Effect nuclear Overhauser

The nuclear Overhauser effect is something very dear to senior NMR researchers. It is the effect which allows us to know which magnetic nuclei are close to other magnetic nuclei, and information on their distances becomes available. Its understanding used to be a must to move towards 2D spectroscopy. Now times are somewhat changed, but... 

We have chosen to dedicate a full chapter to the nuclear Overhauser effect [1,2] (NOE) because its comprehension is of fundamental importance in dealing with nuclear relaxation [3,4], Especially in paramagnetic compounds, it still represents a most powerful technique to detect dipolar connectivities finally it allows the comprehension of two-dimensional spectroscopies based on dipolar coupling. The NOE is the fractional variation of the intensity of a signal when another signal is selectively saturated. 

The NOE is the result of the transfer of spin population (called polarization 

In the following sections we will go through the various classical experiments like steady state, truncated and transient NOE, as well as ROE. The presentation has the twofold purpose of sketching (or refreshing) the basic theory to 

The nuclear Overhauser effect (NOE), which is manifested in certain changes in the intensities of NMR lines, is a consequence of magnetic dipolar relaxation. The name comes from a phenomenon predicted by Albert Overhauser in 1953, when he showed theoretically that saturating the electron magnetic resonance in a metal would cause the nuclear resonance intensity to be enhanced by a factor of the order of 103 (the ratio of /electron/ /nucleus)- lonel Solomon later found that a similar effect occurs between two nuclei, but with a much smaller intensity enhancement—the nuclear Overhauser effect.90 Because the NOE is of great practical im- 

The qualitative basis of the NOE can be readily appreciated from Fig. 8.3. If rf energy is applied at frequency cos, the S transitions thus induced alter the populations of the energy levels, and because of cross relaxation (i.e., transitions W0 and W2, which affect both I and S simultaneously), that change affects the intensities of the I transitions. Quantitatively, Eq. 8.4 shows what happens when the two S transitions are subjected to a continuous wave rf that is intense enough to cause saturation. At the steady state both dlz/dt and Sz are zero, so that Eq. 8.4 (after some rearrangement) gives 

We have substituted ys/y, for S0/I0. Eq. 8.11 gives the fractional change in intensity at steady state, which is often called the nuclear Overhauser enhancement and given the symbol 7). (Often the value given in publications for the NOE is actually 1 + 17, so care must be used in interpreting the results.) 

By substituting the expressions for spectral densities in Eq. 8.11, we obtain an equation that is algebraically cumbersone in general but that can be simplified in either of two regimes (1) homonuclear spins (I = S) or (2) rapid tumbling (extreme narrowing limit). 

For I = S, substitution for the transition probabilities Win Eq. 8.11 gives, after some algebraic manipulation, 

Quantitative analysis of mixtures is achieved by evaluating the integral steps of H NMR speetra. This is demonstrated in Fig. 1.11a for 2,4-pentanedione (acetylacetone) which occurs as an equilibrium mixture of 87 % enol and 13 % diketone. 

Relaxation 2,3,6 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 coherence of nuclear spins built up upon NMR excitation. 

Spin-lattice relaxation is the steady (exponential) build-up or regeneration of the Boltzmann distribution (equilibrium magnetisation) of nuclear spins in the static magnetic field. The lattice is the molecular environment of the nuclear spin with which energy is exchanged. 

The spin-lattice relaxation time, T/, is the time constant for spin-lattice relaxation which is specific for every nuclear spin. In FT NMR spectroscopy the spin-lattice relaxation must keep pace with the exciting pulses. If the sequence of pulses is too rapid, e.g. faster than 3Tlmax of the slowest C atom of a molecule in carbon-13 resonance, a decrease in signal intensity is observed for the slow C atom due to the spin-lattice relaxation getting out of step . For this reason, quaternary C atoms can be recognised in carbon-13 NMR spectra by their weak signals. 

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 (free 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). 

