysis constants strongly depend on temperature and from the relationships logβ_pq = f(T), ΔH ° values have been calculated. Speciation problems of CH₃Sn³⁺ in aqueous solution are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Beziehungen zwischen chemischer Verschiebung und Ladungsdichte

This work is concerned with the relationship between chemical shifts (δ) of protons and their charge densities (q). It can be shown that the relation δ^H = a + bq^H + cq^C (q^C = charge density at the corresponding C-atom) fits best for a prediction of δ-values from calculated charge densities. The smallest standard error for the prediction of δ-values is obtained if the charge densities are calculated by the CNDO- or INDO-method.     

A partial recurrence relation for reduced class coefficients of the symmetric group

An expression for the product of a single-cycle class [(1)^{N - P}(p)]_N and an arbitrary class [(1)^l1(2)^l …? (N)^lN]_N of the symmetric group has recently been conjectured. This expression involves a sum over a relatively small number of reduced class sums, depending on p indices. A further conjecture is formulated and demonstrated, according to which reduced class coefficients (RCCS ) involving cycles whose length is expressed by means of a single index can be related to corresponding coefficients in the product of [(1)^{N - P+1}(p - 1)]_N with an arbitrary class sum. Consequently, the problem of evaluating the general class sum product reduces to that of obtaining a relatively small set of fundamental RCCS containing no single-index cycles. The conjectures mentioned can be used to evaluate the product [(1)^{N - p}(p)]_N · [(1)^{N - q}(q)]_N in terms of fundamental RCCS that can all be obtained from the product [(r)]_r · [(r)]_r, where r = min(p, q). For the latter product, we use a result due to Boccara.     

The Franck—Condon principle for radiationless transitions in molecules and a selection rule for morse oscillators

The Franck—Condon (FC) principle for the tunnel radiationless transition (RT) is formulated. It reads that the RT occurs at constant values of the nuclear coordinates q* and of the classical momenta p*. However, unlike the optical transitions, q* and p* take non-physical values since the tunnel RT is a classically forbidden process. As a result of energy conservation, the potential surfaces of two given electronic states cross with one another at the nuclear configuration q*. It is concluded that the electronic-orbital selection rules and the numerical values of the purely electronic matrix elements are governed by the configuration q* rather than by the equilibrium nuclear configuration as was supposed previously. The configuration q* for the T₁ → S₀ intersystem crossing in aromatic hydrocarbons is described in terms of a large displacement of only one H atom from its equilibrium position along the CH bond (perhaps, there is also some out-of-plane displacement). Using the FC principle, it is found that the anharmonicity of the local CH bond vibrations results in a strong dependence of the T₁ → S₀ intersystem crossing rates upon the sign of the CH bond-length change between two given electronic states, Δq = R_T1 - R_S0. Namely, the following “selection rule” holds: these RTs are allowed at Δq < 0 and they are forbidden at Δq > 0, the prohibition factor being of the order of 10²–10⁴. Finally, an oscillatory dependence of the FC factors upon Δq is explained, using the FC principle, in terms of quantum interference in the total transition probability, of which the amplitude is a sum of the transition amplitudes due to different crossing points q*. The interference effects are believed to be insignificant for RTs in molecules with large energy gaps and so they are eliminated in the usual manner by adding up the partial probabilities rather than the partial amplitudes. The classical FC factor thus obtained smoothly depends upon Δq (and upon other parameters as well). This procedure also provides an analytical continuation of the FC factor to non-integral quantum numbers.     

Pharmacophore generation,atom-based 3D-QSAR,HQSAR and activity cliff analyses of benzothiazine and deazaxanthine derivatives as dual A2A antagonists/MAO‑B inhibitors

Dual inhibition of A_2A and MAO-B is an emerging strategy in neurodegenerative diseases, such as Alzheimer’s disease (AD) and Parkinson’s disease (PD). In this study, atom-based three-dimensional quantitative structure–activity relationship (3D-QSAR) and hologram quantitative structure–activity relationship (HQSAR) models were generated with benzothiazine and deazaxanthine derivatives. Based on activity against A_2A and MAO-B, two statistically signi?cant 3D-QSAR models (r² = 0.96, q² = 0.76 and r² = 0.91, q² = 0.63) and HQSAR models (r² = 0.93, q² = 0.68 and r² = 0.97, q² = 0.58) were developed. In an activity cliff analysis, structural outliers were identified by calculating the Mahalanobis distance for a pair of compounds with A_2A and MAO-B inhibitory activities. The generated 3D-QSAR and HQSAR models, activity cliff analysis, molecular docking and dynamic studies for dual target protein inhibitors provide key structural scaffolds that serve as building blocks in designing drug-like molecules for neurodegenerative diseases.     

