Larmor frequency calculation

Figure 8 Effects of spin diffusion. The NOE between two protons (indicated by the solid line) may be altered by the presence of alternative pathways for the magnetization (dashed lines). The size of the NOE can be calculated for a structure from the experimental mixing time, and the complete relaxation matrix, (Ry), which is a function of all mterproton distances d j and functions describing the motion of the protons, y is the gyromagnetic ratio of the proton, ti is the Planck constant, t is the rotational correlation time, and O) is the Larmor frequency of the proton m the magnetic field. The expression for (Rjj) is an approximation assuming an internally rigid molecule.

Fig. 2. Calculated relaxivities as a function of the water exchange rate for various proton Larmor frequencies and rotational correlation times, tr. The simulations have been performed by using the common Solomon-Bloembergen-Morgan theory of paramagnetic relaxation.

Fig. 4. Inner sphere contribution to the proton relaxivity as a function of the proton Larmor frequency. The curves were calculated on the basis of the Solomon-Bloembergen-Morgan theory for different values of the rotational correlation time, tr, and q — 1, kex — 10 x 106 s-1, tv = 20 ps, A2 = 0.1 x 102Os-2.

The temperature dependent T data are shown in Fig. 9. 7j values decrease from 28 ms at 21°C with increasing temperature, and show a minimum of 6.4 ms at 80° C. These results indicate the presence of the motion with a Larmor frequency of 30 MHz at this temperature. This minimum was found to be attributed to the flipping motion of a phenyl ring from the result of our other experiments discussed in later section.13 The jump rates of the flipping motion were estimated with a two-site jump model that a C-2H bond jumps between two equivalent sites separated by 180°, and that the angle made by the C-2H bond and the rotational axis is 60°. The quadrupole coupling constant of 180 kHz and the asymmetry parameter approximated to zero were used in the calculation. The calculated values for fitting with the... 

The quadrupole perturbed NMR spectriun of Rb (I = 312) consists of the central hne and two satelUte Unes. In D-RADP-x the nuclear quadrupole couphng constant decreases linearly with x from 9.6 MHz (x = 0) to 6.6 MHz (x = 0.95) [10], whereas the Larmor frequency amounts to 98.163 MHz in a Bo field of 7 T. Due to the substitutional disorder, and the corresponding loss of the translational invariance, the satelHte transitions are inhomogeneously broadened that much, that only the central transition can be directly observed. The position of the corresponding resonance line can be calculated using standard NMR-NQR theory [16], where the second order shift is given by ... 

Fig. 3.17. Plot of f ( ), rc) of Eq. (3.16) as a function of the proton Larmor frequency in the high frequency region. The curves are calculated for rc values decreasing from 2 x 109 s (upper curve on the left) in steps of 3 x 10-10 s.

In A2FeFj compounds (A = K, Rb, Cs) an important spin reduction has been detected by neutron diffraction202 203 and Mossbauer resonance measurements230-232. The calculations are based only on the spin-wave theory disregardering the kinematic interactions since the spin value is important. Figure 36 describes the variation of the zero-point spin reduction with the anisotropy factor a. a is here (1 - coA/(oE) 2 where mA and a E are the Larmor frequencies corresponding to the anisotropy and exchange fields, respectively. 

Fig. 10-6. Relative magnetic field effect AR (cf. Eq. (10-9)) as a function of the Larmor frequency (CO in log scale) observed for the triplet exciplex (thionine/p-iodoaniline) in methanol. Points with error bars represent the experimental results obtained in Ref. [6]. Lines are calculated with an equation similar to Eq. (10-17) and the different values for ARiB ao) indicated in the diagram. (Reproduced from Ref [6] by permission from The American Chemical Society)...

The selection rules defined by the tensor-operator matrix elements ( T2, m) restrict the relevant transitions to the Larmor frequency and twice the Larmor frequency. The result of the calculation yields for the Ti relaxation of an isolated spin pair by random dipolar fields... 

We can also calculate the Larmor frequency in angular units, coo, in which case the factor of 1/27T is not needed ... 

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