Yobs is the magnetogyric ratio for the nucleus being measured Yss, is the magnetogyric ratio for the nucleus being saturated 

Solid samples present a number of problems in NMR. Line broadening arises from chemical shift anisotropy, because of the many orientations the different carbon atoms have in a solid sample relative to the applied magnetic field. The chemical shift anisotropy can be eliminated by MAS at 

The spin-lattice relaxation time for in solids is very long (several minutes). Since the nuclei have to relax before another excitation pulse can be sent, this requires hours of instrument time in order to collect a spectrum of reasonable intensity. A pulse technique called cross-polarization can be used to reduce this effect by having the protons interact with the carbon nuclei, causing them to relax more rapidly. FT-NMR systems for solid samples include the hardware and software to produce narrow line spectra from solid samples in a reasonable amount of time using high-power dipolar decoupling, MAS, and cross-polarization. 

The student is encouraged to look at the spectra presented in the earlier figures in the chapter 

Fligh-resolution NMR spectra of organic compounds can be complex, with overlapping resonances and overlapping spin-spin couplings. The use of 2D NMR experiments and even 3D and 4D experiments extends the information obtained into a second (or third or fourth)-frequency dimension. The spectrum becomes easier to interpret and much more structural information is usually provided. Two- and higher-dimensional experiments rely on the selective manipulation of specific 

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Neuhaus D and Williamson M 1989 The Nuclear Overhauser Effect in Structural and Conformational Analysis (New York VCH)... 

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. 

Noggle J H and Schirmer R E 1971 The Nuclear Overhauser Effect (New York Academic)... 

Neuhaus D 1998 Nuclear Overhauser effect Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 3290-301... 

You can often use experimental data, such as Nuclear Overhauser Effect (NOE) signals from 2D NMR studies, as restraints. NOE signals give distances between pairs of hydrogens in a molecule. Use these distances to limit distances during a molecular mechanics geometry optimization or molecular dynamics calculation. Information on dihedral angles, deduced from NMR, can also limit a conformational search. 

The 2-D nuclear Overhauser effect spectroscopy (2-D-NOESY) experiment resembles the COSY however, the cross-peaks arise from... 

Another technique often used to examine the stmcture of double-heUcal oligonucleotides is two-dimensional nmr spectroscopy (see AfAGNETiC SPIN resonance). This method rehes on measurement of the nuclear Overhauser effects (NOEs) through space to determine the distances between protons (6). The stmcture of an oligonucleotide may be determined theoretically from a set of iaterproton distances. As a result of the complexities of the experiment and data analysis, the quality of the stmctural information obtained is debated. However, nmr spectroscopy does provide information pertaining to the stmcture of DNA ia solution and can serve as a complement to the stmctural information provided by crystallographic analysis. 

Although experimental studies of DNA and RNA structure have revealed the significant structural diversity of oligonucleotides, there are limitations to these approaches. X-ray crystallographic structures are limited to relatively small DNA duplexes, and the crystal lattice can impact the three-dimensional conformation [4]. NMR-based structural studies allow for the determination of structures in solution however, the limited amount of nuclear overhauser effect (NOE) data between nonadjacent stacked basepairs makes the determination of the overall structure of DNA difficult [5]. In addition, nanotechnology-based experiments, such as the use of optical tweezers and atomic force microscopy [6], have revealed that the forces required to distort DNA are relatively small, consistent with the structural heterogeneity observed in both DNA and RNA. 

NOE Nuclear Overhauser effect, change of signal intensities (integrals) dining decoupling experiments decreasing with spatial distance of nuclei... 

NOESY Nuclear Overhauser effect spectroscopy, detection of NOE in the HH COSY square format, traces out closely spaced protons in larger molecules... 

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. 

One-dimensional nuclear Overhauser effect (NOE), relaxation measurements in native D. gigas Fdll, and analysis of temperature depen-... 

Figure 1. Pulse sequences of some typical 2D-NMR experiments. COSY = correlation SpectroscopY, DQFCOSY = Double Quantum Filtered COSY, RELAY = RELAYed Magnetization Spectroscopy, and NOESY = Nuclear Overhauser Effect SpectroscopY.

The nuclear Overhauser effect resulting from the broad-band decoupling during the decoupled INEPT experiment also contributes to the signal enhancement of the C lines. 

Hence the population difference between the lower and upper energy states of the two I transitions becomes d + x, as compared to the original difference of d at equilibrium. Thus an intensification of the lines for nucleus 1 will be observed by an amount corresponding to this increased difference x. This is the positive nuclear Overhauser effect that is encountered in small, rapidly tumbling molecules, in which Wj is the predominant relaxation pathway. 

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