Precession frequency

A number of 2D NMR experiments, such as NOESY, have a mixing period incorporated in their pulse sequence. In principle, precession of j magnetization also occurs during the mixing period. Why do we not need to have a third Fourier transformation to monitor the precession frequencies that occur during the mixing period ... 

In order for relaxation to occur through Wj, the magnetic field fluctuations need to correspond to the Larmor precession frequency of the nuclei, while relaxation via requires field fluctuations at double the Larmor frequency. To produce such field fluctuations, the tumbling rate should be the reciprocal of the molecular correlation time, i.e., f), so most efficient relaxation occurs only when voT, approaches 1. In very small, rapidly tumbling molecules, such as methanol, the concentration of the fluctuating magnetic fields spectral density) at the Larmor frequency is very low, so the relaxation processes Wj and do not occur efficiently and the nuclei of such molecules can accordingly relax very slowly. Such molecules have... 

Chemical shift The difference between the nuclear precession frequency and the carrier frequency. 

Larmor frequency The nuclear precession frequency about the direction of Bo. Its magnitude is given by yBo/27T. 

Modulation The variation in amplitude and/or phase of an oscillatory signal by another function, e.g., modulation of the nuclear precession frequency of one nucleus by the nuclear precession frequency of a correlated nucleus in COSY spectra. 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

The instantaneous precession frequency to in a magnetic field gradient G for a moving spin with coordinate x = Xo + vt + at2/2 +... is... 

As a result of the projection theorem [31], the expectation value of the EDM operator d, which is a vector operator, is proportional to the expectation value of J in the angular momentum eigenstate. This fact, in conjunction with Eq. (9), implies that the electric field modifies the precession frequency of the system because of the additional torque experienced by the system due to the interaction between the electric field and the EDM. It can readily be shown that the modified precession frequency is... 

In strongly coupled systems, it is not possible to eliminate chemical shifts by refocusing nor is it possible to describe the evolution in terms of an effective Hamiltonian.44 A 90° or a 180° pulse leads to coherence transfer between various transitions, and a multitude of new effective precession frequencies may appear in the F1 dimension. A detailed analysis shows artefacts resulting of strong coupling induced by the 180° pulse applied on the H channel can be efficiently removed by applying a LPJF before acquisition.42 Likewise, artefacts present in HMBC with a terminal LPJF are suppressed by an LPJF in the beginning of the sequence as in conventional HMBC. 

Interestingly, the precessing proton can only absorb energy from the radio frequency source if the precessing frequency is exactly the same as that of the radio frequency beam and when this particular situation arises, the nucleus and the radio frequency beam are said to be in resonance, thereby justifying the term nuclear magnetic resonance . 

Coils located within the pole gap allow a sweep to be made through the applied magnetic field that produces resonance in the range of precession frequencies. 

This mixed classical/quantum expression is valid for classical nuclear behavior and, strictly speaking, for the case of direct two-site interaction rather than superexchange, as the Landau-Zener expression was derived from the time-dependent Schrodinger equation assuming a two-state (reactant/product) electronic system with direct coupling. Nevertheless, it becomes clear on physical grounds that the form of Eqs. 4-5 can serve to define an effective A in the superexchange case in terms of the Rabi precession frequency characteristic of the two trap sites embedded in the complex system wherein 2A/h would be computed from this net effective Rabi precession frequency. 

The SIN defined by Equation 7.6 for a given NMR resonance is proportional to the square of the nuclear precession frequency (mo, rad/s), the magnitude of the transverse magnetic field (Bi) induced in the RE coil per unit current (/), the number of spins per unit volume (Ns), the sample volume (Vs), and a scaling constant that accounts for magnetic field inhomogeneities. The SIN is inversely proportional to the noise generated in the RE receiver and by the sample (Vnoise) as defined by the Nyquist theorem,... 

The most expensive parts of a conventional NSE instrument are the main solenoids providing the precession field. A closer look at Bloch s equation of motion for the spins (Eq. 2.11) shows that in a coordinate system that rotates with the precession frequency around Bg the spin is stationary, the coordinate system rotation is equivalent to the addition of - to all magnetic fields. By this means the large precession field inside the main coils may be transformed to zero - zero field spin-echo). The flippers are viewed as elements rotating... 

Thus, the precession frequency is proportional to the magnetic strength of the nuclear magnetic moment as well as applied magnetic field. As magnetic field strength increases the precession frequency increases. Table 10.1 shows the relationship between applied field Bo and the precession frequency of a... 

Table 10.1 Precession frequencies of protons in different applied magnetic fields...

Anisotropy is also associated to a magnetic field, whose modulus is Ba = 2 KaIMs, Ms being the crystal magnetization. The precession frequency of the magnetic moment into this field corresponds to the frequency of the peak characterizing the distribution of the transition frequencies. 

When the anisotropy energy is large enough it prevents any precession of the magnetic moment of super-paramagnetic crystals. The magnetic fluctuations then arise from the jumps of the moment between different easy directions. The precession prohibition is introduced into the Freed equations in order to meet that requirement every time the electron Larmor precession frequency appears in the equations, it is set to zero 12). 

Without spin refocusing, the simulations show that R2 reaches a plateau for diameters above 0.02 pm. The corresponding maximum relaxation rate of about 100 s is predicted by the Static Dephasing Regime (SDR) model 22, 23), which assumes that, as depicted above, transverse relaxation is only attributed to differences in precession frequencies of static spins. The relaxation rate is then given by ... 

In pulsed NMR, the magnetic field is turned on for the time necessary to rotate the magnetization vector into a plane called the 90° rotation or 90° pulse. The field is turned off and the magnetization vector rotates at a nuclear precession frequency relative to the coil. This induces an NMR signal that decays with time as the system returns to equilibrium. This signal is called the free induction decay (FID). 

A first pulse create.s transverse magnetization components (coherences) which evolve in the evolution period tl (DO in the schemes) with their characteristic precession frequencies (chemical shift and homonuclear J-coupling). The effect of the second (mixing) pulse is that information from one nucleus that evolves in tl is transferred to another (J-coupled) nucleus, the magentization components of which evolve and are detected in t2. Therefore, the nuclei carry information that relates not only to their own chemical shifts and coupling constants but also the corresponding information about the other, coupled spins. 

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