Calculations of <Superscript>31</Superscript>P Magnetic Shielding Constants of Derivatives of Betaine and Phosphine Molecules Dissolved in Different Solvents by Using Supermolecular Model and Combined Methods of Quantum Chemistry and Molecular Mechanics

Spatial structures of molecular clusters modeling a solvate shell around phosphorus-containing methyl- and butyl-derivatives of phosphine and betaine molecules dissolved in different solvents (acetone, toluene, formamide) have been calculated by using different variants of density functional theory (unrestricted Becke three-parameter Lee–Yang–Parr [UB3LYP], Perdew–Burke–Ernzerhof [PBE], optimized exchange functional [OPTX] developed by Handy and Cohen in conjunction with Lee–Yang–Parr [LYP] correlational functional [OLYP]) with 6-31G(d,p) and 6-31G++(d,p) basis sets. The ³¹P magnetic shielding constants for the structures are calculated with the usage of gauge-including atomic orbitals in UB3LYP/6-31G(d,p) and 6-31G++(d,p) methods. The modeling of molecular clusters is done by using the supermolecular model, the molecular mechanics method and the combination of quantum chemistry and molecular mechanics methods (QM/MM). The own N-layered integrated molecular orbital method (ONIOM) has been applied for modeling and calculating of isotropic ³¹P nucleus magnetic shielding of clusters of trimethylphosphine and trimethylbetaine molecules dissolved in acetone using combinations of UB3LYP/6-31G(d,p) (higher level) and unrestricted Hartree–Fock (UHF)/6-31G(d,p) (lower level) methods. Applicability of the ONIOM approach and different ways of modeling to the calculation of ³¹P nucleus magnetic shielding constants is studied. A comparison of the results obtained by the density functional theory, ONIOM and MM methods is given.     

A Theoretical Study of <Superscript>51</Superscript>V Electric Field Gradient Tensors in Pyrovanadates and Metavanadates

A computational study of the ⁵¹V electric field gradient (EFG) tensors in pyrovanadates, α-Zn₂V₂O₇, Cd₂V₂O₇, β-Mg₂V₂O₇ and BaCaV₂O₇, and the metavanadates, LiVO₃, α-NaVO₃, KVO₃, ZnV₂O₆ and MgV₂O₆, is presented. Restricted Hartree–Fock and hybrid density functional theory calculations have been used to investigate the effects of the size of vanadium-oxygen clusters, basis set size, proton-termination and embedded cluster techniques on the accuracy of the calculated EFG tensors. Good agreement between theory and experiment is obtained for most of the vanadates. A sound methodology is suggested for calculating the EFG tensor in pyrovanadates which contain isolated V₂O₇ ⁴⁻ clusters. For metavanadates, the charges of the bridging oxygen atoms can be differentiated from those of terminal oxygen atoms by terminating the former with hydrogen atoms, and embedded cluster molecular orbital calculations are useful in accounting for the long-range electrostatic interactions which influence the EFG tensor components. EFG tensor orientations vary for different pyrovanadate structural types, and individual components are confined by symmetry elements in the metavanadates. A preliminary comparison is made between ⁵¹V EFG tensors calculated with ab initio and plane wave methods. Theoretical EFG tensor components and orientations, in combination with experimental ⁵¹V solid-state nuclear magnetic resonance data, are demonstrated to be useful tools for prediction of molecular structure. Authors' address: Robert W. Schurko, Department of Chemistry and Biochemistry, University of Windsor, Windsor, Ontario N9B 3P4, Canada     

<Superscript>29</Superscript>Si, <Superscript>27</Superscript>Al, <Superscript>1</Superscript>H and <Superscript>23</Superscript>Na MAS NMR Study of the Bonding Character in Aluminosilicate Inorganic Polymers

