Isochronous groups

The Sm-Nd data were used to create an isochron, which was used to derive and age (Fig. 1). The calculated age, 369 19 Ma, is in excellent agreement with the known age of the complex, 368 4 Ma (Parrish et al. 1987). This age is also consistent with our preliminary LA-ICP-MS zircon U-Pb dating of dykes in the SM and the NS-N groups. 

Alkoxyl and acetoxyl protons in A-acetoxy-A-alkoxybenzamides give rise to sharp signals well below room temperature. In contrast, hydroxamic esters usually exhibit line broadened alkoxyl group resonances in their H NMR spectra at or even signihcantly above room temperature" . In toluene-rfg, the benzylic and acetoxyl methyl resonances of A-acetoxy-A-benzyloxybenzamide (100) showed signihcant line broadening below 250 K but remained isochronous down to 190 K. 

The Pb-Pb isochron was made famous by the determination of the age of the Earth Patterson (1956) grouped meteorite samples with a sediment sample that is supposed to represent the bulk silicate Earth in terms of Pb isotopes (Figure 5-8). The assumption is that the Earth formed at roughly the same time as the meteorites. The colinearity of the data in Figure 5-8 is viewed as verification of the assumption. The age given by Patterson (1956) is 4.55 Ga. 

Often, however, the sample does not lend itself to measurements of multiple phases. In these cases, one can create a model isochron in which the initial isotopic ratio of the daughter element (D(/Dref) is assumed and is used to anchor the -intercept. With this assumption, a single measurement can provide the initial ratio [(NR/Ns)o of an object. A third type of isochron diagram makes the assumption that a group of bodies all formed from the same homogeneous isotopic reservoir at the same time. This whole-rock isochron is constructed from bulk measurements of each sample, and the resulting slope and initial ratio describe the reservoir from which all of the samples formed. 

Nuclear magnetic resonance chemical shift differences can serve as an indicator of molecular symmetry. If two groups have the same chemical shift, they are isochronous. Isochrony is a property of homotopic groups and of enantiotopic groups under achiral conditions. Diastereotopic or constitutionally heterotopic groups will have different chemical shifts (be anisochronous), except by accidental equivalence and/or lack of sufficient resolution. 

For homotopic groups, chemical shifts are indistinguishable in chiral or achiral solvents, that is, the groups are isochronous. 

Enantiotopic groups are isochronous in achiral solvents and distinguishable (anisochronous) in chiral solvents. 

Figures 2.37 and 2.38, show the isochronal curves of the permittivity and loss factor for P2NBM and P3M2NBM as a function of temperature at fixed frequencies. A prominent relaxation associated with the dynamic glass transition is observed in both polymers. Clearly the effect of the methyl substitution in position 3 of the norbornyl group is to decrease the temperature of this relaxational process.

There are two types of molecular symmetry that cause chemical-shift equivalence. Nuclei or groups of nuclei that are interchangeable by a symmetry operation involving a simple n-fold axis of symmetry (Cn) have been termed equivalent, and are isochronous in chiral and... 

Condensation of resorcarenes with primary amines and formaldehyde leads to tetrabenzoxazines 109, usually in excellent yield. First examples were described by Matsushita and Matsui45 without any discussion of the stereochemical aspects. In principle, four regioisomers can be formed in this reaction (see Figure 20) from which the C,- and the Cs-symmetrical isomers can be easily excluded on the basis of the H NMR spectra. The distinction between the C2V- and the C4-symmetrical derivatives relies only upon the difference of the CHR1 groups in the C2V isomer which could be isochronous by chance. 

Conforma- tion Sym- metry group Dihedral angles ) in Sets of isochronous carbons Calculated relative strain energies in kcal/mole H2) BL3) W ) A8)... 

In Section 4-2, the terms isochrony, equivalence, and topicity were introduced to describe nuclei that are of interest in NMR spectroscopy. Isochronous nuclei, or groups, were seen to be chemically (symmetry) equivalent. Magnetic equivalence was, however, found to be a more strict requirement than chemical equivalence, as it is determined by the coupling con-stant(s) of each nucleus in a group of chemically equivalent nuclei. Finally, topicity was seen to be dependent on the nature of symmetry operations that interchange chemically equivalent nuclei or groups. 

Enantiotopic nuclei or groups are capable of fulfilling all or, at least, most of the foregoing symmetry-related expectations. Their chemical shifts depend, in addition, on both the medium in which the NMR experiment is conducted and the spectral resolution of the spectrometer. The latter is influenced by, for example, the magnetic-field strength. Enantiotopic groups are isochronous in achiral or racemic media and constitute A2,X2, etc., systems. Moreover, they are potentially anisochronous in chiral media. 

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