Equilibrium nuclear spin polarization

However, despite their exquisite spectral sensitivity to stmcture, dynamics, and morphology, conventional NMR methods suffer from a common drawback that in many circumstances, can limit their power and applicability - a notoriously low detection sensitivity (especially compared to optical methods). This fundamental insensitivity originates from the miniscule size of nuclear magnetic moments, which results in an exceedingly small (Boltzmann) equilibrium nuclear spin polarization, P, generally given by... 

In another class of experiments, hyperpolarized states are generated by spin-sensitive chemical reactions. These include para-hydrogen-induced polarization (PHIP) [3-5] and chemically induced dynamic nuclear polarization (CIDNP) [6-8]. The latter involves non-equilibrium nuclear spin state populations that are produced in chemical reactions that proceed through radical pair intermediates. CIDNP s applicability has been focused towards the study of chemical reactions and the detection of surface exposed residues in proteins [9], but has so far remained limited to specialized chemical systems. 

By examining the expression for Q ( equation (B1.16.4)). it should now be clear that the nuclear spin state influences the difference in precessional frequencies and, ultimately, the likelihood of intersystem crossing, tlnough the hyperfme tenn. It is this influence of nuclear spin states on electronic intersystem crossing which will eventually lead to non-equilibrium distributions of nuclear spin states, i.e. spin polarization, in the products of radical reactions, as we shall see below. 

Clearly, if a situation were achieved such that exceeded Np, the excess energy could be absorbed by the rf field and this would appear as an emission signal in the n.m.r. spectrum. On the other hand, if Np could be made to exceed by more than the Boltzmann factor, then enhanced absorption would be observed. N.m.r. spectra showing such effects are referred to as polarized spectra because they arise from polarization of nuclear spins. The effects are transient because, once the perturbing influence which gives rise to the non-Boltzmann distribution (and which can be either physical or chemical) ceases, the thermal equilibrium distribution of nuclear spin states is re-established within a few seconds. 

In Section 11.8 we saw how polarization (departure from the equilibrium distribution) of nuclear spin state populations by a nearby unpaired electron can have a profound effect on NMR signal intensity. It turns out that in a l3C 1H experi-... 

Experimentally, CIDNP denotes the occurrence of anomalous line intensities (enhanced absorption or emission) when NMR spectra are recorded during a chemical reaction. These anomalies are due to spin polarizations of the reaction products, that is, populations of their nuclear spin states that deviate from thermodynamic equilibrium. Only reactions involving radical pairs or biradicals exhibit CIDNP. 

For these experiments, gated illumination for aperiod much shorter than the nuclear Ti was applied, and the polarizations were then sampled by an NMR pulse. This protocol results in a very good signal to noise ratio because the number of absorbed photons is large, and the CIDNP intensities are undisturbed by nuclear spin relaxation in the products. However, these experiments would also record the equilibrium NMR signals of unreacted molecules. This was avoided by special pulse sequences, and all spectra shown below are completely free from such background signals and represent pure polarizations only. 

The proton equilibrium nuclear polarization in liquid samples at room temperature is only of the order of 10. In gaseous samples it is even less due to the reduced number of spins in a unit volume. However, the nuclei of gases such as He and Xe can be prepared in a high state of nuclear polarization ( 10 ) by the well-known technique of optical pumping. Such a high degree of polarization is referred to as hyperpolarization... 

Fig. 1. Cartoon depicting the spin-cooling effect of optical polarization on an ensemble of nuclear spins (assuming /= 1/2 and positive gyromagnetic ratio). Normally (at thermal equihbrium), the numbers of spins aligned parallel and antiparallel to the magnetic field (Bq) are nearly equal, yielding a low net spin polarization - and consequently, a tiny detectable magnetization, Mq. However, optical polarization can provide the means to drive the population distribution far away from equilibrium, thereby increasing M by several orders of magnitude. In the spin-temperature model, such polarization can often result in nuclear spin ensembles with miUi-Kelvin effective temperatures. (After Ref [110].)...

The origins of symmetry induced nuclear polarization can be summarized as follows as mentioned above molecular dihydrogen is composed of two species, para-H2, which is characterized by the product of a symmetric rotational wave-function and an antisymmetric nuclear spin wave function and ortho-H2, which is characterized by an antisymmetric rotational and one of the symmetric nuclear spin wavefunctions. In thermal equilibrium at room temperature each of the three ortho-states and the single para-state have practically all equal probability. In contrast, at temperatures below liquid nitrogen mainly the energetically lower para-state is populated. Therefore, an enrichment of the para-state and even the separation of the two species can be easily achieved at low temperatures as their interconversion is a rather slow process. Pure para-H2 is stable even in liquid solutions and para-H2 enriched hydrogen can be stored and used subsequently for hydrogenation reactions [54]. 

Despite considerable progress in the field, NMR spectroscopy still has two significant limitations the intrinsically low sensitivity, due to the low Boltzmann polarization of nuclear spins in thermal equilibrium, and the low dispersion of observed frequencies, due to small differences in nuclear shielding by surrounding electrons for nuclei of the same kind. The first problem is continuously... 

Let IIq and 11 be the polarizations produced per mole of G and F-pairs respectively, where polarization is defined as the difference in the populations of a and 3 nuclear spin states minus the population difference at thermal equilibrium. In addition let Og and be the corresponding reaction probabilities. II and are quantities which include all effects of radical re-encounters and ST mixing and are simply related to the individual reaction probabilities of pairs containing the unique proton in a and states. 

When discussing the general aspects of FTNMR, we have to remember that all principal statements about Fourier methods have been introduced for a strictly linear system (mechanical oscillator) in Chapter 1. In Chapter 2, on the other hand, we have seen that the nuclear spin system is not strictly linear (with Kramer-Kronig-relations between absorption mode and dispersion mode signal >). Moreover, the spin system has to be treated quantummechanically, e.g. by a density matrix formalism. Thus, the question arises what are the conditions under which the Fourier transform of the FID is actually equivalent to the result of a low-field slow-passage experiment Generally, these conditions are obeyed for systems which are at thermal equilibrium just before the initial pulse but are mostly violated for systems in a non-equilibrium state (Oberhauser effect, chemically induced dynamic nuclear polarization, double resonance experiments etc.). 

Empirical equilibrium coupling constants can be compared as a benchmark with calculated equilibrium coupling constants obtained with various methods. A comparison of these empirical equilibrium constants with calculated equilibrium constants suggested that the restricted-active-space self-consistent field (RASSCF) method is the best approach for calculating the indirect nuclear spin-spin coupling constants of small molecules, and that the second-order polarization propagator approximation (SOPPA) and DFT are similar in performance. 

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