Isotopically substituted molecules

The system of labelling isotopically substituted molecules is the same as that used in the text. Except for a very few cases the only nuclei labelled are those which are not the most abundant species. 

The ratio of the amount of n-butane-2-13C to the amount of isobutane produced was, provided measurements were made under conditions where secondary reactions were unimportant (i.e., initial reaction products), constant and independent of temperature, and this ratio was 1/4. At the same time, no scrambling of the 13C occurred i.e, all of the isotopically substituted molecules remained singly labeled. Anderson and Baker (68) speculated that the butane isomerization might have occurred by a recombination of adsorbed surface residues produced by fragmentation of the... 

In instances where bond breaking and bond making at the transition state are not equal, bond breaking is either more or less advanced than bond formation, and the symmetric vibration will not be truly symmetric. In these cases, the frequency will have some dependence on the mass of the central atom, there will be a zero-point energy difference for the vibrations of the isotopically substituted molecules at the transition state and will have values smaller than seven. 

The title indicates the scope of the text. The term isotope effects is used rather than applications of isotopes to indicate clearly that it deals with differences in the properties of isotopically substituted molecules, for example differences in the chemical and physical properties of water and the heavy waters (H2O, HDO, D2O, HTO, etc.). Thus H20, HDO and D2O have different thermodynamic properties. Also reactions in solvent mixtures of light and heavy water proceed at different rates than they do in pure H2O. On the other hand, the differences are not large and consequently, to the extent the difference in properties can be ignored, HDO or HTO can be used as tracers for H2O. An important point, however, is that this book does not deal with isotopes as tracers in spite of the widespread importance of tracer studies, particularly in the bio and medical sciences. Also the title specifically does not mention physics which would necessarily have been included if the term Physical Sciences had been used. Thus the text does not deal with differences in the nuclear properties of isotopic atoms. Such differences are in the realm of nuclear physics and will not be discussed. 

The last step in Urey s derivation is the application of the Redlich-Teller product rule (e.g., Angus et al. 1936 Wilson et al. 1955), which relates the vibrational frequencies, moments of inertia, and molecular masses of isotopically substituted molecules. For CIO,... 

Optimized MUBFF models typically reproduce the input frequencies within 10% or better. In order to reap the maximum possible benefit from the known frequencies, the model ratio of frequencies for isotopically substituted molecules can be multiplied by the measured frequency to give a normalized isotopic frequency, i.e.. 

In addition, G and F matrix elements have been tabulated (see Appendix VII in Nakamoto 1997) for many simple molecular structure types (including bent triatomic, pyramidal and planar tetratomic, tetrahedral and square-planar 5-atom, and octahedral 7-atom molecules) in block-diagonalized form. MUBFF G and F matrices for tetrahedral XY4 and octahedral XY molecules are reproduced in Table 1. Tabulated matrices greatly facilitate calculations, and can easily be applied to vibrational modeling of isotopically substituted molecules. Matrix elements change, however, if the symmetry of the substituted molecule is lowered by isotopic substitution, and the tabulated matrices will not work in these circumstances. For instance, C Cl4, and all share full XY4 tetrahedral symmetry (point group Tj), but... 

All nonlinear molecules have 3n — 6 vibrational modes, where n is the number of atoms. Some of these modes arc active in the infrared spectrum, some are active in the Raman spectrum, and others do not give directly observable transitions. Analyses of these spectra usually make use of isotopically substituted molecules to provide additional experimental data, and in recent years, theoretical calculations of vibrational spectra have aided both in making assignments of the observed bands, and in providing initial estimates of force constants.97 Standard methods are available for relating the experimental data to the force constants for the vibrational modes from which they are derived.98... 

Ethene itself, after adsorption on Pt(lll) at very low temperature, has shown a transition from n- to di-cr-bonding at ca. 50 K (403). As shown very successfully by Zaera (397), who used H/D isotopically substituted molecules, the decomposition of the ethyl group occurs by j3-hydride elimination followed by readsorption, as was envisaged years ago by Kemball (398) to account for patterns of H/D exchange in ethene and ethane produced from the C2H4D2 reaction. This is now widely accepted as constituting the first decomposition step of surface alkyl groups on a variety of metal surfaces (199, 397). 

For a non-linear molecule of N atoms, there are 3N — 6 (3N — 5 if the molecule is linear) internal vibrational coordinates. If we wish to include the off-diagonal force constants then there are (3N — 6) diagonal and (3N — 6)2 — (3N — 6) off-diagonal terms. Only half of the off-diagonal force constants are unique, since (for example) kco.cs must equal kcs.co- In other words, the force constant matrix has to be symmetric. This gives 1/2(3JV — 6)(3N - 5) independent force constants, a number that usually far exceeds the available experimental vibration frequencies. A complete determination of all force constants requires analysis of the spectra of many isotopically substituted molecules. Many of the off-diagonal terms turn out to be very small, and spectroscopists have developed systematic simplifications to the force field in order to make as many of the off-diagonal terms as possible, vanish. 

Normal vibration calculations, if based on a correct structure and correct potential field, would supposedly permit a unique correlation to be made between predicted and observed absorption bands. In most cases this ideal situation is far from being achieved in the study of high polymer spectra. More usually the structure and force field are to some extent unknown, or normal mode calculations are not available, so that other methods must be used in order to establish the origin of bands in the spectrum. Even if complete calculations were available it would be desirable to check their predictions by means other than a comparison of observed and predicted frequency values. One method of doing so is by studying isotopically substituted molecules, and the most useful case is that in which deuterium is substituted for hydrogen. 

