Symmetric spectra

Indirect covariance processing has been further extended by the work of Martin and co-workers83 84 and by Kupce and Freeman85 to include the reconstruction of non-symmetric spectra from pairs of spectra, F and G, that share a common frequency domain according to Equation (3) ... 

Symmetry relationship of cross peak locations has been used for improving the quality of correlation spectra for quite a long time in NMR spectroscopy both for diagonally [21] and laterally symmetric spectra [22]. Such data processing procedures have their advantage but may introduce artifacts and remove real information and therefore should be used with caution [10]. 2Q-HoMQC spectra can be symmetrized directly using the appropriate symmetry function [33], but most commercial software do not provide such option. Also, fine structure of the direct correlation peaks in 2Q-H0MQC spectra is antisymmetric in the SQ dimension which requires extra attention. 

The zeroth moment Mq is simply the area under the curve, represents the normalization constant, and is related to the oscillator strength of the transition. Because e(v) is effectively a probability distribution, it is clear that the first moment for symmetric spectra gives the average frequency... 

V. The second moment for symmetric spectra is related to the width of the transition by a variance = M2/M0 - v. Microscopic models usually are expected to calculate at least some of these moments for comparison with experiments. In computing the moments numerically, integrations are somewhat arbitrarily limited to some finite region spanning the band. 

Barriers for interconversion between BC-3 and its enantiomer, BC-7, have been calculated. Passage through either a BC-5 or a BC-1 conformation, are calculated to be 5.0 kcal mol and 6.7 kcal mol , respectively. The small barriers allow for a rapid pseudorotation between BC-3 and BC-7, even at low temperatures, and account for the symmetric spectra. NMR results on oxocane-2,2,7,7-d4 have allowed a definitive assignment for the H and C chemical shifts. Lanthanide-induced shift reagents provide compelling proof, that the lowest energy conformations are BC-3 and BC-7. 

M. Hovey, B. Shieley and J. Smith, Symmetric spectra, Preprint, 1996. 

The lower boundary corresponds to strong collisions, and the upper one to weak collisions. This conclusion can be confirmed by experiment. According to [259], nitrogen dissolved in SF6 has a symmetrical spectrum of isotropic scattering, indicating that collapse of the spectrum has already occurred. At the same densities, the Q-branch of the anisotropic spectrum is still well separated from the side branches, and in [259] the lower bound for its half-width is estimated as 5 cm-1. So,... 

A symmetric spectrum with g = 2.003 0.001 and All 3 G has been observed when oxygen or nitrous oxide is adsorbed on Ti02, Sn02, and ZnO. Although this spectrum was assigned to the O- species by Kwan (4-7) and later by van Hooff 48), it is inconsistent with the theoretical spectrum, making the assignment doubtful. 

When benzene adsorbed on silica gel was irradiated with 7 rays, a rather complex symmetric spectrum was observed. The spectrum consisted of a triplet of about 48 G splitting with each component being further split into a quartet of lines. The latter splitting was about 10.6 G. This spectrum is attributed to the cyclohexadienyl radical (I) which is formed by the... 

The reaction of 3,4-benzo-l,2-disilacyclobutene (22) with Cgo yields the corresponding disilacyclohexane derivative (23)20. Irradiation of a solution of disilacyclobutene 22 and Cgo in toluene with a low-pressure mercury lamp (254 nm) afforded the brown adduct 23 in 14% yield (based on unreacted Cgo) (equation 8). The FAB mass spectrum of 23 exhibits one peak at m/z 1024-1027 (C7sH32Si2, M+, molecular cluster ion), as well as one for Cgo at m/z 720-723. The -NMR spectrum of 23 showed a symmetrical spectrum with two diastereotopic isopropyl methyl protons, one isopropyl methine proton and a AA BB pattern assigned to phenyl protons. The 13C-NMR spectrum of 23 shows 17 signals for the Cgo skeleton, of which four correspond to two carbon atoms each and 13 correspond to four carbon atoms each one signal appears at 63.93 ppm and the remainder between 130 and 160 ppm (Scheme 7, Figure 10). This pattern is consistent... 

For a symmetrical spectrum the centre of the resonance line Bc is given by... 

Conditions CDCI3 solution, 300 MHz iH and 75 MHz spectra. The spectrum below was obtained with a modified pulse sequence that gives a symmetrical spectrum. The cross-peaks contain doublets because the spectrum is detecting coupled 13C-13C pairs. 

