Isotopic frequency shifts

A recently developed field of research is matrix isolation laser Raman spectroscopy 214a)-d) which allows the study of vibrational Raman spectra with high resolution. Even small isotopic frequency shifts or the influence of crystal structure on the vibrational frequencies may be determined with high precision. This provides an effective constraint on intermolecular forcefields. 

Johansen 269> calculated the isotopic frequency shifts occurring in the molecular crystals of carbon monoxide CO, using the infra-red spectrum of Ewing and Pimentel 270) the ciystal is considered to be an ensemble of harmonic oscillators and the FG-method is used. 

You will note some structure in the Stokes band near 460 which is due to chlorine isotopic frequency shifts. (See Exp. 37 for a discussion of isotope effects in diatomic molecules.) Rescan this region at higher resolution (1 cm or less) with an expansion of the chart display and measure the frequencies of each of the components. Record the ambient temperature near the Raman cell. 

In the G(w)-approximation, introduced by Bigeleisen and Mayer (8) and later extended to higher orders by Bigeleisen (4), the reduced partition function ratio (Equation 1) is expanded in terms of the isotope frequency shifts, Au, = — Ui. The first three terms are... 

The weighting function w u) depends on the distribution of frequencies in a system and on the isotope frequency shifts. Indeed, the ... 

In addition to isotope frequency shifts, mean amplitudes of vibration, Coriolis coupling constants, centrifugal distortion constants, and so forth may be used to refine the force constants of small molecules (see Ref 81). 

SbOs ions in Sb-doped FAp is supported by results from F and P MAS NMR studies (Moran et al. 1992). Ito et al. (1988) showed, on the basis of isotopic frequency shifts (IR), the presence of BOs as replacement for P04 in B- and °B-doped apatites. Schriewer and Jeitschko (1993) emphasized that the apex oxygen atoms of the pyramidal ReOs groups in Baio(Re05)6Cl2 all point approximately down the c-axis, resulting in the loss of the horizontal mirror plane (see also Besse et al. 1979). 

The vm-l band had originally been looked for with Fe " porphyrin complexes. Nakamoto and coworkers first observed the Fe isotopic frequency shift for various... 

CbCb Stretching modes belong to different symmetry species with Cu(OEP) whereas to identical species (Ai) with Cu(OEC) and accordingly their mutual interaction takes place. The Raman bands of Cu(OEC) at 1372(p), and 1362(p) cm" exhibit a isotopic frequency shift and therefore are assigned to the V4- and Vi2-like modes of M(OEP), respectively. 

In addition to providing a (not always unambiguous ) identification of the spedes present, the frequency shift of a normal mode upon deuterium substitution can often be used to quickly identify the particular type of atomic displacements constituting the normal mode. An excellent example is a study of NH P-alumina by Bates et alP in which two bands at 168 and 145 cm" were observed in the Raman spectrum. In a similar measurement of a P-alumina crystal containing ND4 ions, the bandcentre of the 168 cm" mode was shifted to 152 cm". If this band were due to a translational mode, the calculated isotopic frequency shift ratio would be... 

As far as mean amplitudes are concerned, interplay between spectroscopy and electron diffraction may come about in two ways. Firstly, even for comparatively simple polyatomic molecules e.g. the methyl halides ) the general harmonic force field is not well determined from all the spectroscopic data available, i.e. vibration frequencies, isotopic frequency shifts, Coriolis zfita constants, and centrifugal distortion constants. In principle, experimental mean amplitudes from electron diffraction studies should provide valuable additional data. In practice, however, the experimental amplitudes have as yet rarely been of sufficient precision to be helpful. Secondly, for more complex molecules, mean amplitudes calculated from spectroscopic data (by way of what are inevitably very approximate force fields in many cases) are sometimes used as fixed parameters in the electron diffraction analysis in order to reduce the total number of parameters refined. 

Rotation-vibration constants and centrifugal distortion constants have been calculated from various sets of force constants [6,10 to 18]. The constant Dk, which apparently has not been measured so far, is predicted to be 10.30 kHz [15] and 10.098 kHz [16] from accurate force fields capable of reproducing observed frequencies of NF3, centrifugal distortion constants (Dj and Djk from [2] Dj from [3] appears to be in error, cf. footnote of Table 2, p. 190), Coriolis coupling constants [15, 16], and isotopic frequency shifts [15]. 

The general valence force field of pyramidal XY3-type molecules contains six independent constants. In internal coordinates, these are the stretching and bending force constants f and f , and four interaction constants f r for two adjacent bends, fr and fr . for a stretch and an adjacent and a nonadjacent bend, and fo two bends. Besides the four fundamental frequencies, additional spectroscopic data such as isotopic frequency shifts, centrifugal distortion constants, and Coriolis coupling constants are required to fix a unique set of force constants. Various authors have performed such calculations, and the sets so obtained [13, 14, 25, 26, 35 to 38, 45] agree reasonably well. As a representative example, the symmetry and valence force constants, all in mdyn/A, of Sawodny et al. [25] are presented below. 

There is a slight discrepancy between the values of Allan et al. [13] and Otake et al. [14] for the symmetry force constants of species F, F12, and F22, which these authors have fixed using isotopic frequency shifts. The values of [14] come close to those of [25, 35, 38],... 

For the symmetry force constants of species e, F33, F34, and F44, two solutions exist which exactly reproduce the two observed e-mode frequencies, isotopic frequency shifts, centrifugal distortion constants, and Coriolis coupling constants. They differ in the associated normal... 

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