The reaction mechanism was established in the experiments with isotope-substituted molecules (H2sO and >Si<1802 (>Si + 1802=> >Si<1802)). The formation of the following products was detected by IR spectroscopy (Figure 7.26a) ... 

Since the dissociation of the abundant H2 and CO molecules result from photoabsorption at discrete wavelengths, isotopically selective photodissociation based on self-shielding is possible. Two conditions are required for this (1) dissociation via line absorption for each isotopically substituted molecule, and (2) differential photolysis that depends upon the isotopic abundances. Self-shielding occurs when the spectral lines leading to dissociation of the major isotopic species optically saturate, while the other residual lines relevant for dissociation of the minor isotopes remain transparent. As a consequence, such photolysis depends on nucleic abundance rather than the mass of a molecule see Fig. 4.4 (Langer 1977 Thiemens Heidenreich 1983). 

The observed overabundance of deuterated species in molecular clouds and outer disks compared to the measured interstellar D/H ratio of 10 5 is well established. A classical isotopic deuterium fractionation is possible at low temperatures of 10-20 K owing to disbalance between forward and reversed reaction efficiencies H+ + HD 5 H2D+ + H2 + 232K (e.g. Millar et al. 1989 Gerlich et al. 2002). The temperature dependency in an isotope exchange reaction is a consequence of the zero-point vibrational energy difference for the isotopically substituted molecules (Bigeleisen Mayer 1947 Urey 1947). This leads to an elevated ratio ol H2t)+/H compared to HD/H2, which is quickly transferred into other molecules by ion-molecule reactions (see e.g. Roberts Millar 2000 Roberts et al. 2003). For example, the dominant reaction pathway to produce DCO+ is via ion-molecule reactions of CO with H2D+. In disks it results in a DCO+ to HCO+ ratio that increases with radius owing to the outward decrease of temperature (Aikawa Herbst 2001 Willacy 2007 Qi et al. 2008). 

The synthesis of isotopically substituted molecules imposes even greater restrictions on syntheses. For example, consider the synthesis of diben-zotetrathiafulvalene (DBTTF), where the two central carbons are to be labeled with 13C ( ). Two possible routes are shown in Scheme 1. In ad-... 

Chromatographic Considerations. The experimental problem is now reduced to the far from trivial one of determining the ratio of the retention volumes of the two isotopically substituted molecules. Consider a typical chromatogram for two difficultly resolvable isomers such as is sketched in Figure 1. Here to is the time from injection that a completely inert nonadsorbed material is eluted t2 and ti are the corrected retention times P2/P1 = ti/t2) (21) t is the average residence time in the column and tv is the peak width. 

FIGURE 20.6 Moments of inertia for selected classes of molecular structures. In each case, m represents the sum of all the atomic masses in the molecule, (a) Diatomic molecules have a single moment of inertia, uniquely related to the bond length, (b) Linear triatomic molecules also have a single moment of inertia that can be determined from rotational spectra. Because / depends on two bond lengths, additional information is required to determine both. This is accomplished by comparing rotational spectra of isotopically substituted molecules. 

The observed and calculated frequencies of (Gly) I are compared in Table IX. For a detailed discussion of the assignments, and the calculations of isotopically substituted molecules, the original publications should be consulted. We consider here only some salient features of the results. 

Woolley, 1977, p. 397 1986, p. 204 1991), and, thus, his stance is often very much like the one I have adopted. However, he often collapses the correct claim that classical molecular structure is of only limited validity, with the incorrect claim that classical molecular structure cannot be used to interpret and explain the properties of different isomers and isotopically substituted molecules (see Woolley, 1991). 

The observed vibration frequencies of a molecule depend on two features of the molecular structure the masses and equilibrium geometry of the molecule and the potential eneigy surface, or force field, governing displacements from equilibrium. These are described as kinetic and potential effects, respectively for a polyatomic molecule the form and the frequency of each of the 3N—6 normal vibrations depend on the two effects in a complicated way. The object of a force field calculation is to separate these effects. More specifically, if the kinetic parameters are known and the vibration frequencies are observed spectroscopically, the object is to deduce the potential eneigy surface. A major difficulty in this calculation is that the observed frequencies are often insufficient to determine uniquely the form of the potential energy surface, and it is necessary to use data on the frequency shifts observed in isotopically substituted molecules or data on vibration/rotation interaction constants observed in high resolution spectra in order to obtain a unique solution. 

Isotopes (particularly deuterium) are often used as labels to show where a reaction has occurred in a particular molecule. A specialized use of kinetics applied to isotopically substituted molecules provides information about the mechanism that is often not available from other... 

Spectroscopic studies of isotopically substituted molecules do not always involve special synthetic chemistry. For many elements, natural isotopic abundances ensure that ordinary compounds contain several species. For example, in... 

A useful additional constraint for adjusting the frequencies is derived from rates obtained for several isotopically substituted molecules or ions (Dutuit et al., 1991 Baer and Kury, 1982 Kuhlewind et al., 1987). With this approach it is possible to determine directly from the experimental rates the values of certain classes of transition state frequencies. In the fitting of the k E) data for various isotopically substituted benzene ions, it was determined that the transition state C—H frequencies are increased, while the C—C vibrations are lowered relative to the molecular ion frequencies (Kuhlewind et al., 1987). 

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