Coupled spectra

Conditions CDCI3, 25 °C, 100 MHz ( C), 400 MHz H). (a-e) C NMR spectra (a,b) //broadband decoupled spectra (c,d) NOE enhanced coupled spectra (gated decoupling) with expansion (e) of the multiplets in the sp shift range (f) //NMR spectrum with expanded multiplets. 

Finally, a series of papers have been published on the solid state NMR spectra of a number of analgesic drugs. Jagannathan recorded the solid state 13C NMR spectrum of acetaminophen in bulk and dosage forms [60], From the solution-phase NMR spectrum, assignments of the solid state NMR resonances could be made in addition to explanations for the doublet structure of some resonances (dipolar coupling). Spectra of the dosage product from two sources indicated... 

Another important insight gained from the frequency-domain analysis is the optimal shape of the modulation that reduces the decoherence rate. Given a specific coupling spectrum, one should choose a modulation so as to decrease the overlap between the modulation and coupling spectra [29]. This optimal... 

The goal of any practical modulation scheme is to reduce, or, if possible, eliminate, all the elements of the decoherence matrix in Eq. (4.203) (see Ref. [20] for an alternative solution). However, in order to obtain the optimal modulation [29], one must first know the system-bath coupling spectra of the qubits in question. This information is usually not available a priori and thus most experimentalists have resorted to the suboptimal DD (or bang-bang) modulation, which does not require this knowledge. 

Use known, prescribed modulations to reveal the unknown decoherence parameters, that is, the system-bath coupling spectra. 

Equation (4.203) can be expressed via three matrices (i) The coupling spectra matrix, Gy(m), is usually unknown and is the objective of this analysis, (ii) The modulation power spectra matrix, Ff co) = ef j co)e co), can be calculated for each specific known modulation, (iii) The average decoherence matrix, Ry t), can be experimentally obtained via measurements of the decohering system. 

Furthermore, if one has a multipartite system, and thus a decoherence matrix, one must perform multiple modulation schemes that address the different qubits, on top of performing the aforementioned single-qubit scheme for all the qubits. This is essential to ascertain the cross-coupling spectra of all the possible qubit pairs. As discussed in Refs [19, 20, 112], these cross-coupling spectra are extremely important in reducing disentanglement and allow, in certain circumstances, to completely eliminate decoherence. 

To summarize, the methods of applying different modulations or measuring decoherence at different times, effectively sample the frequency-space, , and thus address different bath modes and allow measuring their coupling strength to the system. Thereafter, one can numerically obtain the coupling spectra that best fits the measured data. 

After one obtains the system-bath coupling spectra by applying specific, parameterized modulation schemes, one can finally tailor the specific modulation that would optimally reduce or eliminate decoherence. However, two aspects should be... 

However, these schemes can only be applied after obtaining an approximate form of the system-bath coupling spectra, without which one cannot tailor the local modulations that equate or eliminate specific elements of the decoherence matrix. 

To summarize, after obtaining the general shape of the system-bath coupling spectra matrix of the multipartite system by applying parameterized, known modulations, one can optimize the appropriate QIP-dependent figure of merit while obeying the constraints of the available modulations. 

We have shown that immediately after the measurement, the system and bath always heat-up, that is, get excited. Remarkably, for certain system-bath coupling spectra one can also observe a system that has lower excited-state population than the equilibrium state, that is, a purer system. This occurs despite the fact that the system has effectively recoupled with the bath and has become entangled with it. 

The practical use and the advantage of proton off-resonance decoupling - less multiplet overcrowding and more signal noise relative to coupled spectra - is illustrated in Fig. 2.47. for a triterpene derivative in comparison to modern and more accurate methods for determination of CH multiplicity. An unequivocal assignment of the number of directly attached hydrogens may be possible for all carbons. 

Pulse sequences for non-selective polarization transfer, not only useful for signal enhancement but also for multiplicity selection, are referred to as INEPT [54], abbreviated from Insensitive Nuclei Enhanced by Polarization Transfer . An improved method denoted as Distortionless Enhancement by Polarization Transfer or DEPT" [55] permits the cleanest multiplicity selection known so far, with full enhancement and low sensitivity to individual CH coupling constants. In addition, fully enhanced and undistorted coupled spectra can be recorded. Finally, subspectra for CH, CH2 and CH3 groups can be generated. 

DEPT spectra can be detected with and without proton decoupling. Correspondingly, decoupled and coupled spectra with multiplicity selection are observable. Fig. 2.46 illustrates such experiments with ( — (-menthol, also providing clear analysis of all CH coupling constants of the molecule. 

Our discussions of spin-spin splitting and multiplicity have been based on first-order or weakly coupled spectra which are spin systems where Av/J > 10. The difference in chemical shift in hertz of coupled protons divided by the coupling constant is 10 or more. In such a case clean 1 1 doublets, 1 2 1 triplets, and so on, are observed and coupling constants and chemical shifts can be read directly from line positions in the spectrum. 

As Av/J decreases, the simple multiplets observed in weakly coupled spectra become increasingly distorted new lines can appear and others merge or disappear. Such spectra are termed second-order or strongly coupled spectra. In these cases the chemical shift does not lie in the center of the multiplet and coupling constants are not always obvious. A simple example of such a change is seen... 

S, H) spin-spin coupling in the S spectra of dimethyl sulphone, sulpholane 10, and butadiene sulphone 11 was reported for the first time by Hinton.75 Afterward, the values of /( S, H) in dimethyl sulphone and sulpholane 10 have been estimated by comparing the line width value of the 33S resonance lines in 1H-coupled spectra and in spectra obtained under broadband proton decoupling. 

These sequences produce enhanced proton decoupled 29Si NMR spectra. Coupled spectra can be measured by the same sequences as described below. For the simple case of one silicon coupled to n equivalent protons, the optimum settings of delays r and A and pulse QO is99,106,107. 

In view of the subsequent developments118, the recommendations for a potential user would be for decoupled spectra when only enhancement is required—use INEPT (it is shortest) for spectral editing—use DEPT (less cross talk) for coupled spectra use INEPT- or, if antiphase multiples can be tolerated, use INEPT. To enhance the uniformity of excitation over larger 7 ranges, experiments measured with different r values can be added. 

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