Eight-membered-ring solid-state conformational interconversion via the atom-flip mechanism, a CPMAS 13C NMR and crystallographic stereochemical study

Nefopam methohalide (chloride, bromide, and iodide) medium-ring quaternary ammonium salts of the non-narcotic analgesic tertiary amine drug give crystals belonging to the identical monoclinic P2(1)/c space group, and all of these pseudopolymorphs exhibit the same packing motif. A singular boat-boat (BB) more compact conformation is observed in the nefopam methochloride crystal. Larger halide anions (bromide and iodide) increase the void distance between the 2(1)-screw axis related adjacent ammonium cations to accommodate void-size dependent equilibrium quantities of the twist-chair-chair (TCC) more extended conformation. The BB:TCC occupancy factors are 0.961(5):0.039(5) [193 K], 0.780(5):0.220(5) [293 K], and 0.755(6):0.245(6) [343 K] for the methobromide crystal, while values of 0.657(5):0.343(5) [193 K] and 0.592(7):0.408(7) [293 K] were measured for the methiodide. Above a minimum of ca. 2.53 A, the occupancy factors were found to be linearly correlated to the intermolecular (TCC)Me(eq)-H...H-Me(ax)(TCC) distance between abutting methyl group protons in 2(1)-screw axis related neighbors. Temperature-dependent occupancy factors for the two conformers are interpreted in terms of a medium ring atom-flip facile interconversion between the two low energy conformations in crystals containing the appropriate size intercation void. A BB/TCC atom-flip interconversion in the methochloride unit cell would result in van der Waals interactions due to an estimated 2.31 A close intermolecular (TCC)Me(eq)-H...H-Me(ax)(TCC) distance between adjacent 2(1)-screw symmetry ammonium cations. The 203 K low-temperature CPMAS 13C NMR spectrum of the methiodide salt showed two slow exchange limit (SEL) delta 57.91 [BB] and delta 63.10 [TCC] OCH2CH2N peaks. A variable low-temperature CPMAS NMR investigation of the solid methiodide showed complex dynamic behavior that cannot be interpreted solely on the basis of an atom-flip conformational interconversion. Local magnetic fields from the gem-dimethyl rapidly rotating proton magnetic dipoles provide a distance-dependent T1 relaxation mechanism for neighboring carbons in the solid-state.     

Symmetrized harmonic oscillatorSU 3 states for multi-cluster systems

An algorithm is presented for the construction of single- and multi-cluster harmonic oscillator wave functions that are coupled into well-defined irreducible representations ofSU ₃ as well as of the symmetric groupS _N . The single-cluster harmonic oscillatorSU ₃ wave functions are constructed recursively, using theSU ₃ coefficients of fractional parentage. To construct multi-cluster wave functions with a well-defined permutational symmetry we diagonalize an appropriate set of single-cycle class operators of the symmetric group involving all the constituent particles. The formalism is applicable to the study of multi-cluster systems in nuclear physics where the wave functions are expressed in terms of harmonic oscillatorSU ₃ states     

Correlation of the EPR properties of perchlorotriphenylmethyl radicals and their efficiency as DNP polarizers

Water soluble perchlorinated trityl (PTM) radicals were found to be effective 95 GHz DNP (dynamic nuclear polarization) polarizers in ex situ (dissolution) (13)C DNP (Gabellieri et al., Angew Chem., Int. Ed. 2010, 49, 3360). The degree of the nuclear polarization obtained was reported to be dependent on the position of the chlorine substituents on the trityl skeleton. In addition, on the basis of the DNP frequency sweeps it was suggested that the (13)C NMR signal enhancement is mediated by the Cl nuclei. To understand the DNP mechanism of the PTM radicals we have explored the 95 GHz EPR characteristics of these radicals that are relevant to their performance as DNP polarizers. The EPR spectra of the radicals revealed axially symmetric g-tensors. A comparison of the spectra with the (13)C DNP frequency sweeps showed that although the solid effect mechanism is operational the DNP frequency sweeps reveal some extra width suggesting that contributions from EPR forbidden transitions involving (35,37)Cl nuclear flips are likely. This was substantiated experimentally by ELDOR (electron-electron double resonance) detected NMR measurements, which map the EPR forbidden transitions, and ELDOR experiments that follow the depolarization of the electron spin upon irradiation of the forbidden EPR transitions. DFT (density functional theory) calculations helped to assign the observed transitions and provided the relevant spin Hamiltonian parameters. These results show that the (35,37)Cl hyperfine and nuclear quadrupolar interactions cause a considerable nuclear state mixing at 95 GHz thus facilitating the polarization of the Cl nuclei upon microwave irradiation. Overlap of Cl nuclear frequencies and the (13)C Larmor frequency further facilitates the polarization of the (13)C nuclei by spin diffusion. Calculation of the (13)C DNP frequency sweep based on the Cl nuclear polarization showed that it does lead to an increase in the width of the spectra, improving the agreement with the experimental sweeps, thus supporting the existence of a new heteronuclear assisted DNP mechanism.     

