Overlapping peaks, integration

It is important to note that expression (23) can be applied to the crystalline phase intensities only if we include, in the first integral, its own smooth diffuse background and not just the intensity belonging to the crystalline peaks. In fact, a pure crystalline sample also has a smooth background due to the incoherent inelastic scattering (i.e. Compton scattering), the TDS, disorder scattering and, very often, unresolved tails of overlapped peaks. 

Fig. 14.11. Chromatogram showing overlapping peaks with two separation and integration possibilities dropping a perpendicular from the valley to the baseline, or using a tangent to each peak. Note that these will result in different areas for both peaks.

The second method is to integrate the intensities under the whole arcshaped reflections. The separation of overlapping peaks can be done automatically, once the peak shape has been parameterized from a few well-separated peaks. Occasionally there is a possibility of full overlapping when two or more reflections have the same or almost (within given precision) the same geometrical properties, like dm and Dm values (see equations (8) and (11)). Only then the overlapping reflections cannot be separated. 

Table 2 shows the full NOESY spectral matrix of cyclo(Pro-Gly), - (im = 80 ms) A(0) , recorded at T = 233 K. All cross peaks are integrated from the 2D experiment using Felix (Biosym), and overlapping peaks of Pro and Pro were separated after integration into two components in the proportion obtained from the 3D HMQC-NOESY... 

The uncertainties of K and the response ratio depend upon the ability to measure detector response. Peak height ratios can be used with excellent results (generally better than areas) when the peaks are symmetrical and sharp. Peak hight ratios are also more useful than peak areas in overlapping peaks. For automated systems, peak areas are preferred since the ratios are readily measured, and the data are calculated with electronic integrators and computers. 

Curve A(+), Figure 4,6). Within the uncertainties associated with these measurements, the integrated charge under the two overlapping peaks amounted co about half a monolayer of CO. This is not only consistent with the coverage of C0-c(4x2) but also... 

Figure 19.7 Overlapped peaks and their areas as integrated when a vertical drop is used. The true areas are always 1 3 or 3 1, respectively.

Figure 3.15. Extraction of the integrated intensity for two partially overlapped peaks...

In many laboratories, the NOE cross peaks are automatically integrated into the volume by using programs such as NMRPipe and Pipp.71 The programs are extensively reviewed by Baran et al.23 Since the line-widths can vary remarkably for different resonances, the integration is mandatory. The programs are also effective for the deconvolution of overlapping peaks, and... 

This method is useful for well-defined, non-overlapping peaks. Equation (72) can be integrated in the form... 

We can analyze the multiplicity of each H resonance to reveal how many H s are two or three bonds distant. Put more simply The splitting pattern of one H shows how many other H s are two and three bonds away. Let s start with the resonance at 2.96 ppm. We say that this resonance is a doublet of doublets (d ) because it is composed of two pairs of partially overlapping peaks that together integrate to one H. Because only the protons at position 2 are predicted to show the d splitting pattern, we make the tentative assumption that the resonance at 2.96ppm arises from the H on C2 that is gauche to H3. 

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