Specific isotope shift

Any observable effect of isotopic substitution on the rate or extent of a chemical/physical process. Equilibrium isotopic perturbation measurements can provide valuable information about kinetic isotope effects on enzymic catalysis. NMR shift difference measurements are also useful in detecting the effects of isotopic substitution on a fast (degenerate) equilibrium between two species differing only in their specific isotopic substitution . The... 

The main contribution to the hydrogen-deuterium isotope shift is a pure mass effect and is determined by the term E in (3.6). Other contributions coincide with the respective contributions to the Lamb shifts in Tables 3.2, 3.3, 3.7, 3.9, 4.1, 5.1, and 6.1. Deuteron specific corrections discussed in Subsubsect. 6 and collected in (6.16), (6.28), (6.29), and (6.37) also should be included in the theoretical expression for the isotope shift. 

The ultraviolet absorption spectrum of formaldehyde consists of many sharp discrete bands of Doppler width. The isotopic shifts due to C and O atoms are sometimes 5 to 10 cm-1 in the 3000 to 3100 A region [see Moore (715)]. Hence, it is possible to selectively excite a specific carbon or oxygen isotopic species in mixtures of other isotopic species. 

In order to reconstruct human diet from bone tissue, direct isotopic analysis of animal and plant remains from the same archaeological context is the most reliable way to detect isotopic shifts involving the whole ecosystem due to environmental variation. Since this is often impossible for the lack of these control samples, we have explored the use of 8I80 to assess the environmentally induced variation in 8I3C and 8ISN values from collagen and apatite, and assess the dietary information they represent. This can be done assuming a scarce nutritional role of marine resources and the absence of C4 crops, as seems to be the case in the western Mediterranean and specifically in the Sardinian Neolithic and Bronze Age. 

Here we try to study specific interactions in water in terms of slightly modified hat-curved model with a simplified account of collective (cooperative) effects in water in relation to SWR spectra. Below, in items A-D, we shall shortly describe how the problem of these effects was gradually recognized in our publications [6-9, 11]. At first, we shall draw attention on a small isotope shift of the R-band—that is, on practical coincidence of the peak absorption frequencies vR 200 cm 1 for both ordinary (H20) and heavy (D20) water. 

In Section V the reorientation mechanism (A) was investigated in terms of the only (hat curved) potential well. Correspondingly, the only stochastic process characterized by the Debye relaxation time rD was discussed there. This restriction has led to a poor description of the submillimeter (10-100 cm-1) spectrum of water, since it is the second stochastic process which determines the frequency dependence (v) in this frequency range. The specific vibration mechanism (B) is applied for investigation of the submillimetre and the far-infrared spectrum in water. Here we shall demonstrate that if the harmonic oscillator model is applied, the small isotope shift of the R-band could be interpreted as a result of a small difference of the masses of the water isotopes. 

The change in mean-squared-charge radius is obtained from the isotope shift using standard techniques [HEI74]. For thallium the normal mass shift is approximately 8 MHz between masses and the specific mass shift is smaller than the experimental error. The resulting field shift is proportional, to good approximation, to an electronic factor times 6. For the case of T1 the electronic factor is not directly calculable but should be virtually the same for all isotopes. 

In general, the Hamilton operator H applicable to an experimentally observed resonance is the sum (3.1.1) of operators Hx of different interactions. The lineshape, therefore, is the result of all spin interactions. For observation of just one dominant interaction, special techniques need to be applied such as isotope enrichment, homonuclear multipulse and heteronuclear high-power decoupling. Nevertheless, in C NMR, for instance, despite high-power H decoupling an overlap of chemical shielding powder spectra centred at different chemical shifts is observed in most cases without site-specific isotope enrichment. 

The configurational analysis of compounds 2 to 5 involves determining whether the labeled oxygen (170 in 2 and 4,180 in 3 and 5) occupies the pro-/ or pro-S position. In most cases, the compound is first stereoselectively deriva-tized at one of the two oxygens. The position of 170 or 180 is then determined by one of three methods (i) stereoselective derivatization and degradation followed by mass spectral analysis (ii) isotope shift, effect in 31P NMR or (iii) 170 quadrupolar effect in 31P NMR. Since these methods are straightforward, no further discussion is provided here. Specific examples will be presented in Section IV, E. 

Let us assume that the anharmonicity constant A is large compared to the width T) = 2T (where T is the half-width) of the phonon band. In this case, as was shown in Subsection 6.2.2, the width of the biphonon band is of the order of T /A, i.e. small compared to the width T of the band of optical phonons. Important here is, however, the comparison of the width of the biexciton band with isotope shift. Indeed, in the limiting case of strong anharmonicity, the biphonon energy is E ss 2hui — 2A and the biphonon state 2) is just the coherent superposition of the states of two-fold excited molecules. It is clear then that an elementary generalization of an equation of the type (6.89) can be used to find biphonon local states. Specifically, the equation for the frequency of a local biphonon io, i.e. the localized state split off the biphonon zone, can be written as follows ... 

With respect to the different shifts of S13C-values in the recovery procedure it has to be noted, that a satisfactory determination of carbon isotope ratios depends not only on the analytical methods applied but also on the individual substances analysed. Therefore, in order to evaluate the quality of compound specific isotope analyses of riverine contaminants measurements of field samples have to be accompanied by recovery experiments of individual substances. 

Isotopic shifts or higher variations of the isotope ratios as a result of the analytical procedures applied were observed only for selected contaminants. Therefore, for accurate compound specific carbon isotope analyses of riverine contaminants it is recommended to conduct supplementary recovery experiments of the individual substances. 

Isotope shifts in a spectral line arises not only through differences in the charge distribution, but also from differences in nuclear mass, M. The normal mass shift is simply obtained by replacing the electron mass rr e by the reduced mass fi — me/(l - - m lM), whereas the so-called specific mass shift (SMS) arising from a correlation of orbital momenta through the motion of the... 

So far, we have discussed the nucleus in terms of a specific isotope in our case, P. NMR spectroscopy is only useful to us because there is a difference between phosphoms atoms in different local enviromnents. Each phosphorus atom in its own local enviromnent is assigned its own chemical shift value, measured in ppm. We know from C- and H-NMR that the origin of the chemical shift lies in the influence (shielding and deshielding) that the neighbouring atoms assert on the phosphoms atom. Mathematically, we can describe this phenomenon by the following equation ... 

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