Quantum wave packet calculation of reaction probabilities,cross sections,and rate constants for the C(1D) + HD reaction

The time‐dependent real wave packet method has been used to study the C(¹D) + HD reaction. The state‐to‐state and state‐to‐all reactive scattering probabilities for a broad range of energies are calculated at zero total angular momentum. The probabilities for J > 0 are estimated from accurately computed J = 0 probabilities by using the J‐shifting approximation. The integral cross sections for a large energy range, and thermal rate constants are calculated. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

13C NMR spectra of 2,3-dihydro-1H-benzo[b]azepines: Differentiation of diastereomers

The ¹³C NMR spectra of 23 2,3-dihydro-1H-benzo[b]azepines, including nine pairs of diastereomers separated by chromatography, [(2R*, 3R^*) and (2R^*), 3S^*)] are hereby assigned and discussed. The relative configurations of the diastereomers were assigned by two methods. The first, based on the chemical shifts of the asymmetric carbons C-2 and C-3 (with regression analysis), shows that the values for (R^*, R^*) are approximately 1 ppm lower than those for (R^*, S^*) diastereomers. The second method uses the chemical shifts, δ₃, of the R₃(CH₃) substituents. When these δ₃ values are compared by means of the δ₃-δ_m difference (δ_m is the mean value obtained from compounds where R₂=H), the difference is always negative for (R^*, R^*) and positive for (R^*, S^*). This is attributed to a γ-gauche effect between R₂ and R₃ in the case of (R^*, R^*) diastereomers (R₂ and R₃ are cis). The results corroborate those already obtained by ¹H NMR [J(23)(R^*, R^*)<J(23)(R^*, S^*)] and are a confirmation of the results of a radiocrystallographic examination carried out on two nitrogen acetylated diastereomers.     

Formation of Zinc(II) and Cadmium(II) Complexes with Pyridine Oxime Ligands in Aqueous Solution

Complex formation equilibria involving pyridine-2-carboxaldehyde oxime (1), 1-(2-pyridinyl)ethanone oxime (2) and 6-methylpyridine-2-carboxaldehyde oxime (3), HL, with zinc(II) and cadmium(II) ions were studied in aqueous 0.1 M NaCl solution at 25° C by potentiometric titrations with a glass electrode. Experimental data were analysed with the least-squares computer program SUPERQUAD to determine the complexes formed and their stability constants. With Ligands 1 and 2 the sets of complexes for Zn(II) and Cd(II) are essentially the same, mono- and dinuclear oxime complexes and their deprotonated/hydrolysed products H_pM_q(HL)^2q+p _r. Owing to the steric requirements of the 6-methyl group, sets of complexes formed with 3 are distinctly different. For zinc(II), only dinuclear oximato species H_pZn₂(HL)^4q+p ₂ ( p = ? 2, ? 3, ? 4) are found, while for the larger cadmium(II) ion mononuclear oximato species CdL⁺ and CdL₂ are detected in addition to the dinuclear complex H_pCd₂(HL)^4q+p ₂ ( p = ? 3).     

Small‐angle X‐ray scattering study of a weak polyelectrolyte in water

Small‐angle X‐ray scattering (SAXS) was used to obtain solution parameters of a weak polyelectrolyte in water in the absence of any additives, such as neutralizing agents or salt. Poly(acrylic acid) (PAA) was used as a weak polyelectrolyte from which SAXS data were obtained in the dilute region of 1–10 mg cm^?3. An intrinsic viscosity of 15.7 dL g^?1 was obtained from a plot of reciprocal reduced viscosities versus the concentration. The application of the SAXS data, that is, the contour length (L = 1.97 × 10⁴ Å), the persistence length (a* = 58.5 Å), and the molecular weight (M = 5.9 × 10⁵ Da), to the Yamakawa–Fujii equation suggested that PAA in water at 25 °C could be described as a wormlike chain having a cylindrical body of d = 6 Å. An end‐to‐end distance (r = 1.6 × 10³ Å) was calculated from r = 2a*L ? 2(a*)². The nonisotropic expansion factor (α = 2.9) was calculated for PAA expanding from the random coil in dioxane at 30 °C (Θ temperature) to the wormlike chain in water at 25 °C. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1263–1272, 2003     

