Two-dimensional NOESY experiment

Fig. 18. The pulse sequence used for the two-dimensional NOESY experiment for measuring H- H cross-relaxation rates in soft polymers. The entire experiment is conducted under magic-angle spinning. Gradient pulses are used to remove unwanted coherences, as this allows for much faster experiments than phase cycling.

The solutions to equation (1) may be written down immediately in terms of a matrix exponential. For the two-dimensional NOESY experiment, with appropriate normalization, the initial conditions (at the beginning of the mixing period ) can be written as a unit matrix, i.e., the two-dimensional pulse sequence is equivalent to repeated relaxation experiments in which each spin in turn is displaced from equilibrium. The two-dimensional NOE cross-peak intensity at chemical shifts corresponding to spins i and j is then related to the magnetization of spin i for the experiment in which spin j was initially perturbed. After a mixing time tm, this is just exp(—Rrm),. ... 

Figure 3.1 The various time periods in a two-dimensional NMR experiment. Nuclei are allowed to approach a state of thermal equilibrium during the preparation period before the first pulse is applied. This pulse disturbs the equilibrium ptolariza-tion state established during the preparation period, and during the subsequent evolution period the nuclei may be subjected to the influence of other, neighboring spins. If the amplitudes of the nuclei are modulated by the chemical shifts of the nuclei to which they are coupled, 2D-shift-correlated spectra are obtained. On the other hand, if their amplitudes are modulated by the coupling frequencies, then 2D /-resolved spectra result. The evolution period may be followed by a mixing period A, as in Nuclear Overhauser Enhancement Spectroscopy (NOESY) or 2D exchange spectra. The mixing period is followed by the second evolution (detection) period) ij.

In many cases, the analytical tasks are simply to detect and quantify a specific known analyte. Examples include the detection and quantification of commonly used buffer components (e.g., Tris, acetate, citrate, MES, propylene glycol, etc.). These simple tasks can readily be accomplished by using a standard one-dimensional NMR method. In other situations, the analytical tasks may involve identifying unknown compounds. This type of task usually requires homonuclear and heteronuclear two-dimensional NMR experiments, such as COSY, TOCSY, NOESY, HSQC, HMBC, etc. The identification of unknown molecules may also require additional information from other analytical methods, such as mass spectrometry, UV-Vis spectroscopy, and IR spectroscopy.14... 

The most important two-dimensional NMR experiments for solving stmctural problems are COSY (Correlation SpectroscopY), NOESY (Nuclear Overhauser Enhancement SpectroscopY), HSC (Heteronuclear Shift Correlation) and TOCSY (Total Correlation SpectroscopY). Most modem high-held NMR spectrometers have the capability to routinely and automatically acquire COSY, NOESY, HSC and TOCSY spectra. 

Figure 6.48 Two-dimensional NOESY spectrum (mixing time = 2 s) of the ether glucuronide of 3-methoxy-paracetamol at 600 MHz in a 3-mm cryogenic probe head (total experiment time 20 h). The sample was recovered from a conventional 3-mm LC probe head after a triple trapping SPE-NMR run (result shown in Eigure 6.41). Reproduced from [59] with permission from Elsevier.

Distinguish clearly between a one-dimensional NMR experiment that uses a time increment, such as the inversion-recovery technique (Section 2.9 and Fig. 8.8a), and a two-dimensional NMR experiment, such as NOESY. 

The resolntion that is gained by the additional freqnency dimension (N in this case) is illnstrated in Figure 3.6. The two-dimensional NOESY spectrnm of a 50 residne a-helical protein is shown in the left part of this fignre. In this experiment, the magnetization is transferred from proton H to proton Hy by dipolar coupling. The first freqnency dimension corresponds to the chemical shift of H and the second frequency dimension corresponds to the chemical shift of Hy. As with the NOESY-HSQC described previously, the intensity of the peak is related to the distance between H and Hy. Note the large number of unresolved overlapping peaks in the... 

Zumbulyadis et al. [86] selected a fluorinated polyphosphazene, containing CF3CF2CF2CF2CH2O side chains (attached to phosphorus atoms in the polymer backbone) to explore the potential of F MAS/NOESY experiments. MAS at 3.82 kHz sufficed to resolve all four F sites, though effects of isotropic indirect coupling were obscured by the linewidths. Cross peaks are seen in the two-dimensional NOESY spectrum. The authors argue that these arise from NOE processes and not from spin diffusion. 

