Effect of a 90 Pulse

Equation 11.39 shows that the 90° pulse has nulled the on-diagonal elements of p and has created nonzero off-diagonal elements (coherences). We can also express Eq. 11.39 in the simple algebraic form 

The same result could have been obtained more succinctly by starting with Eq. 11.40 and carrying out the manipulations algebraically (as in Eq. 11.38). The algebraic calculations depend on the fact that the matrices for Ix, Iy, and lz are traceless and on the cyclic permutation relations IrIs = ilt among Ix, Iy, and I2. 

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Can the simple vector presentation be used to display the effects of a 90° pulse on zero- or multiple-quantum magnetizations ... 

For example, starting from equilibrium (Iz), the effect of a 90° pulse on the y axis is... 

The effect of a 90° pulse can be duplicated in cw NMR although with more difficulty than in pulse NMR. When a resonance line is swept rapidly in the conventional cw high resolution experiment, a ringing pattern follows the line if phase detection is used. Such a ringing pattern occurs in the following way As one sweeps into resonance, the mag-... 

FIGURE 10.6 The effect of a 90° pulse (M is the bulk magnetization vector for the sample). 

FIGURE 10.4 The effect of a 90 pulse on the net magnetization vector of a proton. lies along the positive z axis, (a) a proton as a spinning particle, (b) the net magnetization vector, (c) a 90 pulse, and (d) relaxation. 

Fig. 2.1. Preferred nuclear precession about the direction of the magnetic field (a) and the effect of a 90°. radio frequency pulse (b).

At the end of the 90° pulse with B on the x axis, the net magnetization is on the —/ axis, and we have no z component. We will refer to this spin state as —Iy. Because the z component of net magnetization results from the population difference between the a and states, we can say that there is no population difference at the end of a 90° pulse (Fig. 6.7). With the 90° pulse, we have effectively converted the population difference into coherence. If we record the FID right after this pulse, we would get a normal spectrum with a positive absorptive peak. 

The effect of pulses is very simple each individual operator is acted on by the pulse, and replaced by the result of that rotation about the Bi vector. For example, consider the effect of a 90° XH pulse on the x axis ... 

These are exactly the same as the vector rotations, and you should draw a small set of coordinate axes in the margin of your paper to figure out these rotations as you work with product operators (Fig. 7.12). Note that 13C net magnetization is not affected by a XH pulse (S-y - Sy). The effect of a 90° 13C pulse on the y axis is likewise the same as the vector model predicts ... 

There is a key observation that makes coherence pathway selection possible by phase cycling. Starting with a pure 1+ (p = 1) coherence, consider the effect of changing the phase of a 90° pulse on the phases of the resulting coherences ... 

The effects of three general phenomena over time must be explored ( ) pulses, (2) chemical shifts, and (3) spin-spin coupling. To express the effect of a 90°(tt/2) pulse along the x axis on magnetization that exists initially along the z axis, we use the formalism... 

Then, consider the effect of a 90°(x) pulse applied to all three spins. After this pulse, you should find one term which represents a diagonal-peak multiplet, one which represents a cross-peak multiplet between spin 1 and spin 2, and one which represents a cross-peak multiplet between spin 1 and spin 3. What does the fourth term represent ... 

For large molecules, such as proteins, the main method in use is a 2D technique, called NOESY (nuclear Overhauser effect spectroscopy). The basic experiment [33, 34] consists of tluee 90° pulses. The first pulse converts die longitudinal magnetizations for all protons, present at equilibrium, into transverse magnetizations which evolve diirhig the subsequent evolution time In this way, the transverse magnetization components for different protons become labelled by their resonance frequencies. The second 90° pulse rotates the magnetizations to the -z-direction. 

Figure 1.18 Effect of applying a 90° pulse on the equilibrium magnetization Continuous application of a pulse along the x -axis will cause the magnetization vector (Ml) to rotate in the y z-plane. If the thumb of the right hand points in the direction of the applied pulse, then the partly bent fingers of the right hand point in the direction in which the magnetization vector will be bent.

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