Rotational bands in 169Re

Based on the systematic investigation of the data available for nuclei with A≥ 40, a Z ^1/3-dependence for the nuclear charge radii is shown to be superior to the generally accepted A ^1/3 law. A delicate scattering of data around R _c/Z ^1/3 is inferred as owing to the isospin effect and a linear dependence of R _c/Z ^1/3 on N/Z (or (N - Z)/2) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. With the linear isospin dependence provided by the data and RCHB theory, a new isospin-dependent Z ^1/3 formula for the nuclear charge radii is proposed. Received: 23 September 2001 / Accepted: 21 January 2002     

Proton shielding function for hydrogen chloride

For a diatomic molecule the nuclear shielding constant σ(ξ) of either nucleus can be expanded as a power series in the relative displacement from equilibrium ξ. Thus the nuclear shielding function is

where ξ=(r-r _e)/r _e with r the actual bond length and r _e the equilibrium bond length. The σ_e ⁽ⁱ⁾ are molecular parameters. By experimental observation of the temperature dependence of the proton magnetic shielding of hydrogen chloride gas it is possible, after allowing for intermolecular effects, to obtain the values σ_e ⁽⁰⁾=32·48 (±0·33) p.p.m. and σ_e ⁽¹⁾=-100 (±24) p.p.m. for the coefficients of the proton shielding function. Using this data it is possible to show that the isotope shift between H³⁷Cl and H³⁵Cl is about 0·001 p.p.m. By a comparison with earlier results for molecular hydrogen it would appear that in some instances differences in vibrational and rotational averaging may alter chemical shifts between different compounds by amounts considerably larger than the experimental error in chemical shift measurement.     

Magnetic octopole contributions to the ‘pseudo-contact’ chemical shift

Magnetic multipole contributions to the neighbour-anisotropy or ‘pseudo-contact’ shift are examined theoretically. Truncation of the multipolar expansion of the nuclear magnetic shielding at the dipolar terms is shown to be satisfactory for shift reagents relying on paramagnetic anisotropy in metal ions. However, this procedure is unreliable for benzene and macrocyclic shift reagents such as porphyrins. For molecules of this type, the ratio of the octopolar to the dipolar shielding is in the order of a ²/R ² where a is the ‘ molecular radius ’ and R the distance between the centre of the ring system and the nucleus of interest.     

The concentration dependence of the proton chemical shift and the deuterium quadrupole coupling parameter for binary solutions of ethanol

Concentration dependent experimental measurements of the ethanol hydroxyl proton chemical shift σ_H for binary solutions were carried out. The solvents used were carbon tetrachloride (CCl₄), benzene, chloroform, acetonitrile, acetone and dimethylsulphoxide (DMSO). The chemical shift values range from 0.69 ppm (relative to TMS) for dilute ethanol (extrapolated to infinite dilution) in CCl₄ to 5.34 ppm for neat liquid ethanol. Ab initio calculations of the ethanol-solvent hydrogen bond energies show a correlation with the values for the chemical shift. The hydrogen bond energies for ethanol-solvent dimers range from 0.63 kcal mol^?1 for ethanol-CCl₄ to 9.34 kcal mol^?1 for ethanol-DMSO. Theoretical calculations show a linear correlation between the deuterium quadrupole coupling parameter XD ^ar d the isotropic proton chemical shift σ_H: X_D(kHz) = 291.48 ? 14.96 σ_H, where σ_H is the proton chemical shift in ppm relative to TMS (R ² = 0.99). Using the concentration dependent chemical shift data and this equation, X_D ia observed to range from 280 kHz for very dilute concentrations in CCl₄, where the primary species is ethanol monomer, to 210 kHz for the neat liquid that is comprised primarily of cyclic pentamers.     

Dependence of NMR isotropic shift averages and nuclear shielding tensors on the internal rotation of the functional group X about the C-X bond in seven simple vinylic derivatives H2C=CH-X

