Motional effects chemical shift tensors

The dependence of the principal components of the nuclear magnetic resonance (NMR) chemical shift tensor of non-hydrogen nuclei in model dipeptides is investigated. It is observed that the principal axis system of the chemical shift tensors of the carbonyl carbon and the amide nitrogen are intimately linked to the amide plane. On the other hand, there is no clear relationship between the alpha carbon chemical shift tensor and the molecular framework. However, the projection of this tensor on the C-H vector reveals interesting trends that one may use in peptide secondary structure determination. Effects of hydrogen bonding on the chemical shift tensor will also be discussed. The dependence of the chemical shift on ionic distance has also been studied in Rb halides and mixed halides. Lastly, the presence of motion can have dramatic effects on the observed NMR chemical shift tensor as illustrated by a nitrosyl meso-tetraphenyl porphinato cobalt (III) complex. 

Figure 5 P-NMR spectra of phospholipids with different modes of molecular motion, a rigid limit b fast axial rotation about X-axis averages Y- and Z-components of the chemical shift tensor. In the spectrum one can observe two principal values of = 112(ayy + azz) and ct =oxx c a typical case of fluid membrane. Along with fast X-axial rotation molecular motion also partially averages ct and ctj. In the spectrum one observes effective values a n < CT I and a < CT. d Isotropic case (high resolution NMR) a/5o = 1/3(axx + cryy-Pazz)-...

The need for extensive basis sets is common to post-HF and DFT approaches. Another common problem is the high sensitivity of the chemical shift tensor to the geometry chosen for the calculation. The problem is, really, much more complicated because, for very precise calculations, one even has to consider the effects of averaging over the vibrational motion of the nuclei. However, as a first approximation it is often possible to simply use r0 instead of re for calculations if the corresponding corrections were not introduced into the experimental data a priori (see ref [88] for more details). 

The chemical shift is due to the orbital effects of the nearby electrons. When an atom or a molecule is placed in a static magnetic field, the electrons produce a small auxiliary field the direction and the magnitude of which depend in a complex way on the electronic structure of the atom or molecule. Because the ability of the electrons to shield the nucleus depends in part on the direction of the magnetic field with respect to the electronic orbits, the chemical shift is a tensor quantity. The shift observed in liquids as well as that in MAS experiments are motional averages of the tensor components. 

Now Retails is the transition probability from the spin state j3 to the spin state a and Raa/sis = R/3/3aa- The diagonal part of Eq. (5.25) is a second-rank equation of motion for evolution of the density matrix under the effect of a random perturbation. There are two important second-rank relaxation mechanisms the dipole-dipole and the quadrupole interactions. Chapter 2 showed that these interactions and the anisotropic chemical shift can all be written as a scalar product of two irreducible spherical tensors of rank two, that is. 

Proceeding to the situation most relevant to membranes, let us now allow rapid motion of limited amplitude of the 1 axis of the phosphodiester moiety, retaining the rapid motion about the 1 axis (Fig. 2C). The 1 axis now moves in a cone, and there is partial averaging of the former and <7 to yield new, smaller effective values and a[. The effective tensor still has axial symmetry, but the total chemical-shift anisotropy (CSA) represented by the spectrum, A[Pg.451]

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