Dipolar oscillations

For the case of anisotropic dipolar oscillators, the dispersional forces have been discussed by London and De Boer. On neglecting the anisotropy of electron oscillation frequency, the dispersional energy of interaction between two anisotropic molecules becomes, in a dipole-dipole approximation > ... 

Fourier transformation over an incremented Hartmann-Hahn evolution period yields the eigenfrequencies of the (effective) Hartmann-Hahn Hamiltonian. In solid samples with resolved heteronuclear dipolar couplings (Muller et al., 1974), this approach yields heteronuclear dipolar oscillation spectra (Hester et al., 1975) if the heteronuclear spins are Hartmann-Hahn matched during the evolution period of the experiment. In liquid state NMR, Fourier transformation over incremented homonu-clear Hartmann-Hahn transfer periods yields so-called coherence-transfer... 

Cis is a constant. In cases where the CP occurs between relatively isolated spins (e.g. pairs) the spin thermodynamic description cannot be applied. Rather than a smooth, continuous build-up of magnetisation, the CP curve shows structure, termed dipolar oscillations (Muller et al. 1974). The magnetisation oscillates between the proton and the X-nucleus. In the case where the system is exactly Hartmann-Hahn matched, the magnetisation of the S-spin is given by (Levitt et al. 1986)... 

A density matrix description of the polarization inversion process has been presented enabling the visualization of the role of the process in the suppression of zero-frequency peaks in SLF-2D NMR experiments based on the dipolar oscillations during CP. It has been shown that, during this process, a doubling of the amplitude of the Oscillatory component occurs accompanied by a reduction of the initial intensity of the non-oscillatory component to zero. 

Woessner [56] also considered the effects of proton exchange on the dipolar oscillations arising from oriented water in chabazite and vermiculite. This paper involves a nice application of the density matrix for calculation of the effect of exchange on the FID. Comparisons are made between the proton exchange rate measured for interlayer water and pure water, and it was found that the rate was very dependent on the clay structure and cation involved. Fripiat reviewed the area of proton exchange on acid catalysts in 1976 [59]. The findings of Woessner [56] are not in complete agreement with conclusions reached in this review, which assert that dissociation of water is more pronounced in layered materials. Woessner s results seem to indicate that this is not necessarily the case. 

Fig. 3 Distance measurements between paramagnetic centers by EPR spectroscopy. Below 0.5 nm. distance estimates are unreliable for 0.5

What are the possible explanations for lone cell rotation in a simple oscillating field The most compelling reason seems to be that of an internal dipolar oscillation within the cell. This oscillation would be present only with live cells since upon the death of the cell spinning ceases. This seems to be supported by the fact that the cells spin at a much lower rate than that being applied by the external field. The cell rotates at somewhere between 0.1 and 30.0 Hz, while the external field oscillates at, say, 600 kHz. The presence of an internal dipolar field oscillation would interact with the externally applied field to provide a rotational torque and thus induce the spinning. 

Fig. 1.15. A schematic illustration of the excitation of the dipole surface plasmon oscillation by the electric field component of the light wave. The dipolar oscillation of the electrons has the same frequency as that of the incoming light wave...

Table 1 Molecular Cg coefficients from the dipolar oscillator orbited method, using LDA, PBE, RHF and sr-LDAdr-RHF deteminrmts in aug-cc-pVTZ basis set and Boys localized orbitals ...

It has been shown that, using projected dipolar oscillator orbitals to represent the virtual space in a localized orbital context, the equations involved in long-range ring coupled cluster doubles type RPA calculations can be formulated without explicit knowledge of the virtual orbital set. The P(X) virtuals have been constructed directly from the localized occupied orbitals. The matrix elements and the electron... 

Appendix 1 Dipolar oscillator orbitals in local frame... 

Figure 4-11. Recoupled dipolar spectra (right column) and corresponding time domain signals (left column) obtained with different CP-SLF approaches for the Oj-carbon of the RufHSO sample in the columnar phase at 80 °C (spinning frequency = 8 kHz). Polarization inversion (PI) prior the dipolar evolution period increases the dipolar oscillation amplitude...

The transverse and longitudinal relaxation of pumped spins does not play a significant role in DEER sensitivity, unless the longitudinal relaxation of pumped spins gets comparable or faster than the transverse relaxation of detected spins. In the latter case some part of dipolar oscillations could be damped due to spontaneous flips of the pumped spin during the evolution period. 

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