Scaled coupling constant

NMR), chemical shift, S scale Coupling constant, direct AB Hz ... 

Chemical shifts depend on the strength of the applied magnetic field B0 according to eq. (1.8 c) when measured on the frequency scale. Coupling constants remain constant when the strength of the magnetic field BQ changes. 

As an essential feature of these theories, crossover behavior is governed by two physical parameters [317] (1) a scaled coupling constant u which reflects the strength and range of the intermolecular forces as represented by 0 and (2) a cutoff wave number A which is assumed to be inversely proportional to a structural length When = 0, one has only one length scale, and one recovers the Ginzburg number with Afa oc (wA)2. 

Bohr magneton Bohr radius Chemical shift, 8 scale Coupling constant (indirect) spin-spin direct (dipolar) reduced spin-spin Delay time... 

Linear scaled coupling constants evaluated using the Fermi contact term only, averaged over the five different basis sets. 

Chemical shift, 8 scale Coupling constant 8 dimensionless... 

The magic angle must be set very accurately on the real sample an error of as little as 0.1° leads to line broadening of 50 Hz, which is comparable to the scaled coupling constants [6]. 

As long as 8 is positive, the scaled coupling constant g is also positive and is a stable well, in the shape of the solid curve in Fig. 8. Since the behavior of the asymptotic expansion depends on the singularity structure within an infinitely small circle in the 8 plane centered at the origin, we must also consider what happens as 8 approaches zero from below. If 8 is negative, then g is also negative and Vejj looks like the dashed curve in Fig. 8. The dashed curve is not stable at the bottom of the well since the particle can tunnel out to oo. Hikami and Brezin... 

In the following 55 problems, the chemical shift value (ppm) is given in the scale below the spectra and the coupling constant (Hz) is written immediately above or below the appropriate multi-plet. Proton NMR data are italicised throughout in order to distinguish them from the parameters of other nuclei ( C, N). 

Contrary to lUPAC conventions, chemical shifts 5 in this book are scaled in ppm in the spectra, thus enabling the reader to differentiate at all times between shift values (ppm) and coupling constants (Hz) ppm (parts per million) is in this case the ratio of two frequencies of different orders of magnitude, Hz / MHz =1 10 without physical dimension... 

The moment of inertia 1 determines the rotational constant 0 = h /IT, which is the parameter that controls the strength of quantum effects. The other parameter of the model, which is the quadrupolar coupling constant K, can be conveniently taken as the energy and temperature scale. We can thus reduce all quantities related to energies by K, and define, e.g., the dimensionless temperature = k T/K, energy = E/K, and rotational... 

Phosphorus has only one stable isotope, J P, and accordingly (p. 17) its atomic weight is known with extreme accuracy, 30.973 762(4). Sixteen radioactive isotopes are known, of which P is by far the most important il is made on the multikilogram scale by the neutron irradiation of S(n,p) or P(n,y) in a nuclear reactor, and is a pure -emitter of half life 14.26 days, 1.7()9MeV, rntan 0.69MeV. It finds extensive use in tracer and mechanistic studies. The stable isotope has a nuclear spin quantum number of and this is much used in nmr spectroscopy. Chemical shifts and coupling constants can both be used diagnostically to determine structural information. 

Eq. (1) has potential application to other types of measurements of substituent effects besides those specifically considered in this paper e.g., nmr coupling constants and shifts for other nuclei, ir and uv spectral shifts and intensities. We caution (with emphasis) in these applications the needed use of data sets of high quality, both with respect to the precision of the measurement and substituents considered (i.e., a full complement of substituent o/ and Or properties must be encompassed for a meaningful correlation to be obtained). There is, of course, no requirement that all data sets will be uniquely fitted by eq. (1) using one of the four or scales of Table V. For example, the data for the ionization of the conjugate acids of pyridine-N-oxides (30), HjO, 25° is found to fit equally well the or(ba.) or Or scales (SD=. 14 /=. 072). The data (31) for the rates of alkaline ("OMe) cleavage of ArSnMea are not fitted to acceptable precision (fs >. 23) by any of the Or parameters. This data set is nevertheless indicated... 