²⁹Si, ²⁷Al, ¹H and ²³Na solid-state magic-angle spinning (MAS) nuclear magnetic resonance (NMR) has been used to relate nominal composition, bonding character and compressive strength properties in aluminosilicate inorganic polymers (AIPs). The ²⁹Si chemical shift varies systematically with Si-to-Al ratio, indicating that the immediate structural environment of Si is altering with nominal composition. Fast ¹H MAS and ²⁹Si T _SiH/T _1ρ relaxation measurements demonstrated that occluded pore H₂O mobility within the disordered cavities is slow in comparison with H₂O mobility characteristics observed within the ordered channel structures of zeolites. The ²⁷Al MAS NMR data show that the Al coordination remains predominantly 4-coordinate. In comparison with the ²⁹Si MAS data, the corresponding ²⁷Al MAS line shapes are relatively narrow, suggesting that the AlO₄ tetrahedral geometry is largely unperturbed and the dominant source of structural disorder is propagated by large distributions of Si–O bond angles and bond lengths. Corresponding ²³Na MAS and multiple-quantum MAS NMR data indicate that Na speciation is dominated by distributions of hydration states; however, more highly resolved ²³Na resonances observed in some preparations supported the existence of short-range order. New structural elements are proposed to account for the existence of these Na resonances and an improved model for the structure of AIPs has also been proposed. Authors' address: John V. Hanna, NMR Facility, Institute of Materials and Engineering Science, Lucas Heights Research Laboratories, Australian Nuclear Science and Technology Organisation, Private Mail Bag 1, Menai, NSW 2234, Australia     

<Superscript>1</Superscript>H and <Superscript>19</Superscript>F NMR relaxation time studies in (NH<Subscript>4</Subscript>)<Subscript>2</Subscript>ZrF<Subscript>6</Subscript> superionic conductor

¹H and ¹⁹F spin-lattice relaxation times in polycrystalline diammonium hexafluorozirconate have been measured in the temperature range of 10–400 K to elucidate the molecular motion of both cation and anion. Interesting features such as translational diffusion at higher temperatures, molecular reorientational motion of both cation and anion groups at intermediate temperatures and quantum rotational tunneling of the ammonium group at lower temperatures have been observed. Nuclear magnetic resonance (NMR) relaxation time results correlate well with the NMR second moment and conductivity studies reported earlier.     

Crystalline Aluminium Borates with the Mullite Structure: A <Superscript>11</Superscript>B and <Superscript>27</Superscript>Al Solid-State NMR Study

²⁷Al magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectra were acquired at 8.45, 14.1 and 16.45 T for a series of aluminium borates with the mullite structure (Al_6−x B _x O₉, where x has nominal values of 1 to 4) augmented with ²⁷Al multiple-quantum MAS NMR spectra at 8.45 T. Even though the ²⁷Al NMR spectra are complex, simulation of the combined set of data produced a relatively well-defined set of parameters (e.g., quadrupolar interaction, isotropic chemical shift, etc.) for each site. The ¹¹B MAS NMR spectra of the same compounds were also acquired at 14.1 T. Linear changes in the X-ray a-, b- and c-cell parameters with composition suggest that these compounds constitute a continuous series. Based on a Rietveld structural refinement of the compound synthesized as Al₄B₂O₉, the resulting site occupancies and relative site distortions allow the identification of particular sites with specific NM resonances. Changes in the ²⁷Al and ¹¹B MAS NMR spectra of the related compounds with x = 1–4 show at the lowest Al contents a greater degree of asymmetry in the Al sites of the octahedral chains. A fairly distorted cross-linking tetrahedral site, which persists throughout the composition range, is accompanied in the lower Al compositions by two 5-fold coordinated Al–O units which are replaced by two more-regular tetrahedral Al–O sites as the Al content increases. In the compounds of lowest Al composition (i.e., highest B content) both the tetrahedral and trigonal cross-linking sites are distinguishable, but as the Al content increases, the BO₄ units progressively disappear. Authors' address: Kenneth J. D. MacKenzie, School of Chemical and Physical Sciences, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand     

Calculation of properties of the ozone molecule by the multiconfigurational self-consistent field method

For the ground state of the ozone molecule, by using the multiconfigurational self-consistent field method, we calculated the electric and magnetic properties — quadrupole moment, polarizability, tensor of magnetic susceptibility, nuclear quadrupole interaction constant, and the rotational g-factor. Qualitative agreement between the calculated parameters and experimental values was obtained. The tensors of chemical shielding in the spectrum of the nuclear magnetic resonance for the ¹⁷O isotopes have also been predicted (without allowance for the contribution made by the spin of the electrons). __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 713–716, November–December, 2005.     

