Resonance overlap

The coupled resonance overlaps with the solvent peaks. For additional information see Refs. 116 and 117. 

Fig. 3. Secondary chemical shifts for 13C , 13CO, H , and 13C as a function of residue number in apomyoglobin at pH 4.1. Bars at the top of the figure indicate the presence of NOEs the smaller bars indicate that the NOE was ambiguous due to resonance overlap. Black rectangles at the base of the top panel indicate the locations of helices in the native holomyoglobin structure (Kuriyan et al, 1986). Hashed rectangles indicate putative boundaries for helical regions in the pH 4 intermediate, based on the chemical shift and NOE data. Reproduced from Eliezer et al (2000). Biochemistry 39, 2894-2901, with permission from the American Chemical Society.

Figure 19. Correlations in the HSQC-1,1-ADEQUATE spectrum allow the overlapped resonances of the 2-(p-hydroxyethyl)piperidine moiety incorporated in the structure to be assigned (Figures 20 and 21). There are, however, resonance overlaps that complicate the F1SQC-1,1-ADEQUATE spectrum by virtue of artefact responses contained in the spectrum that are enclosed in boxes in Figure 21. Given the considerable overlap in the proton spectrum, the presence of artefact responses in the GIC processed HSQC-1,1-ADEQUATE spectrum is not surprising. It is also somewhat uncertain whether or not the 1,1-ADEQUATE spectrum itself would be tractable because of the proton resonance overlaps.

To estimate the critical value of the external filed strength ecr we use Chirikov s resonance overlap criterion (Zaslavsky, 1988 Jensen, 1984), which can be written as ... 

Applying resonance overlap criterion to this Hamiltonian we get the following estimate for the critical field strength ... 

Thus we have treated the chaotic dynamics of the quarkonium in a time periodic field. Using the Chirikov s resonance overlap criterion we obtain estimates for the critical value of the external field strength at which chaotization of the quarkonium motion will occur. The experimental realization of the quarkonium motion under time periodic perturbation could be performed in several cases in laser driven mesons and in quarkonia in the hadronic or quark-gluon matter. 

As in the case of the HN(CO)CA-TROSY scheme, the HN(CO)CANH-TROSY experiment can be readily expanded to a four-dimensional HN(CO)CANH-TROSY experiment without increasing the overall length of the pulse sequence. This can be accomplished by labelling the 13C (f) chemical shift during additional incremented time delay, implemented into the 13C — 13C INEPT delay. As a result, a well-dispersed 13C (i- 1), 13C (i- 1), 15N(i), Hn(0 correlation map is obtained with minimal resonance overlap albeit with the inherent sensitivity loss by a factor of y/2. 

The larger the protein, the greater the resonance overlap. Often several different residues have degenerate 13Ca frequencies which will make an unambiguous assignment difficult or even impossible. In these cases, additional information from different NMR experiments is required. One possibility is to use the carbonyl chemical shift instead of the Ca chemical shift and measure the HNCO/HN(CA)CO pulse sequence pair [37, 45, 46, 49, 50]. As with the HNCA/HN(CO)CA combination, one of the experiments, the... 

The high level of deuteration enormously reduces the line broadening due to the 1H-1H dipole-dipole relaxation of the methyl protons of Met, lie and Thr. Furthermore, the selective 13C labeling of these methyl groups can be used to resolve the methyl proton resonance overlap. 

Considering an estimated experimental error of 10-20% for the STD data as well as some systematic errors in the estimates from resonance overlap, the analysis suggests a generally reasonable correspondence between the crystal structure and the solution state. At the same time, our data suggest that the crystallographic structure of the complex may not be entirely compatible... 

This is a consequence of resonance overlap of lone pair electrons from the nitrogen provides an iminium system, with the negative counter-charge on the P-carbon. 

An analytical theory for the study of CC of radiationless transitions, and in particular, IC leading to dissociation, in molecules possessing overlapping resonances is developed in Ref. [33]. The method is applied to a model diatomic system. In contrast to previous studies, the control of a molecule that is allowed to decay during and after the preparation process is studied. This theory is used to derive the shape of the laser pulse that creates the specific excited wave packet that best enhances or suppresses the radiationless transitions process. The results in Ref. [33] show the importance of resonance overlap in the molecule in order to achieve efficient CC over radiationless transitions via laser excitation. Specifically, resonance overlap is proven to be crucial in order to alter interference contributions to the controlled observable, and hence to achieve efficient CC by varying the phase of the laser field. 

R. A. Marcus Perhaps the following remark relates to Stuart Rice s question regarding invertibility and quantum chaos . One might regard quantum chaos as corresponding to the overlapping of a number of internal resonances. In that case, if your method doesn t apply when several resonances overlap, it wouldn t, of course apply and probably wasn t intended to apply, to quantum chaos . 

M. Shapiro If the resonances overlap to such an extent that we can no longer break the frequency resolved spectrum to a sum of Fano lines in a unique way, then my analysis would not be unique. However this is an extreme situation and even in this case one can try to fit the spectrum (admittedly in a non-unique way) to a sum of Fano lines (or complex energy poles). 

F. Remade In the case of HO2 described by Prof. Schinke, the resonances overlap and I would expect a prompt and a delayed branch... 

The proton NMR spectrum of oxymyoglobin is shown in the lower part of Fig. 30. Even though the individual resonances overlap rather strongly some spectral features can be recognized, and there are two well-resolved lines of relative intensities one and six at +2.8 and +0.1 ppm. Very similar spectra were observed after replacement of O2 with CO or with ethylisocyanide (Shulman et al. (101)). 

In closing the section on non-Hermitean approaches to continuum processes in atomic and molecular physics, we will also mention accurate examinations on resonance parameters in molecular predissociation displaying unexpected resonance overlapping [46,89]. The phenomenon of predissociation by rotation in HgH was analyzed via an isotopically combined potential due to Stwalley [120]. The potential, i.e., a relatively shallow energy curve with a nonzero /-value giving rise to a rotational barrier, supported novel metastable states above the dissociation limit. The Weyl s method was able to resolve the closely lying vibrational states v = 3 and v = 4 for the rotational quantum number K = 9. 

There seems no simple unitary transform of the time-delay matrix QSim, such as Eq. (72), if more than two resonances overlap each other. Instead, we may take advantage of the rank 1 of the projection matrix Pv of Eq. (61) in Qv of Eq. (69). Thus, for the eigenvalue equation... 

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