Relaxation of Nuclear Spins

The stimulated transitions between the four energy levels of two coupled spins result in two distinct types of relaxation. The first is called spin-lattice relaxation. This form of relaxation involves the net loss of energy from the excited state and is analogous 

The rotational correlation time can easily be thought of as the time constant for loss of memory regarding the previous orientation of the molecule. It is roughly equal to the time it takes a molecule to rotate 1 radian while undergoing random rotational motion. Small molecules have short x values while large molecules have long Xc values. 

The key point is the effect of molecular weight on the spectral density function. As the molecular size increases, the intensity of fluctuations with a frequency close to the zero quantum transitions also increases. Hence, the spin-spin relaxation rate increases as the molecular weight increases. This has two very important consequences. First, the spectral line width will increase as the molecular size increases. Consequently, the NMR spectra of larger proteins show increased degeneracy because of the increased number of resonances and the increased line width. The second consequence of the shortened lifetime of the excited state is a reduction in the efficiency by which magnetization can be passed from one nucleus to another 

FIGURE 3.3 Effect of molecular weight on the spectral density function. The spectral density function, J(C0), is plotted vs. the frequency of the magnetic field fluctuations. The spectral density functions for a large protein (25 kDa) and a small protein (2.5 kDa) are shown. The frequency for single quantum transition of the H spins is indicated by the arrow. 

FIGURE 3.4 Illustration of the process of acquiring a one-dimensional NMR spectrum. The steps involved in obtaining an NMR spectrum are shown. The sample is a tetra-peptide (Val-Ala-Ser-Ala). A short (10 asec) intense RF pulse is applied to the sample. This pulse excites all of the nuclei and they emit energy at their characteristic absorption frequencies. This signal is called the free induction decay (FID) and is collected as a function of time. This time domain signal is converted to spectrum by Fourier transformation. Note the characteristic chemical shifts for amide protons (H v), a-protons, (i-protons, and methyl protons. Also note that the two alanine residues, although chemically equivalent, have different chemical shifts because they experience different local environments. 

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Reif, B., Steinhagen, H., Junker, B., Reggelin, M., Griesinger, C. Determination of the orientation of a distant bond vector in a molecular reference frame by cross-correlated relaxation of nuclear spins. 

To create a quantum computation system based on a qubit ensemble and to decrease the required magnetic field and its gradient the modification of the cluster structure was proposed [1,2]. It consists in utilization of nuclear spin chains on the steps of the silicon surface which serve as the qubit ensemble. Resonance frequencies of a magnetic isotope nucleus 29Si are divided between neighboring chains. In this case the efficiency of quantum computation is determined by the decoherence rate for a quantum state. The decoherence rate depends on the number of nucleus in a qubit and on the time of transverse relaxation of nuclear spin polarization. The aim of the present work is calculation of the decoherence rate of the quantum state of the qubit ensemble built on the basis of these nuclei. 

Relaxation of nuclear spins occurs under two modes longitudinal and transverse relaxation characterized respectively by time constants T- and T2. The quadrupolar interaction i.e. the interaction of the quadn olar moment of the nucleus witH the electric field gradient present at the sodium site, provides the predominant relaxation mechanism. Due to the rather symmetrical environment of the solvated sodium ion - for instance (Na )6H20 " weak electric field gradient is expected. Upon complexation by a bionolecule, the alkali ion coordinates both with solvent and substrate molecules, which both increase the electric field gradient, and decreases by a considerable amount the cation rotational motion. Both these effects generate a relaxation rate enhancement. 

Figure 2.4 Sequence of the process of relaxation of nuclear spins (a) application of a n 12 RF pulse (b) to (e) time evolution of the transverse and longitudinal components of the magnetization. Note that the transverse relaxation has been concluded in (d), but the process of longitudinal relaxation continues up to (e), indicating the common situation of T > T2-...

Dayie K T, Wagner G and Lefeevre J F 1996 Theory and practice of nuclear spin relaxation in proteins Anna. Rev. Phys. Chem. 47 243-82... 

Relaxation refers to all processes which regenerate the Boltzmann distribution of nuclear spins on their precession states and the resulting equilibrium magnetisation along the static magnetic field. Relaxation also destroys the transverse magnetisation arising from phase coherenee of nuelear spins built up upon NMR excitation. 

Spin-spin relaxation is the steady decay of transverse magnetisation (phase coherence of nuclear spins) produced by the NMR excitation where there is perfect homogeneity of the magnetic field. It is evident in the shape of the FID (/fee induction decay), as the exponential decay to zero of the transverse magnetisation produced in the pulsed NMR experiment. The Fourier transformation of the FID signal (time domain) gives the FT NMR spectrum (frequency domain, Fig. 1.7). 

Gordon R. G. Kinetic theory of nuclear spin relaxation in gases, J. Chem. Phys. 44, 228-34 (1966). 

Methods of disturbing the Boltzmann distribution of nuclear spin states were known long before the phenomenon of CIDNP was recognized. All of these involve multiple resonance techniques (e.g. INDOR, the Nuclear Overhauser Effect) and all depend on spin-lattice relaxation processes for the development of polarization. The effect is referred to as dynamic nuclear polarization (DNP) (for a review, see Hausser and Stehlik, 1968). The observed changes in the intensity of lines in the n.m.r. spectrum are small, however, reflecting the small changes induced in the Boltzmann distribution. 

Radicals escaping from a radical pair become uncorrelated as approaches zero. In the free (doublet) state they are detectable by e.s.r. spectroscopy. However, just as polarization of nuclear spins can occur in the radical pair, so polarization of electron spins can be produced. Provided that electron spin-lattice relaxation and free radical scavenging processes do not make the lifetime of the polarized radicals too short. 

R. Y. Dong, M. Bloom 1970, (Determination of spin-rotation constants in flu-orinated methane molecules by means of nuclear spin relaxation measurements), Can. J. Phys. 48, 793. 

Further, neglecting the effect of nuclear spin relaxation, the acquired signal dS in an element of volume dr at position r with spin density p(r) is given by... 

CCR can easily be explained in a simplified form all coherences between nuclear spins, that finally give rise to NMR signals, relax (decay) with a certain rate, and eventually disappear. In dipolar relaxation, the relaxation of a spin is mediated by the fluctuating electromagnetic field caused by adjacent... 

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