Ion-beam irradiation (77 K) of DNA hydrated to T = 18 DjO/ nucleotide resulted in a DNA-phosphorus-centered radical. Samples were irradiated with 60 MeV/u, or 100 Mev/u Ar +. The ESR results showed the presence of an axially symmetric spectrum with large phosphorus couplings (Aj = 77.5 mT and = 61.0 mT, = 2.000,= 2.001), from a radical that constituted ca. 0.1% to 0.2% of the total radical concentration. Earlier literature regarding the origin and ESR spectra of such radicals existed and it was concluded that the radical was a phosphoryl radical (ROPOj, Scheme 6), formed from the electron gain path. In DNA, such a radical could result only from P-O bond cleavage at either the C3 or C5 of the deoxyribose sugar... 

Fig. 2.—Multiple quantum spectrum of benzene (15 mol %) in />-ethoxybenzylidene-n-butylaniline (EBBA) at 20 C. The three pulse sequence was PI = n/2, P2 = 7t/2, P3 = k/2. The magnitude spectra obtained for 11 values of t spaced at 0.1 ms intervals from 9.6 to 10.7 ms were added. The value of /i ranged from 0 to 13.824 ms in 13.5 fis increments for each t. A single sample point was taken at 2 = r after Pj, One half of a symmetrical spectrum is shown.

Figure 12.14 shows the CP NMR spectra of the oriented PPTA block sample, whose fiber axis is set parallel (A) and perpendicular (B) to Bq. Although the narrow linewidth of the peak in Fig. 12.14(A) indicates a highly oriented PPTA sample, a symmetric spectrum would be observed for both...

The symmetric spectrum observed by irradiation at room temperature was assumed to be caused by the following reaction ... 

An isolated 12CH3 group in a nematic solution gives rise to a symmetrical spectrum of three lines with relative intensities of 1 2 1 (8, 4). The separation between the lines is given by ... 

The I spectrum [96] of IFg" contrasts with IFg (Fig. 15.23) in having a large chemical isomer shift of +2-45 mm s and an asymmetry parameter of close to unity. The latter results in a symmetrical spectrum because when j 1 the sign of becomes an arbitrary definition as = —Vyy. 

The resolution of rhombic g-factors in powder spectra of apparent axial symmetry spectra at low frequency can be more easily obtained for species having larger -anisotropy as schematically shown in Fig. 4.5 using parameters for the carbon dioxide radical, C02 , with g =2.0032, gy = 2.0014, gz =1.9975 obtained from single crystal measurements. The powder spectrum at X-band shows an apparent axial symmetric spectrum shape. With a typical line-width of ca 0.2-0.4 mT, the gn and gy features are resolved already at Q-band. The anisotropic g-factors can be directly measured at the absorption-(gx) and emission-(gz) like lines and at the centre (gy) of the 1st derivative Q-band spectrum. 

Figure 2. (Left) Normalized absorption and dispersion (left) for a single Lorentzian line (frequency in units of 1/t). (Right) Plot of dispersion versus absorption (OISPA) for the right-hand half of each (symmetrical) spectrum at left, to give the upper half of the DISPA "reference" circle for a single Lorentzian line.

The direct covariance matrix multiplication of a homonuclear NMR spectrum yields a homonuclear covariance map whose square root is equivalent to the NMR spectrum obtained from Fourier transformation. As can be readily seen from Fig. 5.1 A, the higher resolution of the direct dimension is mapped onto the indirect dimension. Hence, a symmetric spectrum... 

A study was conducted which did not employ a frequency symmetric experiment prior to direct covariance processing. Zhang et al. [80] subjected a 2D C—C INADEQUATE data set of 2048 x 1024 data points to covariance NMR. They thus transformed the common double-quantum representation of an INADEQUATE spectrum into a symmetric singlequantum map. The resulting symmetric spectrum was considered easier to interpret. Menthol 2 was used as reference compound. 

Bone that has been heated above about 350 reveals this fact clearly in the replacement of the symmetric spectrum of charred collagen by the spectrum of Figure 7. This spectrum is most easily recognized from its g value, near 2.0043,... 

The sources of the spectra are of interest. As we have mentioned, the symmetric spectrum that is observed in samples that have been heated between 100 and 350 °C can be assigned to charring of the organic material in the bone. It is believed that this material has patches that are mostly carbon networks, embedded in less carbonized material. The patches contain one or more unpaired electrons. As heating progresses, the patches eventually coalesce, with pairing of the electrons, and concomitant reduction of the ESR signal. 

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