Instabilities of the Conventional Nucleus-Nucleus Interactions for (<Superscript>3</Superscript>H<Superscript>4</Superscript>He) Proton Pickup Cross-Sections

The angular distributions of the ²⁶Mg, ²⁸Si, ³⁰Si(³H, ⁴He) reactions have been analyzed using the exact finite-range DWBA calculations. The optical model potential is assumed to have the conventional spin-orbit potential. The obtained cross-sections with the spin-orbit potential are not significantly different from those calculated using the phenomenological Woods–Saxon form factors in the forward angle regions. The inclusion of the spin-orbit potential gives the best fit to the data and greatly improves the large angle cross-sections. Different reasonable spectroscopic factors are found to account well for the cross-section magnitudes.     

<Superscript>1</Superscript>H and<Superscript>13</Superscript>C chemical shift assignments and stereochemistry of matrine and oxymatrine

Matrine and oxymatrine were extracted fromSophora flavescens, and their¹H and¹³C nuclear magnetic resonances (NMR) were unambiguously assigned by a combination of different two-dimensional 2-D¹H-¹³C and¹H-¹H correlation experiments of HMQC, HMQC-TOCSY and MAXY. The technique of using those experiments to make the assignment of the heavily overlapped spectrum is demonstrated. The coupling constants of matrine were measured by 2-DJ-resolved spectrum and 1-D spectra extracted from the slices of 2-D MAXY spectrum. The stereochemistry of the titled compounds was established from the NMR spectroscopy.     

<Superscript>17</Superscript>O and<Superscript>23</Superscript>Na nuclear quadrupole double resonance of sodium formate and sodium acetate

The¹⁷O and²³Na nuclear quadrupole resonance spectra of powdered sodium formate and sodium acetate have been determined at room temperature by proton-¹⁷O and proton-²³Na double resonance. All¹⁷O sites have been found to be chemically equivalent. The nonzero value of the asymmetry parameter of the electric field gradient tensor at the¹⁷O site shows that the electron density distribution is not cylindrically symmetric around the C−O bond axis.     

Form factors,branching ratio and forward–backward asymmetry in B→K<Subscript>1</Subscript>ℓ<Superscript>+</Superscript>ℓ<Superscript>-</Superscript> decays

We study long-distance effects in the rare exclusive semileptonic decays B→K₁ℓ⁺ℓ^-, where K₁ is the axial vector meson. The form factors describing the meson transition amplitudes of the effective Hamiltonian are calculated using the Ward identities, which are then used to calculate the branching ratio and the forward–backward asymmetry in these decay modes. The zero of the forward–backward asymmetry is of special interest and provides us with a precision test of the standard model.     

Polarization phenomena in the intermediate energy elastic deuteron scattering from <Superscript>16</Superscript>C and <Superscript>16</Superscript>O nuclei

A model based on the multiple diffraction scattering theory and the α-cluster model with dispersion of target nuclei is proposed for describing the behavior of observables for the elastic deuteron scattering from ¹²C and ¹⁶O nuclei at intermediate energies. Differential cross-sections and analyzing powers calculated within this approach for incident-deuteron energies of 400 and 700 MeV are in a reasonable agreement with experimental data.     

Density-constrained time-dependent Hartree-Fock calculation of <Superscript>16</Superscript>O + <Superscript>208</Superscript>Pb fusion cross-sections

We present a fully microscopic study of the ¹⁶O + ²⁰⁸Pb fusion using the density-constrained time-dependent Hartree-Fock theory. The calculated fusion cross-sections are in good agreement with the experimental data for the entire energy range indicating that the incorporation of dynamical effects is crucial in describing heavy-ion fusion.     