Since the only angle dependence conies from 0 , and the actions /, L are constant. From this point onwards we concentrate on motion under the reduced Hamiltonian which depends, apart from the scaling parameter y, only on the values of scaled coupling parameter p and the scaled detuning term p. In other words, we investigate the monodromy only in a fixed J (or polyad number N = 2J) section of the three-dimensional quanmm number space. 

So far we have dealt with the chemical shift and coupling constant information in the proton spectrum. What we have not considered is the third important parameter, the signal intensity this forms the vertical axis of the spectrum, but is not scaled since we do not use intensity units. 

Intramethyl couplings in ellipses. Upper and lower set of sign combinations fit spectrum equally well. (B) NMR spectra of AcAlaNHMe in 42%/wt CsPFO in D20. Frequency scale with 0 Hz = 0 ppm. (a) Isotropic spectrum at 47°C. (b) Oriented LX-NMR spectrum at 25°C. (c) Simulated spectrum using best-fit coupling constants shown in (A). From Poon et al., (2000)./. Am. Chem. Soc. 122, 5642-5643, 2000, Reprinted with permission from the American Chemical Society. 

Figure 12 Comparison of Vch artefacts intensity illustrated with ID rows taken from a BIRD-HMBC (A), (D) and (G) a G-BIRD-HMBC (B), (E) and (H) and a double tuned G-BIRD-HMBC (C), (F) and (I) experiments showing the Vch artefacts and nJCH responses of C-6 at 135.6 ppm (A), (B) and (C), C-l at 67.2 ppm (D), (E) and (F) and C-10 at 27 ppm (G), (H) and (I) of the 1,3-butadiynyl (tert-butyl) diphenylsilane molecule dissolved in CDCl3. For the BIRD-HMBC and G-BIRD-HMBC experiments, the delays S were adjusted to aV-value of 190 Hz, as an average value for the extreme range of coupling constants for this molecule (125-260 Hz). For the double tuned G-BIRD-HMBC, the /ch nnax and /ch nnin values were set to 240 and 145 Hz, respectively. The corresponding values for the S and S delays were 3.13 and 2.17 ms, adjusted toj values of 160 and 230 Hz, respectively. For both G-BIRD-HMBC experiments, 192 is BIP 720-100-10 pulses have been used for 13C inversion. The same vertical scale is used for all spectra. Residual /ch signals are denoted with arrows.

At the same time, two different coupling constants J13 15 were observed in the spectrum of the SiMe3 derivative of 1,1 -dinitroethane, in which the sterically hindered Z isomer is present at very low concentration. By this reason, the process of 1,5-0,0-migration of the SiMe3 group is unobservable on the NMR time scale (272) (Scheme 3.79). 

Fig. 10.12. Pulse sequence for amplitude modulated 2D J-resolved spectroscopy. The experiment is effectively a spin echo, with the 13C signal amplitude modulated by the heteronuclear coupling constant(s) during the second half of the evolution period when the decoupler is gated off. Fourier transformation of the 2D-data matrix displays 13C chemical shift information along the F2 axis of the processed data and heteronuclear coupling constant information, scaled by J/2, in the F1 dimension.

Fig. 10.13. 2D J-resolved NMR spectrum of santonin (4). The data were acquired using the pulse sequence shown in Fig. 10.12. Chemical shifts are sorted along the F2 axis with heteronuclear coupling constant information displayed orthogonally in F . Coupling constants are scaled as J/2, since they evolve only during the second half of the evolution period, t /2. 13C signals are amplitude modulated during the evolution period as opposed to being phase modulated as in other 13C-detected heteronuclear shift correlation experiments.

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