Equal Peaks

In principle, every nucleus in a molecule, with spm quantum number /, splits every other resonance in the molecule into 2/ -t 1 equal peaks, i.e. one for each of its allowed values of m. This could make the NMR spectra of most molecules very complex indeed. Fortunately, many simplifications exist. 

Figure 6 Theoretical and experimental results for an ordered and a disordered system on the left theoretical data for a CusPt single crystal and on the right experimental findings for a CusPt alloy overlayer on a platinum substrate. The spectra for the ordered species are traced with continuous lines, whereas those for the disordered species are given in dotted lines. The spectra were normalized to equal peak height.

The average SSMAXCOV curve for the PhA had a clear complete peak with the highest covariance of. 04 the MIS curve was flat with the highest covariance under. 03 and the PAS curve had two equal peaks with... 

Compound 22 can be conveniently prepared in multigram quantities and has been found to be useful for assessing the enantiomeric purity of 1,2-glycols. Because the ketal carbon represents a new chiral center, the formation of four diastereomers is possible. However, the diastereomeric pair 23a and 23b (or 23c and 23d) shows 1 1 peak height in 13C NMR or equal peak areas in HPLC the diastereomer composition measured by the ratio of 23a to 23b or 23c to 23d reflects the enantiomer composition of the original 1,2-glycol. 

For example, peak 1 of G1 produces peak 10 of G2 together with peak 17 of G3. Likewise peak 6 of G2 yields peak 5 in G1 and peak 11 in G3. Peaks 2 and 4 of G1 produce each just one peak in G2 but produce each two peaks in G3 with equal peak areas. Finally, peak 3 of G1 again gives just one peak in G2 but produces peaks 13,14 and 15 in G3 with relative area ratios of 1 4 1. 

The different types (doublet, triplet, and so on) exhibit a characteristic ratio of intensities. Doublets are equally intense. Triplets have a more intense central peak flanked by two equal peaks of lesser intensity. A quartet has two equally intense central peaks with two smaller outer peaks that are equal to each other in intensity. See Figure 5-4 for the NMR spectrum of ethanol. 

In chromatography separations operated under gradient elution, one simple method of obtaining an equal peak width of a specific solute in columns of different dimensions is to keep the numbers of theoretical stages of both columns equal. 

Catechol shows two nearly equal peaks, at 6970 and 7060 cm 1. Of the three configurations... 

The two equal peaks observed for tetrabromocatechol at 6820 and 6920 cm-1 similarly correspond to the structure... 

Ions containing Cl or Br have distinctive isotopic peaks shown in Figure 22-7.11 In the mass spectrum of 1-bromobutane in Figure 22-8, two nearly equal peaks at mlz 136 and 138... 

Figure 5.8. Left to right sequence gives the profile of a pair of Gaussian zones of equal a at increasing levels of resolution, as shown. Top row shows this sequence for two zones of equal peak height middle and bottom rows show the sequence for 2 1 and 5 1 peak height ratios (profiles courtesy of Joe M. Davis).

We first divide the resonance position (3.56 ppm) into two equal peaks (1 1 ratio) by moving left 5.0 Hz (7/2) and right 5.0 Hz (7/2) (Fig. 2.5). Then each of these peaks is divided again into two equal peaks (1 1 ratio) by the 4.0-Hz coupling 2.0 Hz to the left and 2.0 Hz to the right. This results in a pattern we call a doublet of doublets or (more concisely) a double doublet (abbreviated dd ). In the literature we would report the peak like this 53.56 (dd, 10.0,4.0). To deconstruct (analyze) the pattern, we first note that all four peaks are of the same height, and because 4 is a power of 2 (22 = 4), we assume that there is no overlap of... 

Coupling to deuterium, 2H, is observed for deuterated solvents and their residual peaks (from solvent molecules with one 2H replaced by1H).1H-2H coupling constants are proportional to the corresponding H / value, reduced by a factor of about 7 (kh/Kd = 6.51) due to the weaker nuclear magnet of deuterium. Because deuterium has a spin of 1, it has three spins states almost equally populated, and so it splits the H signal into three equal peaks centered on the H chemical shift position. Multiple 2H splittings can be... 

Figure 14.11 Site-specific experimental valence X-ray photoelectron spectrum of the rutile Ti02 single-crystal sample, obtained using the XRSW technique, in comparison with the calculated partial density of states (corrected for individual angular-momentum-dependent photoionization cross sections) [32]. (a) Ti, (b) O. The spectra are normalized to equal peak height.