The ‘Gauge Including Atomic Orbitals’ (GIAO) approach is used to investigate the question of intramolecular rotation. Ab initio GIAO calculations of NMR chemical shielding tensors carried out with GAUSSIAN 94 within the SCF-Hartree-Fock approximation are described. In order to compare the calculated chemical shifts with experimental ones, it is important to use consistent nuclear shieldings for NMR reference compounds like TMS. The influence of rotating functional groups X=CH₃, CHO, NO₂, NH₂, CONH₂, COOH or C₆H₅ on the shielding tensors in seven vinylic derivatives H₂C=CH-X is studied; the molecules are propene, acrolein, nitroethylene, ethyleneamine, acrylamide, acrylic acid and styrene. We observe a marked dependence of nuclear shielding and chemical shift on the torsional movement. Different Boltzmann averages over the conformational states are considered and compared for gas phase, liquid and solid state NMR. Their applicability to model cases for rigid or freely rotating molecules and for fixed molecules (e.g. polymers or proteins) with rapidly rotating groups is discussed and simple calculation models are presented. On the basis of this work it can be concluded that intramolecular rotation clearly affects the observed averages. Effects of up to 2 ppm have been observed for isotropic chemical shifts, and up to 17 ppm difference have been observed for individual tensor components, for example, of the carboxylic ¹³C atom in acrylic acid. The variation of the shielding tensor on a nucleus in a fixed molecular backbone resulting from an attached rotating group furthermore leads to a new relaxation mechanism by chemical shift anisotropy.     

The neutron/proton ratio of fast nucleon emission in antiproton annihilation on nuclei

The measurement of fast protons and neutrons emitted after antiproton annihilation at rest on²³⁸U and⁶³Cu reveals a large neutron/proton ratioR. Its value for⁶³Cu is larger than expected from the conventional model of intranuclear pion rescattering. A value ofR essentially constant over the whole range of mass number, from¹²C up to²³⁸U, is also announced by the experimentalists. It is shown that, on the contrary, the conventional scheme predicts a regular increase ofR with mass number. Alternative explanations of the effect are looked for. Within the usual scheme, an excess of negative pions, leading to more emitted neutrons, is not compatible with final pion multiplicities. The influence of meson resonances on the neutron/proton ratio is considered, as well as the possible occurrence of annihilations on two nucleons. They cannot warrant an increase ofR at low mass targets sufficient to explain a constant value over the whole range of target masses.     

Temperature dependence of the EPR spectrum of ruby

The small splitting of the⁴ A ₂ ground state of Cr³⁺ centers in Al₂O₃ has been measured with an EPR spectrometer in the temperature range from 88 K to 575 K. It is shown that the temperature dependence of this zero-magnetic-field splitting of about 2D=0.38 cm^–1 is due to the thermal expansion of the lattice. It is found that whereR is the interparticle distance.A new calculation of the ground state splitting is then used to explain this number as well as the splitting itself. Crystal field parameters are taken from optical measurements and from theg-factors.     

On quadratic lagrangians in General Relativity

Theories of gravitation similar to General Relativity but with an additionalR ² term in the Lagrangian are explored. The Schwarzschild metric is not the exterior solution that can be continued to the interior of the body to give a positive definite mass distribution. The experimental consequences ofR ² terms are investigated. Furthermore, it is shown that a theory with anR ² term only possesses an interesting singular dependence on the coupling constant.     

Measurements of the spin rotation parameter A in the elastic pion-proton scattering in the D13(1700) resonance region

The spin rotation parameters A and R were measured for the elastic pion-proton scattering by the PNPI-ITEP collaboration in the D₁₃(1700) resonance region. The main goal of the experimental program is to resolve the current partial-wave analyses (PWA) uncertainties. Simultaneously with A and R the polarization parameter P was measured with the purpose to improve the experimental database and estimate systematic errors. The constraint which demands a smooth energy dependence of all π^- p transverse amplitude zeros in the complex plane together with the new experimental data on A parameter can lead to the conclusion that the Barrelet branch of “zero trajectories" is chosen improperly in PWA of the Carnegie-Mellon-Lawrence-Berkely-Laboratory groups at the range of the pion beam momentum near 1.0 GeV/c. The setup included a longitudinally polarized proton target with superconductive magnet, multiwire spark chambers and carbon polarimeter with thick filter. The experiment was performed at the ITEP proton synchrotron, Moscow. Received: 17 August 2001 / Accepted: 13 September 2001     

Dynamical structure of α-Ag0.99Cu0.01I crystal by Cu NMR chemical shift, spin-lattice relaxation time and molecular dynamics simulation