Iron plasma: Sensitivity of photoelectric cross sections to different models and general features of the Fermi-Amaldi-Modified model

Photoelectric cross sections in several atomic models are presented as a function of temperature and density. The models discussed are Thomas-Fermi (TF), Fermi-Amaldi-Modified (FAM), and Debye-Hückel-Thomas-Fermi (DHTF). We also present some systematic results for the less known FAM potential model regarding predictions for: electrostatic potentials, bound electron level energies, pressures, and branching ratios of photoelectric cross sections. The pure iron plasma which we explored had a temperature in the range of 0.2–3 keV and a density in the range of 50–1000 g/cm³. Our conclusion is that except near threshold the photoelectric cross sections per fully occupied subshell are less sensitive to changes in density and temperature, at least in the ranges of our investigation, than other factors, such as occupation numbers.     

Limitations on the validity of the non-relativistic dipole approximation for photoelectron angular distributions

We present results which exhibit hazards in the use of the non-relativistic dipole approximation in the interpretation of experimental photoelectron angular distributions. Significant deviations from the non-relativistic dipole approximation occur for both low and high Z atoms. In light elements these effects are found in the keV range and even below. In heavy elements they are found even for energies very close to threshold. For total cross sections, in contrast to this angular distribution situation, the surviving integrated relativistic and multipole corrections tend to cancel, so that the non-relativistic dipole approximation holds to surprisingly high energies.     

A Century of Turbulence

A brief, superficial survey of some very personal nominations for highpoints of the last hundred years in turbulence. Some conclusions can be dimly seen. This field does not appear to have a pyramidal structure, like the best of physics. We have very few great hypotheses. Most of our experiments are exploratory experiments. What does this mean? We believe it means that, even after 100 years, turbulence studies are still in their infancy. We are naturalists, observing butterflies in the wild. We are still discovering how turbulence behaves, in many respects. We do have a crude, practical, working understanding of many turbulence phenomena but certainly nothing approaching a comprehensive theory, and nothing that will provide predictions of an accuracy demanded by designers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamic nuclear polarization assisted spin diffusion for the solid effect case

The dynamic nuclear polarization (DNP) process in solids depends on the magnitudes of hyperfine interactions between unpaired electrons and their neighboring (core) nuclei, and on the dipole-dipole interactions between all nuclei in the sample. The polarization enhancement of the bulk nuclei has been typically described in terms of a hyperfine-assisted polarization of a core nucleus by microwave irradiation followed by a dipolar-assisted spin diffusion process in the core-bulk nuclear system. This work presents a theoretical approach for the study of this combined process using a density matrix formalism. In particular, solid effect DNP on a single electron coupled to a nuclear spin system is considered, taking into account the interactions between the spins as well as the main relaxation mechanisms introduced via the electron, nuclear, and cross-relaxation rates. The basic principles of the DNP-assisted spin diffusion mechanism, polarizing the bulk nuclei, are presented, and it is shown that the polarization of the core nuclei and the spin diffusion process should not be treated separately. To emphasize this observation the coherent mechanism driving the pure spin diffusion process is also discussed. In order to demonstrate the effects of the interactions and relaxation mechanisms on the enhancement of the nuclear polarization, model systems of up to ten spins are considered and polarization buildup curves are simulated. A linear chain of spins consisting of a single electron coupled to a core nucleus, which in turn is dipolar coupled to a chain of bulk nuclei, is considered. The interaction and relaxation parameters of this model system were chosen in a way to enable a critical analysis of the polarization enhancement of all nuclei, and are not far from the values of (13)C nuclei in frozen (glassy) organic solutions containing radicals, typically used in DNP at high fields. Results from the simulations are shown, demonstrating the complex dependences of the DNP-assisted spin diffusion process on variations of the relevant parameters. In particular, the effect of the spin lattice relaxation times on the polarization buildup times and the resulting end polarization are discussed, and the quenching of the polarizations by the hyperfine interaction is demonstrated.