Renormalization group functions of the φ<Superscript>4</Superscript> theory from high-temperature expansions

It has been previously shown that calculation of the renormalization group (RG) functions of scalar ϕ⁴ theory reduces to analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG functions of the four-dimensional theory can be calculated for arbitrary coupling constant g with an accuracy of 10⁻⁴ for the Gell-Mann-Low function β(g) and with an accuracy of 10⁻³–10⁻² for anomalous dimensions. The expansions of the renormalization group functions up to the 13th order in g ^−1/2 have been obtained.     

Exclusive B→K<Subscript>1</Subscript>ℓ<Superscript>+</Superscript>ℓ<Superscript>-</Superscript> decay in model with single universal extra dimension

Decay rate and forward–backward asymmetries in B→K₁ℓ⁺ℓ^-, where K₁ is the axial vector meson, are calculated in the universal extra dimension (UED) model. The dependence of these physical quantities on the compactification radius R, the only unknown parameter in UED model, is studied, and it is shown that the zero of the forward–backward asymmetry is sensitive to the UED model; therefore they can be a very useful tool to establish new physics predicted by the UED model. This work is briefly extended to B→K^*l⁺l^-.     

Interaction of intermediate-energy protons with <Superscript>20</Superscript>Ne and <Superscript>24</Superscript>Mg nuclei within the multiple-scattering model

Observables of the elastic and inelastic scattering of 800- and 250-MeV protons on ²⁰Ne and ²⁴Mg nuclei were calculated on the basis of the theory of multiple diffractive scattering and the dispersive α-cluster model. The ²⁰Ne and ²⁴Mg nuclei were assumed to consist of a core (¹⁶O nucleus) and additional alpha-particle clusters, which could be situated with the highest probability both in the vicinity of the center of mass of the core and outside the core. The multiparticle densities of these nuclei and single-particle nucleon-distribution densities as obtained from the dispersive α-cluster model were used in the calculations. The differential cross sections and polarizations for elastic and inelastic p ²⁰Ne and p ²⁴Mg scattering at the energy of 800 MeV are in better agreement with experimental data than the analogous calculations at the energy of 250 MeV. The spin-rotation functions calculated in the singleparticle approximation for elastic p ²⁰Ne and p ²⁴Mg scattering at these two energy values differ qualitatively from their counterparts calculated on the basis of the dispersive α-cluster model.     

Study of the isobar configurations in the <Superscript>12</Superscript>C and <Superscript>16</Superscript>O ground states

Experimental research on positive-pion photoproduction on the oxygen nucleus in the ¹⁶O(γ, π⁺p) reaction at high recoil momenta of the residual nuclear system was performed. The yield for the ¹⁶O(γ, π⁺p) reaction was analyzed using a model that takes Δ-isobar configurations in nuclei ground states into account, together with the earlier-measured yield of the¹²C(γ, π⁺p) reaction. The estimated number of isobars per nucleon N _Δ = 0.012 ± 0.005 was obtained for the ¹²C nucleus, and ¹⁶O N _Δ = 0.018 ± 0.004 was obtained for the ¹⁶O nucleus.     

Formation of Eu<Superscript>2+</Superscript> and Eu<Superscript>3+</Superscript> centers in synthesis of CaF<Subscript>2</Subscript>:Eu luminophores

We have studied the effect of CaF₂:Eu luminophore synthesis methods on the charge state of europium. We have shown that Eu³⁺ predominates over Eu²⁺ in samples obtained by coprecipitation of europium with calcium fluoride, and the ratio Eu³⁺/Eu²⁺ grows as the total amount of europium increases. Partial charge conversion of the europium occurs during calcination of the samples, due to changes in the excess fluorine balance. We studied the luminescence, magnetic susceptibility, and EPR of the synthesized samples. We have shown that in a solid solution, europium forms large ordered clusters, determining both the luminescent and the magnetic properties of the material. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 6, pp. 773–779, November–December, 2007.