The full width at half-maximum (FWHM) of the Lorentzian curve of Fig. 11.54 is FWHM/ = 3.1905 for the Gaussian of equal peak height, FWHMg = 2.3549 at equal peak heights, a Gaussian lineshape is narrower, while the Lorentzian is broader—that is, has more intensity far from the peak. In practice, NMR or EPR lineshapes can also be intermediate between Lorentzian and Gaussian. 

The weight ratio of the internal standard to the sample should be such that the internal standard and the component sought produce approximately equal peaks. This is, of course, not possible if several components of interest are at different levels of concentration. 

The axial and equatorial methyl and methylene absorptions have essentially equal peak areas. This spectrum is therefore consistent with the product s being the cis isomer, 11a. For the trans isomer one might expect a preference for the conformer with the diequatorial ethyl groups, lib. In this case the axial and equatorial absorptions should not have equal intensities. Such a preference is expected to be small, however, and the NMR spectrum must be regarded as consistent with the trans... 

Unfortunately, the direct algebraic transformation of expression (2-19) into some form of functional dependence of R on k, a, and N is impossible. Knox and Thijssen were the first to independently propose the transformation based on the assumption of equal peak width (w2 = Wi ) and consideration of the retention of the first peak of the pair (A i). The resulting expression is... 

Equidistance deviation from equal peaks resolution RunTime - fo Comparison of starting systems... 

The ultimate stereochemical identity test is, of course, the direct resolution of the enantiomers using chiral liquid or gas chromatography (9). When compared to a reference standard of the racemate, and under experimental conditions that will resolve the peaks of both enantiomers, the occurrence of two equal peaks will identify the racemate, and one peak will signify an enantiopure material. A proof of the stereochemical identity of the analyte can be provided, based on a match of retention times with a reference standard of known stereochemistry. Inequality between the peaks is a measure of enantiomeric enrichment. Therefore, it is conceivable that both stereochemical identity and purity can be established from a single experiment. 

When attempting quantitation of a mixture of polymorphs, the first step is to identify which peaks are due to each polymorph, and to select two well-resolved peaks corresponding to the same carbon in each polymorph. A multiple-contact time experiment is then acquired to determine the rates of magnetization transfer (7ch) and decay (Tip) for each form. If these rates are identical in each form, direct integration of the peaks will provide quantitative data, with the relative areas representing the amount of each form present in the mixture. An example of the results of a multiple-contact time experiment is shown in Fig. 2—a plot of the natural logarithm of relative peak area as a function of contact time for neotame forms A and It is clear from this plot that spectra acquired at any contact time will not give equal peak area for both forms. 

A neat reference mixture was prepared that contained 17 pure NHCs plus pyridine and quinoline as retention index markers (Table 1 Fig. 2). Relative amounts were adjusted to give approximately equal peak sizes. Triplicate analyses were performed on the 65 °C headspace above this mixture and above several wastewaters. To minimize any effect of column aging on peak retention times, the reference and wastewater replicates in each test series were alternated. Reproducibilities were excellent with standard deviations averaging 0.12 retention units overall and 0.05 retention units for the reference mixture. Reference-peak to sample-peak correlations were performed by a variety of statistical procedures including z tests. Student-t tests and, later, the procedure described in Section 3.2. 

For half the molecules, then, absorption by a secondary proton is shifted slightly downfield, and for the other half of the molecules the absorption is shifted slightly upheld. The signal is split into two peaks a doublet, with equal peak intensities (Fig. 13.9). 

Problem 22.2 At room temperature, the nmr spectrum of 1-ethylaziridine (III) shows the triplet-quartet of an ethyl group, and two other signals of equal peak area. When the temperature is raised to 120, the latter two signals merge into a single signal. How do you interpret these observations ... 

The path described above can be constructed by two smooth pulses, associated with the Rabi frequencies D, (t) and Q2(/j, with a time delay x. To a sequence of such pulses corresponds a closed loop in the parameter plane Oj and 02. Each of the two black curves [labeled (a) and (b)] correspond to a sequence of two smooth pulses of equal length T and equal peak Rabi frequencies Qmax = max2[fli(f)] = maxjf f)], separated by a delay such that the pulse 1 is switched on before the pulse 2. This path has been redrawn as a function of time on Fig. 16b, using sin2 envelopes of length T = 100/5 and a delay of x = T/3, shown in Fig. 16a. Details of this dynamics of bichromatic processes, in particular in relation with the initial condition for the photon field, are given and discussed in the next subsection. Path (c) needs two pulses with different peak amplitudes. 

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