Solid ⁶³Cu NMR and Molecular Dynamics (MD) methods have been used to investigate the dynamical structure of Ag_0.99Cu_0.01I crystal, through the viewpoint of the chemical shift and the spin-lattice relaxation. In the superionic phase (α-phase), we obtained the temperature variation of the chemical shift as −0.2 ppm/K, and the activation energy of the Cu⁺ ion diffusion as 11 kJ/mol. The temperature dependence of the chemical shift was explained by the calculated chemical shielding surface based on ab initio MO calculation, and by the probability density of Cu⁺ ion estimated by MD simulation. The spin-lattice relaxation was also analyzed by using the MD method in which we assumed two jumping models as the diffusion process of the mobile cations. It is concluded that the temperature dependence of the chemical shift is dominated by the shielding in the vicinity of the 24(h) site, and the observed activation energy is due to the diffusion process of the mobile cations jumping from the 6(b) intrasub-lattice to the nearest-neighbor 6(b) sub-lattice.     

Through-bond and through-space effects on proton chemical shifts. The magnetic anisotropy effects of freely rotating -XY3 groups upon distant protons

A general expression is presented for calculating the contributions of the magnetically anisotropic X-Y bonds of freely rotating -XY₃ groups to the shielding of protons of a freely rotating methyl group elsewhere in the same molecule. The expression can also be modified to calculate (a) the anisotropy contribution of a freely rotating -XY₃ group to the shielding of a fixed proton and (b) the contribution of a fixed anisotropic X-Y bond to the shielding of a freely rotating methyl group. Application is made to calculate the contribution of magnetic anisotropy changes, when a hydrogen atom is replaced by a methyl group, to the aryl and methyl proton chemical shifts of the methylbenzenes relative to benzene and toluene, respectively. Although the contribution of magnetic anisotropy is not negligible it is insufficient to account for the observed shifts. This conclusion applies also to the acetylenic proton chemical shifts of some methyl derivatives of acetylene. Some comments are made on the values of magnetic anisotropy obtained by the N.M.R. method.     

13C NMR Chemical Shifts of Heterocycles: 3∗. Empirical Substituent Effects in 2-Halomethyl-2-hydroxy-tetrahydrofurans and -5,6-tetrahydro-4H-pyrans

Abstract

Evaluation by empirically derived equations for the Substituent effect (α, β, γ, δ) on the ¹³C NMR chemical shifts for C-2, C-3, C-4, C-5, C-6, the halomethyl-substituted carbon (C-7) and the cyano or oxymic carbon (C-8) in 2-halomethyl-2-hydroxy-tetrahydrofurans 1a-c, 2, 3a, b, 4a and -5,6-tetrahydro-4H-pyrans 5a-c, 6a [with C-2-substituents (R²): CF₃, CCl₃ or CHCl₂, C-3-substituents (R³): CN, C(Me)=NOH, CH=NOMe, C(Me)=NOMe or CH=NOH], taking as reference the 2-trifluoromethyl-2-hydroxy-tetrahydrofuran (la), is reported. From the additivity properties of the α-, β-, γ-, δ-and ?-effects for each Substituent it is possible to predict the chemical shift of each carbon of the compounds 1–6.

     

13C NMR Chemical Shifts of Heterocycles: Empirical Substituent Effects in 5-Halomethylisoxazoles

Evaluation by empirically derived equations for the Substituent effect (α, β, γ, δ) on the ¹³C NMR chemical shifts for C-3, C-4. C-5 and halomethyl-substituent carbon (C-6) in isoxazoles 1-5 [where C-3 substituent (R¹) = H, alkyl or phenyl, C-4 Substituent (R²) = H, alkyl, and C-5 substituent (R³) = di-or trihalomethyl, methyl and H], taking as reference the compound la, is reported. From the calculated values for the α, β, γ, δ effects for each substituent it was possible to estimate the chemical shift of each carbon of the compounds 1–5. The ¹³ C chemical shifts of the C-3, C-4, C-5, C-6 of these compounds, can be estimated with good precision: 94% of the calculated chemical shifts are found to be within ±1.0ppm, and 100% are found to be within ±1.5ppm.     

Semi-empirical calculations of the magnetic properties of condensed hydrocarbons

Coupled Hartree-Fock perturbation theory is used to calculate the non-local contribution to ¹H chemical shifts and magnetic susceptibilities of alternant benzenoid, alternant non-benzenoid and non-alternant conjugated hydrocarbons. It is shown that the agreement between theory and experiment is satisfactory. For the calculation of the coupled first-order orbitals a simplified iterative procedure is proposed.     

