Multiplet lines

Taking these methylene groups into account, interpretation of the HH COSY plot leads directly to the HH relationships C even if the protons at Sh = 2.34 and 4.58 do not show the expected cross signals because their intensity is spread over the many multiplet lines of these signals. 

Increasing the number of dimensions from two to three may result in a reduction in the signal/noise (S/N) ratio. This may be due either to the distribution of the intensity of the multiplet lines over three dimensions or to some of the coherence transfer steps being inefficient, resulting in weak 3D cross-peaks. 

When several magnetically equivalent nuclei are present in a radical, some of the multiplet lines appear at exactly the same field position, i.e., are degenerate , resulting in variations in component intensity. Equivalent spin-1/2 nuclei such as 1H, 19F, or 31P result in multiplets with intensities given by binomial coefficients (1 1 for one nucleus, 1 2 1 for two, 1 3 3 1 for three, 1 4 6 4 1 for four, etc.). One of the first aromatic organic radical anions studied by ESR spectroscopy was the naphthalene anion radical,1 the spectrum of which is shown in Figure 2.2. The spectrum consists of 25 lines, a quintet of quintets as expected for hyperfine coupling to two sets of four equivalent protons. 

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

For the measurement of cross-correlated relaxation rates, there are mainly three methods that have been used in practice. In the /-resolved constant time experiment, the multiplet Hnes exhibiting differential relaxation are resolved by the f couplings, and the line width is translated into intensity in a constant time experiment (Fig. 7.19a,d). In the J-resolved real time experiment the line width of each multiplet line is measured instead (Fig. 7.19b, d). This experiment has been applied so far only for the measurement of... 

Then, each of the correlation peaks exhibits a doublet of doublet structure along co2 because of the evolution of the (H.N) and the 1J(Ca,Ha) coupling during t. The intensity of the individual multiplet lines is affected by the dipole, dipole cross-correlated relaxation rate rcHN c H as well as the sums of two dipole/CSA cross-correlated relaxation rates r°HN C + rcHN N and r°c H c + r°c H N. By forming the ratios... 

Heteronuclei such as 13C (this magnetically active nucleus has 1.1% natural abundant) and 15N (0.3% natural abundance) are routinely measured with modem NMR spectrometers. Proton decoupled 13C NMR spectra in natural abundance exhibit singlets for each specific carbon atom, which are easier to count than overlapping multiplet lines in H NMR. ID 13C NMR can be used to investigate whether a peptide exhibits a single set of lines or a double (or more) set, which indicate conformational or configurational isomers (see Section 7.5.3). However, ID 13C NMR is rather insensitive and if there is not enough material or the solubility is low, more sensitive techniques have to be applied. 

The most recent calculations, however, of the photoemission final state multiplet intensity for the 5 f initial state show also an intensity distribution different from the measured one. This may be partially corrected by accounting for the spectrometer transmission and the varying energy resolution of 0.12, 0.17, 0.17 and 1,3 eV for 21.2, 40.8, 48.4, and 1253.6 eV excitation. However, the UPS spectra are additionally distorted by a much stronger contribution of secondary electrons and the 5 f emission is superimposed upon the (6d7s) conduction electron density of states, background intensity of which was not considered in the calculated spectrum In the calculations, furthermore, in order to account for the excitation of electron-hole pairs, and in order to simulate instrumental resolution, the multiplet lines were broadened by a convolution with Doniach-Sunjic line shapes (for the first effect) and Gaussian profiles (for the second effect). The same parameters as in the case of the calculations for lanthanide metals were used for the asymmetry and the halfwidths ... 

The multiplet lines in the 13C spectrum of acetone are equidistant. The distance (quoted in Hz) between any two neighboring lines is termed the coupling constant. The coupling constant of an AmXn system is given the symbol JAX. 

The intensities of the multiplet lines arise from the number of spin configurations belonging to each total spin (Fig. 1.12). For n coupling nuclei X the intensity ratios are equal to the nlh binominal coefficients (Table 1.3). 

Table 1.3. Multiplet Line Intensity Ratios of Signal A due to Coupling with n Equivalent Nuclei X Ux = D-...

However, off-resonance multiplets are distorted, in that the multiplet lines on the side of the decoupling frequency are weaker than those on the opposite side. Further, off-resonance splittings of higher than first order may be observed for substructures such as... 

Next, consider the molecule D2CH2. Each of the two D nuclei can adopt three orientations. Therefore, two D nuclei can adopt nine [(21 + l)2] spin combinations corresponding to five (2nl + 1) spin states (M = 2, 1, 0, -1, -2). These are shown in Figure 8.12. Notice that the 1 2 3 2 1 population ratio of these states (which is the same as the relative intensity of the multiplet lines coupled to them) is different from that predicted by Pascal s triangle, which only applies to 7 = nuclei. At any rate, the H spectrum of D2CH2 shows a five-line pattern, with intensity ratio 1 2 3 2 1 and line spacing 2yHD. 

Assume for the moment that all three coupling constants in our AMX system are positive, and focus your attention on the A and M multiplets. Lines A and A2 correspond to the up orientation of nucleus X, while lines A3 and A4 correspond to the down orientation of X. Similarly, lines M, and M2 correspond to the up orientation of nucleus X, while lines M3 and M4 correspond to the down orientation. We describe this situation by saying that the A -A2 doublet is connected (via the similar spin state of nucleus X) with the M,-M2 doublet, and the A3-A4 doublet is connected with the M3-M4 doublet. These connections are shown below the spectrum. If we simultaneously saturate only lines A and A2 (by focusing v2 between them and carefully adjusting its power), only the connected lines (doublet Mj-M2) will collapse to a singlet. Lines M3 and M4 would remain intact. 

For a given number, , of coupled nuclear spins of spin quantum number the A signal will be split into (2 f f -i- 1) multiplet lines (e.g. Fig. 1.9). 

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