Creep recovery of acrylate urethane oligomer/acrylate networks. 2. Investigation of different modes of molecular motion

The creep recovery and dynamic mechanical properties of acrylate urethane oligomer/acrylate networks were investigated. The retardation spectra L_CR obtained from the creep recovery experiments were significantly different from the corresponding retardation spectra L_DMA obtained from the dynamic mechanical measurements. The reduced frequency ω^* dependence of L_DMA and the relaxation spectra H_DMA in the higher ω^* region were approximately represented as L_DMA ∝_ω^*−p and H_DMA ∝_ω^*q, although L_CR decreased faster than L_DMA with an increase in ω^*. The exponents q were close to ½ characterizing the Rouse modes in the systems containing an acrylate urethane oligomer of M_w = 5000 but less than ½ in the system containing an acrylate urethane oligomer of M_w = 12,000. For the latter systems, significant thermorheological complexity was observed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2543–2550, 1997     

Small-angle x-ray scattering measurements on dilute solutions of polyisobutene by use of kratky cone collimation

SAXS measurements on dilute solutions of polyisobutene in n-hexane (M _ν = 25,600?3.55 × 10⁶, c < 53 g/liter) were carried out by combining conventional slit collimation with the new cone collimation technique. With a fractionated sample (M _ν = 25,600; U < 0.2) the radius of gyration (R = 48 Å), the cross-sectional radius of gyration (R_q = 3.9 Å), the molecular weight per unit length (M/L = 22.8 Å^?1), and the Porod persistence length (a^* = 8.1 Å) are found. The persistence length appears to be dependent on the molecular weight. The partial specific volume ν of polyisobutene in n-hexane also depends on the molecular weight according to ν = 1.025 + 105/M _ν (cm³/g).     

Coulombic and ring-shaped potentials treated in a unified way via a nonbijective canonical transformation

This paper is concerned with the three-dimensional potentialV _q =² (2a ₀/r–q a ₀ ²/r ² sin² ) ₀ which comprises as particular cases the ring-shaped potential (q = 1) and the Coulomb potential (q = 0). The Schrödinger equation for the potentialV _q is transformed via a nonbijective canonical transformation, viz., the Kustaanheimo-Stiefel transformation, into a coupled pair of Schrödinger equations for two-dimensional harmonic oscillators with inverse-square potentials. As a consequence, the discrete spectrum for the potentialV _q is obtained in a straightforward way. A special attention is paid to the caseq = 0. In particular, the coupled pair of Schrödinger equations for two-dimensional harmonic oscillators is tackled in the situations where the spectrum for the potentialV ₀ is discrete, continuous, or reduced to the zero point. Finally, some group-theoretical questions about the potentialV _q are mentioned as well as a connection, via the Kustaanheimo-Stiefel and the Levi-Civita transformations, between the quantum-mechanical problems for the potentialV _q and the Sommerfeld and Kratzer potentials.     

Gaussian vs. Slater representations of d orbitals: An information theoretic appraisal based on both position and momentum space properties

A detailed appraisal of Gaussian-type orbital (GTO) and Slater-type orbital (STO) expansions of 3d orbitals is carried out for the ²S state of copper—a case that should be maximally unfavorable for STOs. The appraisal is based on a wide variety of both position and momentum space properties and utilizes an information theoretic quality assessment technique. It is found that GTO expansions are not as useful as STO expansions for the prediction of 〈p⁸〉, 〈p⁷〉, and 〈r^?6〉 because these properties probe the functional deficiencies of GTOs at small r and large p. On the other hand, GTO expansions can predict accurate values of large r properties like 〈r⁸〉 despite the fact that their position space asymptotic decay is too fast. Unlike the case of s orbitals in helium, there does not seem to be any consistent ordering between accuracy in position space and accuracy in momentum space. The quality measures are found to be very useful for pinpointing the deficiencies of various expansions. This information enables us to construct easily a new GTO and a new STO expansion that are more accurate than any of the others in the literature. It is suggested that one STO is worth no more than two GTOs in the case of d orbitals.