Calculations of intermolecular interactions and their influences on structure and13C,1H magnetic shielding constants of solute molecules

On the basis of an improved method of molecular mechanics the spatial structures of molecular clusters modelling the solvate shell of methane in acetone and benzene, 2,9,10-trimethyl-1,3-dithia-5,6-benzocycloheptene in carbon disulfide have been calculated. The nuclear magnetic shielding constants for these structures are calculated by quantum chemical methods in the approach of the density functional theory of the B3LYP/6-31(d,p) level with the usage of gauge-invariant atomic orbitals. It is shown that the increase of the number of the solvent molecules results in better agreement of the calculated and experimental values of¹H and¹³C chemical shifts.     

Nuclear magnetic shielding tensors of207Pb2+ in Pb(NO3)2

The NMR signals of²⁰⁷Pb were observed in a single crystal of Pb(NO₃)₂ and could be assigned to the four different Pb²⁺ sites by the dependence of the linewidths on the orientation. Four different nuclear magnetic shielding tensors with equal principal values but with different characteristic vectors could be determined. The symmetry of the shielding tensors is in agreement with the symmetry at the Pb²⁺ sites. It is shown, that intermolecular contributions can not account for the anisotropy of the nuclear magnetic shielding, which is 3 of the isotropic absolute magnetic shielding.     

The effects of vibration-rotation on the quadrupole moment,rotational g-factor and spin-rotation parameters of the water molecule

Ab initio SCF surfaces for the quadrupole moment, rotational g-factor and spin-rotation parameters of the water molecule have been obtained from the magnetizability and nuclear shielding surfaces. Values of these properties in low vibration-rotation states of the more important isotopomers are presented.

Vibrational averaging (with an accurate empirical force field) brings calculated values to within 1 per cent of experimental values for the quadrupole moment components and 3 per cent for the g-tensor components. Substantial vibrational effects on the proton, deuteron and ¹⁷O spin-rotation parameters are predicted but the calculated values differ significantly from experiment. This is attributed to inadequacy of the SCF calculation of paramagnetic shielding.     

Double-quantum filtration under rotational-resonance conditions: numerical simulations and experimental results

The dependence of the performance of a recently introduced pulse sequence to achieve double-quantum excitation under the n = 1 rotational-resonance condition (T. Karlsson, M. Edén, H. Luthman, and M. H. Levitt, 2000, J. Magn. Reson. 145, 95–107) on different spin-system properties is investigated by means of numerical simulations and ¹³C MAS NMR experiments. For spin systems where chemical shielding anisotropies amount to only an insignificant fraction of the isotropic chemical shielding difference, high efficiencies are found for large and small dipolar coupling interactions. In the presence of significant chemical shielding anisotropies the overall efficiencies decrease and become strongly dependent on the duration of the excitation period. It is demonstrated that those spin-system parameters which are sensitively encoded in the lineshapes of a conventional n = 1 rotational-resonance spectrum are similarly sensitively encoded in the corresponding rotational-resonance double-quantum-filtered lineshapes and may be quantitatively recovered by iterative lineshape-fitting approaches. In certain favorable circumstances, the in-built selectivity of the rotational-resonance double-quantum-filtration approach permits successful application of the experiment on spin systems with more than two spins.     

On the significant relativistic heavy atom effect on 13C NMR chemical shifts of β- and γ-carbons in seleno- and telluroketones

Unexpectedly large ‘Heavy Atom on Light Atom’ (HALA) effects have been found in ¹³C NMR (Nuclear Magnetic Resonance) chemical shifts of β- and γ-carbons of seleno- and telluroketones established by means of the high-accuracy calculations of ¹³C NMR chemical shifts in three representative real-life compounds, 2,2,5,5-tetramethyl-3-cyclopentene-1-selone, selenofenchone and 1,1,3,3-tetramethyl-1,3-dihydro-2H-indene-2-tellurone. The proposed computational scheme consists of the combination of accurately correlated coupled-cluster singles and doubles model approach for the non-relativistic calculations of shielding constants taking into account the solvent, vibrational and relativistic corrections, the latter obtained within the 4-component fully relativistic gauge-including atomic orbitals KT2 approach resulting in a very good agreement of the performed calculations with the experiment. The stereochemical dependence of the ‘long-range’ γ-HALA effect on the dihedral angle has been established in the model seleno- and telluroketones providing the largest shielding effect in the orthogonal orientation of the X=C_α–C_β–C_γ (X=Se, Te) moiety.