Spin population inversion

The earliest of the magnetization transfer experiments is the spin population inversion (SPI) experiment [27]. By selectively irradiating and inverting one of the 13C satellites of a proton resonance, the recorded proton spectrum is correspondingly perturbed and enhanced. Experiments of this type have been successfully utilized to solve complex structural assignments. They also form the basis for 2D-heteronuclear chemical shift correlation experiments that are discussed in more detail later in this chapter. 

Fig. 5 Naj Li (left side) and Naj Li (right side) SEDOR results on the model compound LiNaS04. Solid curves show fits to the equation shown, where the inversion factor f takes into account the incomplete spin population inversion caused by strong quadrupolar splittings. The dotted curve shown on left is the theoretical prediction for f=1.00 in the Naj Li SEDOR experiment. Reproduced from [56]...

An approach to solving the inverse Fourier problem is to reconstruct a parametrized spin density based on axially symmetrical p orbitals (pz orbitals) centered on all the atoms of the molecule (wave function modeling). In the model which was actually used, the spin populations of corresponding atoms of A and B were constrained to be equal. The averaged populations thus refined are displayed in Table 2. Most of the spin density lies on the 01, N1 and N2 atoms. However, the agreement obtained between observed and calculated data (x2 = 2.1) indicates that this model is not completely satisfactory. 

Consider the 13C— H bond as a two-spin system. CH coupling occurs between one nucleus with small population difference (13C) and another one with large polarization (1H). Fig. 2.43(a) illustrates this situation by the number of dots on the energy levels. Population inversion of the proton levels 1 and 3 connected by the transition 1H1 is achieved by an appropriate 180° pulse, which turns the double cone of precession shown in Fig. 2.1 upside down. Thereafter, the inverted proton population difference controls both carbon-13 transitions (Fig. 2.43(b)). This is the polarization or population transfer making up an enhanced absorption signal for one transition (e.g. 13Ci in Fig. 2.43 (b)) and an enhanced emission on the other (e.g. 13C2 in Fig. 2.43(b)). 

The transitions corresponding to w2 and u>o involve simultaneous changes in spin state of both nuclei. The difference between W2 and wq tells us how the variation in population of J affects the equilibrium of /. In other words, one can think in terms of transfer of spin population from J to I when J is saturated. The larger the cross relaxation, the larger the dipolar coupling. The NOE on I is proportional to the cross relaxation from J and inversely proportional to the capability of / to return to equilibrium once its equilibrium is perturbed through cross relaxation. 

If UE > UG and NE = N( then formally, if Eq. (4.18.1) holds, then T = oo. Going further, if population inversion occurs (NE > Nc), as occurs with lasers before stimulated light emission, or with nuclear spins upon saturation of the excited state, then T must be "negative." This absurd notion, which flies in the face of conventional thermodynamics, arises when Eq. (4.41) is forced to hold even under conditions for which it was never designed. 

There are two things to note at this point. First, the 180,. pulse inverts M (rotates it 180° around the x axis) to the -z axis, giving an excess of spins.in the higher energy spin state (a population inversion). The 180y- pulse inverts M around they axis. Such a pulse will become important in the next section. ... 

Figure 12.12a depicts the coupled C-H spin system of HCC13, a composite of Figures 12.3 and 9.2a. There are two 13C transitions (vCi < vC2), each with intensity proportional to population difference 2AC, and two H transitions (vHi < vH2), each with intensity proportional to population difference 2Ah (Ah = 4Ac). In the selective population inversion (SPI) experiment, we will irradiate only one specific hydrogen... 

In 1960 s, CIDEP was less popular than CIDNP because CIDEP did need much faster measuring techniques than CIDNP. This is due to much faster relaxation times (usually less than 1 /r s) of polarised electron spins than those (usually a few second for protons) of nuclear spins. In 1968, Smaller et al. [2] observed a population inversion for the cyclopentyl radical with a 2-MHz ESR apparatus coupled with a 15 MeV electron beam with pulse duration of 0.5 -4.0 /z s. The response time of the system corresponded to a time constant of 1.6/z s. In 1970, Atkins et al. [3] obtained the photo-CIDEP for the ketyl radical from benzophenone in paraffin solvents with a 2-MHz ESR apparatus coupled with a 20-ns laser flash. Under favorable chemical conditions, Wong and Wan [4] demonstrated that the photo-CIDEP for some semiquinone radicals in alcohol solvents could be observed with a commercial ESR spectrometer having a 100-kHz modulation unit and a custom-designed rotating sector giving light pulses. 

Continuous wave operation of COIL is facilitated by the hyperfine structure of the atom. Iodine has a nuclear spin of, so the P /2 and Pz/2 levels are split by hyperfine interactions. Figure 8 shows the allowed transitions between the hyperfine sublevels and a high resolution emission spectrum. The F = 3 — F" = 4 transition is most intense, and this is the laser line under normal conditions. Collisional relaxation between the hyperfine sub-levels of Pz 2 maintains the population inversion, while transfer between the Fi/2 levels extracts energy stored in the F = 2 level. Hence, if it is not sufficiently rapid, hyperfine relaxation can limit power extraction. 

The experiment described above is termed selective population transfer (SPT), or more precisely in this case with proton spin inversion, selective population inversion, (SPI). It is important to note, however, that the complete inversion of spin populations is not a requirement for the SPT effect to manifest itself. Any unequal perturbation of the lines within a multiplet will suffice, so, for example, saturation of one proton line would also have altered the intensities of the carbon resonance. In heteronuclear polarisation (population) transfer experiments, it is the heterospin-coupled satellites of the parent proton resonance that must be subject to the perturbation to induce SPT. The effect is not restricted to heteronuclear systems and can appear in proton spectra when homonuclear-coupled multiplets are subject to unsymmetrical saturation. Fig. 4.20 illustrates the effect of selectively but unevenly saturating a double doublet and shows the resulting intensity distortions in the multiplet structure of its coupled partner, which are most apparent in a difference spectrum. Despite these distortions, the integrated intensity of the proton multiplet is unaffected by the presence of the SPT because of the equal positive and negative contributions (see Fig. 4.19d). Distortions of this sort have particular relevance to the NOE difference experiment described in Chapter 8. 

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