Resonances overlapping

Resonance poles lying within the widths of each other are called overlapping resonances. When they occur, the rapid rise of the phase shift due to one pole begins before the rise due to an adjacent pole finishes. In this sense, the effects of overlapping resonances on the phase shift and, in particular, on the cross section are difficult to separate, in general. Nonetheless, the overlapping Lorentzian profiles in the time-delay spectrum 

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Proton chemical shift spectra over the range of 0—15 ppm ( 0.1 ppm) TFA, ttifuoroacetic acid DMSO, dimethyl sulfoxide. When complex spectra caused by second-order effects or overlapping resonances were encountered, the range was record (11,12). 

To lessen experimental time, the null-point method may be employed by locating the pulse spacing, tnun, for which no magnetization is observed after the 180°-1-90° pulse-sequence. The relaxation rate is then obtained directly by using the relationship / , = 0.69/t n. In this way, a considerable diminution of measuring time is achieved, which is especially desirable in measurements of very low relaxation-rates, or for samples that are not very stable. In addition, estimates of relaxation rates for overlapping resonances can often be achieved. However, as the recovery curves for coupled spin-systems are, more often than not, nonexponential, observation of the null point may violate the initial-slope approximation. Hence, this method is best reserved for preliminary experiments that serve to establish the time scale for spin-lattice relaxation, and for qualitative conclusions. 

Resolution of even highly overlapping resonances /-spectroscopy... 

The physical significance of Eq. (53) is clear. At an isolated resonance the excitation and dissociation processes decouple, all memory of the two excitation pathways is lost by the time the molecule falls apart, and the associated phase vanishes. The structure described by Eq. (53) was observed in the channel phase for the dissociation of HI in the vicinity of the (isolated) 5sg resonance. The simplest model depicting this class of problems is shown schematically in Fig. 5d, corresponding to an isolated predissociation resonance. Figures 5e and 5f extend the sketches of Figs. 5c and 5d, respectively, to account qualitatively for overlapping resonances. 

Firstly, catheter sample 1 was dissolved in deuterated trifluoroacetic acid, and the solution analyzed by [H NMR spectroscopy. The [H NMR spectrum of the sample is shown in Figure 52. The peaks at 1.16 ppm, 2.56 ppm, and 3.40 ppm are consistent with a polyamide-12 (PA-12) structure. The signal at 3.58 ppm can be attributed to tetramethylene glycol (TMG) protons adjacent to the ether linkages. The signal at 1.60 ppm is composed of overlapping resonances from both components. The smaller peaks are most likely due to polymer end groups or protons at the junction of two blocks the material is an amide-ether block... 

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.

Mies FH (1968) Configuration interaction theory, effects of overlapping resonances. Phys Rev 175 164... 

The application of the Chebyshev recursion to complex-symmetric problems is more restricted because Chebyshev polynomials may diverge outside the real axis. Nevertheless, eigenvalues of a complex-symmetric matrix that are close to the real energy axis can be obtained using the FD method based on the damped Chebyshev recursion.155,215 For broad and even overlapping resonances, it has been shown that the use of multiple cross-correlation functions may be beneficial.216... 

Topsom, 1976) and to treat them separately. In this review we will be concerned solely with polar or electronic substituent effects. Although it is possible to define a number of different electronic effects (field effects, CT-inductive effects, jt-inductive effects, Jt-field effects, resonance effects), it is customary to use a dual substituent parameter scale, in which one parameter describes the polarity of a substituent and the other the charge transfer (resonance) (Topsom, 1976). In terms of molecular orbital theory, particularly in the form of perturbation theory, this corresponds to a separate evaluation of charge (inductive) and overlap (resonance) effects. This is reflected in the Klopman-Salem theory (Devaquet and Salem, 1969 Klop-man, 1968 Salem, 1968) and in our theory (Sustmann and Binsch, 1971, 1972 Sustmann and Vahrenholt, 1973). A related treatment of substituent effects has been proposed by Godfrey (Duerden and Godfrey, 1980). 

In Section 5.1 usual strategies to obtain reliable calibration by external and internal references are reported. Section 5.2 presents techniques for analysing overlapping resonance lines with symmetric and well-defined lineshapes. Section 5.3 shows a more suitable approach for differentiation of IMCL and EMCL in the complex signal patterns of lipids in muscle spectra. 

NMR (CeDg, 125.7 MHz, 25°C) 139.8, 132.5, 128.8-129.1 (overlapping resonances), 124.6, 17.0 (br). B NMR (CgDg, 128.3 MHz, 25°C) -10.96 ppm. The compound is a versatile precursor to a wide range of transition metal complexes supported by the tris(phosphino)borate ligand. It is air- and water-stable for extended periods, and, unlike the lithium and ammonium salts of [PhB(CH2PPh2)3] , it is both soluble and stable in chloroform and dichloromethane for days, making these useful solvents available for subsequent trans-metallation chemistry. 

In this section, we review the projection formalism used in the PT and the emergence of the overlapping resonances as the central element in this approach, which plays a key role in conceptually linking diverse physical phenomena and processes discussed in Section 9.3. 

The important feature of resonances is that when the widths of states in Q are larger than their associated level spacing, such states, termed now overlapping resonances, can interfere with one another. The quantum dynamics of systems with overlapping resonances show a rich variety of interesting physical phenomena furthermore, in such systems there is potential for quantum control... 

In this section, we apply the TOR in a variety of physical phenomena and processes, thus establishing the existence of overlapping resonances in such systems as the crucial element for understanding their dynamical properties. 

In Reference [31], the suppression and enhancement of IVR in a collinear model of OCS [61,62] is investigated. The intent is to assess the extent of control in such a system and to establish the relationship between control and overlapping resonances. From all the vibrational states obtained, it is observed that control is best when considering a superposition of states, that is near the dissociation onset. The energy differences between these states are relatively small ( 0.0004 a.u.), whose inverse corresponds to a timescale of 60 fs, thus giving rise to a high density of states with timescales comparable to vibrational relaxation. The result is... 

Pulse-Based CC in Systems with Overlapping Resonances... 

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. 

The CC pulse train experiments in Refs [63-65] utilize shaped pulses that use a transform-limited (TL) Gaussian pulse its phase is modulated in the frequency domain with a sine function, p ( ) = a sin( -I- c), while keeping the amplitude profile intact. The parameters a, b, and c are further varied to control molecular populations. In Reference [35], the effect of different values of these parameters on the IC dynamics of pyrazine and / -carotene is investigated and the significant role of overlapping resonances is exposed. 

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