COSY

COSY was the first 2D experiment attempted and in many ways serves as the prototype, as we discussed in Chapter 10. Now that we can apply product operator formalism, let s return to a further consideration of the mechanism for COSY and look at some of the factors that make it a more complex technique than was apparent in our initial treatment. 

For the four pathways in Table 12.1 that lead to observable / signals and the four that arise from S, we can use the procedure in Section 11.7 to write expressions for the evolution during t2  

11 The rotation operators Ix and S, represent 90° rotations ft/, and n.S, represent evolution of I and S, each under the influence of its chemical shift and JIXSX represents evolution under the influence of spin coupling. For each evolution, the upper branch implies multiplication by the appropriate sine term, and the lower branch implies multiplication by the appropriate cosine term. 

Of the 13 final coherences, Ix and Iy give diagonal peaks, and Sx and 5, give cross peaks. The remaining coherences are unobservable—antiphase magnetization, double quantum coherence, and longitudinal magnetization. 

We can picture the peaks more easily if we use trigonometric identities to obtain for expressions (3) and (4), that is, one diagonal and one cross peak, the following  

It was stated in the opening remarks of this chapter that COSY was the first two-dimensional sequence proposed, and it is in fact that given in Fig. 5.2 above, utilising just two 90 pulses. The sequence, which correlates the chemical shifts of spins that share a mutual J-coupling, is most often applied in proton spectroscopy although is equally applicable to any high-abundance nuclide. It is without doubt the mostly widely used of all two-dimensional methods, and is thus considered first. This section provides an introduction to 

The COSY experiment, despite its simplicity, is, however, subject to a number of limitations and caveats that one should also be aware of. The correlation 

The homonudear 2-D NMR experiments that use I-coupling indude the correlation spectroscopy (COSY, and variants induding gradient-selected COSY or gCOSY, double-quantum filtered COSY or DQF-COSY) experiment, the total correlation spectroscopy (TOCSY) experiment, and the incredible natural abimdance double quantum transfer experiment (INADEQUATE) [3]. 

Coherence selection. The isolation of a particular component of the total magnetization, often accomplished with the application of pulsed field gradients (PFGs). 

The COSY pulse sequence does not lend itself to explanation with visual images and spin gymnastics. To arrive at a better imderstand-ing of coherence selection in NMR pulse sequences, we can study the product operator formalism. Fortimately, an intimate grasp of how the COSY pulse sequence works is not required to use the method. 

A homonudear 2-D COSY NMR spectrum shows chemical shifts from the same nuclide on both the fj and fj axes. Signal normally appears on the diagonal where the analogous 1-D spectrum contains resonances (5j = 82). A signal off the diagonal is called a cross peak (81 52). The COSY cross peaks appear whenever the spins with resonances at 5j and 82 are coupled to each other. The intensity of COSY cross peaks varies in direct proportion to the magnitude of the J-cou-pling between the two resonances. 

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More generally, note that the applieation of almost any multiple pulse sequenee, where at least two pulses are separated by a time eomparable to the reeiproeal of the eoupling eonstants present, will lead to exehanges of intensity between multiplets. These exehanges are the physieal method by whieh eoupled spins are eorrelated in 2D NMR methods sueh as eorrelation speetroseopy (COSY) [21]. 

Figure Bl.11.12. H- H COSY-45 2D NMR spectrum of methyl-a-gliicopyranose (structure shown). The coupling links and the approximate couplings can be deduced by inspection.

Many variations of the basic homonuclear COSY experiment have been devised to extend its range. A brief guide to some classes of experiment follows, along with a few of the connnon acronyms. 

A H(detected)- C shift correlation spectrum (conmion acronym HMQC, for heteronuclear multiple quantum coherence, but sometimes also called COSY) is a rapid way to assign peaks from protonated carbons, once the hydrogen peaks are identified. With changes in pulse timings, this can also become the HMBC (l eteronuclear multiple bond coimectivity) experiment, where the correlations are made via the... 

Figure Bl.15.10. FT EPR. (A) Evolution of the magnetization during an FT EPR experiment (rotating frame representation). (B) The COSY FT EPR experiment.

Figure Bl.17.9. A CoSi grain boundary as visualized in a spherical-aberration-corrected TEM (Haider et a/ 1998). (a) Individual images recorded at different defocus with and without correction of C(b) CTFs in the case of the uncorrected TEM at higher defocus (c) CTF for the corrected TEM at only 14 nm underfocus. Pictures by courtesy of M Haider and Elsevier.

WebSpectra includes 75 problems All the problems display the and C spectra several with DEPT or COSY enhancements A number include IR spectra Organic Structure Elucidation contains 64 problems all with and C NMR IR and mass spectra The exercises in both WebSpectra and Organic Structure Elucidation are graded according to difficulty Give them a try... 

One kind of 2D NMR is called COSY, which stands for correlated spectroscopy With a COSY spectrum you can determine by inspection which signals correspond to spin coupled protons Identifying coupling relationships is a valuable aid to establishing a molecule s connectivity... 

Although the ID H spectium of 2 hexanone is simple enough to be mteipieted dnectly you can see that COSY offeis one moie tool we can call on m moie complicated cases... 

The July 1995 issue of the Journal of Chemical Educa t/on (pp 659-661) contains an undergraduate laboratory experiment in which COSY is used to analyze the products of a chemical reaction... 

A second 2D NMR method called HETCOR (heteronuclear chemical shift correlation) is a type of COSY in which the two frequency axes are the chemical shifts for different nuclei usually H and With HETCOR it is possible to relate a peak m a C spectrum to the H signal of the protons attached to that carbon As we did with COSY we 11 use 2 hexanone to illustrate the technique... 

Section 13 19 2D NMR techniques are enhancements that are sometimes useful m gam mg additional structural information A H H COSY spectrum reveals which protons are spin coupled to other protons which helps m deter mining connectivity A HETCOR spectrum shows the C—H connections by correlating C and H chemical shifts... 

COSY (Section 13 19) A 2D NMR technique that correlates the chemical shifts of spin coupled nuclei COSY stands for... 

Suppression of the tme diagonal peaks by double-quantum filtering (DQF-COSY) may resolve such problems. Finally, quantitative measurements of the magnitude of the coupling constants is possible using the Z-COSY modification, These experiments ate restricted to systems of abundant spins such as H, and which have reasonably narrow linewidths. 

Heteronuclear chemical shift-correlated spectroscopy, commonly called H-X COSY or HETCOR has, as the name implies, different and F frequencies. The experiment uses polarization transfer from the nuclei to the C or X nuclei which increases the SNR. Additionally, the repetition rate can be set to 1—3 of the rather than the longer C. Using the standard C COSY, the ampHtude of the C signals are modulated by the... 

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

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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