Isotopic shift model

In a natSi sample doped with 34S, a negative sulphur IS of — 76 jeV (—0.61cm 1) with respect to 32S is observed for the Is (T2) line of S°, and this IS becomes —87peV (—0.70 cm-1) for the 2p (S2°) line in a sample doped with natS [233], in agreement with the isotopic shift model of [132]. Inversely,... 

Figure 5.3. Model describing expected carbon isotopic shifts in direction of matrix values for browsers and grazers. Large arrows represent large shifts, small arrows the converse.

Isotopic shifts for molecular transitions are of order of 1% and thus easy to observe. Suitable molecules with transitions accessible to CRIRES are CO, CN and SiO. The Si isotopes appear particularly interesting as they can provide for a neutron dosimeter during the AGB-phase. Models for the thermonuclear... 

A number of other models were considered and tested (for example, direct B—H bonding). The most significant test was the IR vibrational spectrum, where a sharp absorption band at 1875 cm-1 was found, corresponding to the Si—H stretch mode softened by the proximity of the B-atom. Had the hydrogen been bonded to boron, a sharp absorption band at 2560 cm-1 would have been expected. Also, Johnson (1985) showed that deuteration produced the expected isotopic shift. The most definitive and elegant proof of the correctness of the Si-H-B bonding model was provided by Watkins and coworkers (1990), on the basis of a parametric vibrational interaction between the isotopes D and 10B. 

The low frequency Raman spectrum of the 6-coordinate models is distinctly different from the low frequency spectrum of the 5-coordinate sites of the Ni gjobins. In fact only one line, a very weak shoulder on the 300-cm line, is obserYed in the expected metal-ligand stretching region below 300 cm. Further no predominately Ni stretches are found in the 100-500-cm region. Instead, in both the 6- and 5-coordinate c mp xes many of the low frequency Raman lines show small (< 1 cm ) Ni isotopic shifts indicating some pyppole... 

The C—C bond was found to be slightly more perturbed than in the monolithium species (i.e., LiC2H4) and the Li—C interactions somewhat more rigid. The normal coordinate analysis showed that such a model is capable of satisfactorily reproducing the measured isotopic shifts on the observed 12 fundamentals. However, the very important Li—Li vibration, which could prove the proposed geometry, was not detected in the expected far-infrared spectral region ... 

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. 

A. Previous models of water (see 1-6 in Section V.A.l) and also the hat-curved model itself cannot describe properly the R-band arising in water and therefore cannot explain a small isotope shift of the center frequency vR. Indeed, in these models the R-band arises due to free rotors. Since the moment of inertia I of D20 molecule is about twice that of H20, the estimated center of the R-band for D20 would be placed at y/2 lower frequency than for H20. This result would contradict the recorded experimental data, since vR(D20) vR(H20) 200 cm-1. The first attempt to overcome this difficulty was made in GT, p. 549, where the cosine-squared (CS) potential model was formally (i.e., irrespective of a physical origin of such potential) applied for description of dielectric response of rotators moving above the CS well (in this work the librators were assumed to move in the rectangular well). The nonuniform CS potential yields a rather narrow absorption band this property agrees with the experimental data [17, 42, 54]. The absorption-peak position Vcs depends on the field parameter p of the model given by... 

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. 

We shall show now that (i) The R-band arises due to rotational motion of a polar H-bonded molecule determined by the elastic force constant k. (ii) The dimensionless absorption Astr(v) (463) agrees qualitatively with the g(vstr) frequency dependence found in Section IX.B. (iii) The used SD model describes a small isotopic shift of the R-band also in terms of the ACF method. 

The average Mo=0 bond distance of the (MPT)Mo(0)2(S-eys) cofactor of sulfite oxidase is 1.68 A by EXAFS (Figure 14). The RR results are consistent with bis(oxido) coordination of MoVI and the two expected Mo=0 stretching modes are found at 903 and 881 cm-1 [119,139], Upon reduction and reoxidation in the presence of H2180 the Mo=0 bands shift to 890 and 848 cm-1, respectively [119,139], The difference in the 180 isotopic shifts for the symmetric and asymmetric bands is consistent with labeling of only one of the oxido ligands. This observation has precedent in the labeling of bis(oxido) model complexes and is supported by normal coordinate analysis [140],... 

Prior to about 1955 much of the nuclear information was obtained from application of atomic physics. The nuclear spin, nuclear magnetic and electric moments and changes in mean-squared charge radii are derived from measurement of the atomic hyperfine structure (hfs) and Isotope Shift (IS) and are obtained in a nuclear model independent way. With the development of the tunable dye laser and its use with the online isotope separator this field has been rejuvenated. The scheme of collinear laser/fast-beam spectroscopy [KAU76] promised to be useful for a wide variety of elements, thus UNISOR began in 1980 to develop this type of facility. The present paper describes some of the first results from the UNISOR laser facility. 

Based on the experimental frequencies and isotope shifts, a Quantum-Chemistry Assisted Normal Coordinate Analysis (QCA-NCA) has been performed. Details of the QCA-NCA procedure of I, including the f-matrix and the definition of the symmetry coordinates, have been described previously (12a). The NCA is based on model I (vide supra). Assignments of the experimentally observed vibrations and frequencies obtained with the QCA-NCA procedure are presented in Table II. The symbolic F-matrix for model I is shown in Scheme 3. Table III collects the force constants of the central N-N-M-N-N unit of I resulting from QCA-NCA. As evident from Table II, good agreement between measured and calculated frequencies is achieved, demonstrating the success of this method. 

The ground-state vibrational normal modes of uracil have also been extensively studied, both experimentally and computationally. The IR and Raman spectra in Ar matrix have been measured for the 5-d, 6-d, 5,6-d2, 1,3-d2, l,3,5-<73, 1,3,6-d3, and d4 isotopomers [120-122], Vibrational spectra in the crystalline phase have been reported for the 5,6-d2, 1,3-d2, and d4 isotopomers of uracil [123] and of the 2-1S0, 4-lsO, 3-d, 5-d, 6-d, 5,6-d2 and l-methyl-<73 isotopomers of 1-methyluracil [124], UV Resonance Raman spectra have been reported for natural abundance, 2-lsO, 4-lsO, and 2,4-1802 uracil in neutral aqueous solution [125]. These data have been modeled successfully by both ab initio [94, 117, 126-132] and semi-empirical [133, 134] calculations. However, most of these caculations ignore electron correlation effects on the vibrational properties of uracil, particularly the Raman and resonance Raman spectra. However, the most robust reconciliation of experiment and computation is a recent attempt to computationally reproduce the experimentally observed isotopic shifts in 4 different uracil isotopomers [116], The success of that attempt is an indication of the reliability of the resulting force field and normal modes for uracil. The resonance Raman vibrations of uracil, and their vibrational assignments, are given in Table 9-2. 

Fig. 26. Heavy bars give approximate 6 " 0 of the oceans, based on the assumptions that the isotopic shift between cherts and sea water has remained constant at 34%o, and that the highest value for 6 0 from a suite of rocks is most likely to be primary. Solid lines are three calculated models, all with present ocean mass 3.89 10 moles O2, and S = 0 (Chase and Perry, 1972).

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