To establish interpulse delays for two-dimensional NMR experiments, it is frequently convenient to run a very quick proton Tj relaxation measurement. Given the sensitivity of modem spectrometers, this can usually be done with only a single or a few transients for each of the r values in the series, and typically requires 10 min or less. By visual inspection, the Tj relaxation time can be estimated from the r value at which response intensity is zero. A knowledge of the Tj relaxation time is also useful for establishing mixing times for NOESY and ROESY experiments. 

Two-dimensional NMR experiments can also be used in the solid state to study the structure and dynamics of polymers, and 2D solid-state NOESY has been used to provide a molecular-level assignment for the polyethylene a transition observed by dielectric and dynamic mechanical spectroscopy [32]. One proposal is that this transition can be assigned to chain diffusion between the crystalline and amorphous regions [33], Two peaks are observed in the C-CPMAS spectra of polyethylene that can be assigned to chains in crystalline and amorphous environments. Figure 3.27 shows the 2D spin exchange... 

The nuclear Overhauser effect was described in Chapter 6, Sections 6.5 and 6.6. A two-dimensional NMR experiment that takes advantage of the nuclear Overhauser effect is nuclear Overhauser effect spectroscopy, or NOESY. Any H nuclei that may interact with one another through a dipolar relaxation process will appear as cross peaks in a NOESY spectrum. This type of interaction... 

These experiments use pulse sequences similar to that of the spin-echo experiment. There are a number of experiments with different pulse sequences. The different experiments are commonly named with acronyms. For example, COSY (Correlation SpectroscopY) was the original two-dimensional NMR experiment. Some other experiments are NOESY (Nuclear Overhauser Effect SpectroscopY) and HETCOR (HETeronuclear CORrelation). The usual goal of a COSY experiment is to determine which lines belong to which multiplet in a complicated spectrum with overlapping multiplets. We will give a simplified description of the COSY experiment for proton NMR (this is sometimes called HH-COSY). 

They are most often combined with traditional two-dimensional experiments such as NOESY and TOC-SY to yield a three-dimensional experiment. For example, in the case of an HSQC-NOESY spectrum of a protein, two of the axes represent the heteronuclei such as and the protons which are directly attached to the nitrogen nuclei, while the third axis contains chemical shifts of protons which share an NOE effect with the amide proton. This offers a significant increase in resolution compared to a traditional two-dimensional NOESY. A large array of these types of three-dimensional, heteronuclear-edit-ed experiments have been designed to extract structural information in various situations. 

Previously, only one-dimensional nuclear magnetic resonance (NMR) spectroscopic data had been reported for the 3,6-anhydroglucal 7 in the literature [17]. We carried out additional two-dimensional NMR experiments ( H- H COSY, NOESY, and HMQC) to fully characterize the compound. The proposed anhydro structure was supported by the observation of long-range coupling between the vinylic proton (C2) and the bridgehead proton (C4 1.5 Hz). We were also able to obtain crystals for 3,6-anhydroglucal 7 and an x-ray structure was obtained [26]. 

The nuclear Qverhauser effect was described in Chapter 4, Sections 4.5 and 4.6 (pp. 184-189). A two-dimensional NMR experiment that takes advantage of the nuclear Overhauser effect is nuclear Qverhauser effect spectroscopy, or NOESY. Any nuclei that may interact with one another through a dipolar relaxation process will appear as cross peaks in a NOESY spectrum. This type of interaction includes nuclei that are directly coupled to one another, but it also includes nuclei that are not directly coupled but are located near to one another through space. The result is a two-dimensional spectrum that looks very much like a COSY spectrum but includes, besides many of the expected COSY cross peaks, additional cross peaks that arise from interactions of nuclei that interact through space. In practice, the nuclei must be within 5 A of each other for this spatial interaction to be observed. 

Generally, the most powerful method for stmctural elucidation of steroids is nuclear magnetic resonance (nmr) spectroscopy. There are several classical reviews on the one-dimensional (1-D) proton H-nmr spectroscopy of steroids (267). C-nmr, a technique used to observe individual carbons, is used for stmcture elucidation of steroids. In addition, C-nmr is used for biosynthesis experiments with C-enriched precursors (268). The availability of higher magnetic field instmments coupled with the arrival of 1-D and two-dimensional (2-D) techniques such as DEPT, COSY, NOESY, 2-D J-resolved, HOHAHA, etc, have provided powerful new tools for the stmctural elucidation of complex natural products including steroids (269). 

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