Motional regime

Figure Bl.13.7. Simulated NOESY peak intensities in a homoniielear two-spin system as a fiinetion of the mixing time for two different motional regimes. (Reprodiieed by pennission of Wiley from Neiihaiis D 1996 Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chiehester Wiley) pp 3290-301.)...

Since TD-DFT is applied to scattering problems in its QFD version, two important consequences of the nonlocal nature of the quantum potential are worth stressing in this regard. First, relevant quantum effects can be observed in regions where the classical interaction potential V becomes negligible, and more important, where p(r, t) 0. This happens because quantum particles respond to the shape of K, but not to its intensity, p(r, t). Notice that Q is scale-invariant under the multiplication of p(r, t) by a real constant. Second, quantum-mechanically the concept of asymptotic or free motion only holds locally. Following the classical definition for this motional regime,... 

Fig. 3. Variation of the completely reduced dipole-dipole spectral density (see text) for the model of a low-symmetry complex for S = 3/2. Reprinted from J. Magn. Reson., vol. 59,Westlund, RO. Wennerstrom, H. Nordenskiold, L. Kowalewski, J. Benetis, N., Nuclear Spin-Lattice and Spin-Spin Relaxation in Paramagnetic Systems in the Slow-Motion Regime for Electron Spin. III. Dipole-Dipole and Scalar Spin-Spin Interaction for S = 3/2 and 5/2 , pp. 91-109, Copyright 1984, with permission from Elsevier.

Its dynamical range covers both the slow and the fast motion regime (lO -lQii Hz)... 

For a fixed value of Tc, the frequency dependence of either term is a Lorentzian centred at zero frequency. In the tc dependence two regimes are distinguished In the fast motion regime (coiTc spectral density is proportional to tc and does not depend on the measuring frequency a>i, whereas in the slow motion regime (a>iTc > l) it is proportional to ( Tc) i.e. the relaxation rate exhibits dispersion. 

In contrast to critical behaviour, where the NMR relaxation rate shows a max-imiun (or a corresponding Ti minimiun) at Tc, thermally activated slowing down provides a Ti minimiun for lTc = 1, i.e. at the border between the fast motion and the slow motion regimes. Since according to Eq. 11 In(rc) is proportional to T Ti is usually plotted in logarithmically versus T", as for example shown in Fig. 11a. The slopes above and below the minimum are proportional to the activation energy E, . In Fig. 11b a typical tempera-... 

They can serve therefore as a test for Ti dispersion. In Fig. 12 the relaxation results are shown for D-RADP-15. The solid lines are a fit of the theory [19] to the data. Above Tc the lit is excellent, whereas below Tc it probably suffers from the fact that the phase transition is already diffuse and only nearly of second order. This proves that a soft mode component is needed to explain the data. Furthermore, the fact that the ratio ti/t2 remains unchanged above and below Tc proves that the order parameter fluctuations are in the fast motion regime on both sides of the transition. 

Fig. 13 Comparison of the inverse relaxation rates ti and T2 versus 1/T at vi = 98.163 MHz for D-RADP-25 and D-RADP-50. Whereas D-RADP-50 exhibits a pure thermally activated behaviour, in D-RADP-25 a soft mode contribution to the relaxation rate can be observed in the fast motion regime [17]...

However, both NOE and NOESY experiments can fail for medium-sized molecules, in particular when using high field spectrometers, if their motional regime is close to the NOE null (cuqTc = 1.12 see eq. (1)). 

This suppression scheme has been shown to work well together with HMQC experiments of small molecules at natural abundance. Even cleaner spectra are obtained, if the BIRD sequence is combined with HSQC experiments already containing a spin-lock purge pulse. Drawbacks of the BIRD pulse scheme are the fact that the relaxation delay between scans cannot be chosen freely anymore and that complete suppression of all C-bound proton signals is impossible, if they have different relaxation times. Furthermore, the BIRD pulse scheme is not applicable to molecules in the slow motional regime, since negative NOEs between the inverted proton spins and the non-inverted C-bound proton spins would reduce the magnetization of the latter. 

Therefore, for a complete characterization of the cross-relaxation network, it is best to do all three experiments and to extract from each of them information that can be interpreted unambiguously. If the number of possible experiments is limited, then in the extreme-narrowing and the spin-diffusion regime it is best to record NOESY and in the intermediate motional regime ROESY or T-ROESY spectra. 

In the spin diffusion motional regime (small molecules at low temperatures or macromolecules at all temperatures) the cross-relaxation is so efficient that it can hardly be limited to a single-step magnetization transfer. The multistep magnetization transfer is known as spin diffusion. It manifests differently in NOESY and ROESY spectra, as can be illustrated by writing eq. (29b) explicitly for the process of cross relaxation ... 

Fig. 1. Depiction of the motional timescale sensitivity of various NMR methods for studying dynamics. For comparison, the approximate motional regimes for various biological motions are also indicated.

Fig. 5. The applicability of different approaches to the analysis of RDCs depends on the nature of the dynamics of the molecule. For this purpose, three different motional regimes may be specified. (A) Molecules which exist in several completely different conformations, thus precluding the determination of a single order tensor. (B) Some well structured regions exist, but may exhibit extensive motions relative to one another. (C) The molecule can be described in terms of a mean conformation about which motional excursions occur.

Ratios between RiM and for dipolar and contact contributions in the various motional regimes... 

Signs of ID difference spectra or 2D cross peaks arising from dipole-dipole or chemical exchange interactions in fast (FM) and slow (SM) motion regimes a... 

In addition to the semiquantitative approach, more quantitative analytical approaches have been reported. For example, in the fast motion regime (t 10 11—10 9 s at X-band), one can compute the nitroxide rotational correlation time based on the measured line-widths and amplitudes (Marsh, 1981 Qin et al., 2001 Xi et al., 2008). Furthermore, it is possible to simulate a nitroxide spectrum based on quantum mechanics and specific motional models (Columbus et al., 2001 Grant et al., 2009 Hustedt et al., 1993 Liang et al., 2000 Qin et al., 2006 Schneider and Freed, 1989). The details of these advanced analysis techniques are not discussed here, interested readers are instead referred to a recent review (Sowa and Qin, 2008) and the relevant literatures. 

R is always smaller than 1. If qEA 0. A 2D NMR experiment, thus always the measurement of R(x —> oo), and always the determination of qEA, in the slow motion regime, where the determination of qEA from line shape is no longer possible. 

At lower temperatures, the A - - B and A B intra-H-bond exchange time becomes low on the NMR time scale so that we are in the slow motion regime (Am 1). The deuteron NMR frequency now depends on the instantaneous value of the pseudo-spin S,z... 

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