Molecules isotopic substitution

For a non-linear triatomic molecule three parameters are needed to specify (the assumed) fixed geometry, but only two moments of inertia can be measured. The situation becomes rapidly worse for larger molecules. Isotopic substitution may be used to produce more data, but the situation where sufficient data are available for a unique solution is rare. In the final analysis measured spectra may well be consistent with an assumed molecular conformation, without excluding many other classical or non-classical possibilities. 

As stated in Sec. 1.14, the vibrational frequencies of isotopic molecules are very useful in refining a set of force constants in vibrational analysis. For large molecules, isotopic substitution is indispensable in making band assignments, since only vibrations involving the motion of the isotopic atom will be shifted by isotopic substitution. 

If one wishes to determine the vibrational force constants for a polyatomic molecule, isotopic substitutions are essential. Die general valence force field for a non-linear polyatomic molecule, expressed in internal coordinates, contains a total, of (3N-6)(5N-5) force constants. Some of these may equal others by the symmetry of the molecule, but a maximum of only (3N-6) vibration frequencies may be observed. 

Isotopic designators in chemical formulas These generally follow common usage, which is to place a superscript number before the atom to indicate the mass of the isotope that replaces the natural isotope at that position, regardless whether it replaces the natural isotope in all molecules (isotopic substitution) or only some molecules (isotope labeling). 

The use of isotopic substitution to detennine stmctures relies on the assumption that different isotopomers have the same stmcture. This is not nearly as reliable for Van der Waals complexes as for chemically bound molecules. In particular, substituting D for H in a hydride complex can often change the amplitudes of bending vibrations substantially under such circumstances, the idea that the complex has a single stmcture is no longer appropriate and it is necessary to think instead of motion on the complete potential energy surface a well defined equilibrium stmcture may still exist, but knowledge of it does not constitute an adequate description of the complex. 

Recently, this observation has been confirmed experimentally through neutron scattering studies, making use of isotopic substitution . These studies have revealed that the water molecules in the... 

However, even for a small molecule such as HgCO, determination of the rotational constants in the v = 1 levels of all the vibrations presents considerable difficulties. In larger molecules it may be possible to determine only Aq, Bq and Cq. In such cases the simplest way to determine the structure is to ignore the differences from A, and Cg and make sufficient isotopic substitutions to give a complete, but approximate, structure, called the Tq structure. 

An improvement on the rg structure is the substitution structure, or structure. This is obtained using the so-called Kraitchman equations, which give the coordinates of an atom, which has been isotopically substituted, in relation to the principal inertial axes of the molecule before substitution. The substitution structure is also approximate but is nearer to the equilibrium structure than is the zero-point structure. 

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. 

Consider a reactant molecule in which one atom is replaced by its isotope, for example, protium (H) by deuterium (D) or tritium (T), C by C, etc. The only change that has been made is in the mass of the nucleus, so that to a very good approximation the electronic structures of the two molecules are the same. This means that reaction will take place on the same potential energy surface for both molecules. Nevertheless, isotopic substitution can result in a rate change as a consequence of quantum effects. A rate change resulting from an isotopic substitution is called a kinetic isotope effect. Such effects can provide valuable insights into reaction mechanism. 

The molecules most profitably studied in connection with purely steric isotope effects have been isotopically substituted biphenyl derivatives. Mislow et al. (1964) reported the first more or less clearcut example of this kind in the isotope effect in the configurational inversion of optically active 9,10-dihydro-4,5-dimethylphenanthrene (7), for which an isotopic rate ratio ( d/ h) of 1-17 at 295-2°K in benzene solution was determined. The detailed conformation of the transition state is not certain in this case, as it involves the mutual passage of two methyl groups, and thus it is difficult to compare the experimental results with... 

The simple harmonic oscillator picture of a vibrating molecule has important implications. First, knowing the frequency, one can immediately calculate the force constant of the bond. Note from Eq. (11) that k, as coefficient of r, corresponds to the curvature of the interatomic potential and not primarily to its depth, the bond energy. However, as the depth and the curvature of a potential usually change hand in hand, the infrared frequency is often taken as an indicator of the strength of the bond. Second, isotopic substitution can be useful in the assignment of frequencies to bonds in adsorbed species, because frequency shifts due to isotopic substitution (of for example D for H in adsorbed ethylene, or OD for OH in methanol) can be predicted directly. 

In this study where we are interested in isotope substituted systems, that is in systems with the same electronic wave function, a more global approach can be used. From Table 2 it is obvious that MP3 calculations give the best overall results. The compensation of errors that we find here is a general characteristic of this level of wave function, as illustrated by previous calculations on various series of molecules [16]. Thus, we will use the MP3 level of theory together with the formula... 

Ideally, those molecules that are involved in the catalytic reaction should be the best characterizers of catalytic sites. Indeed, the path of the development of organic reaction mechanisms is paved with clever examples of stereochemistry and isotopic substitution that reveal the nature of activated complexes and intermediates and allow the unambiguous interpretation of the stereorelations... 

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... 

Figure 16.1 The general design of an ICAT reagent consists of a biotinylation compound with a spacer arm containing stable isotope substitutions. The reactive group is used to label proteins or peptides at particular functional groups and the biotin affinity tag is used to isolate labeled molecules using immobilized (strept)avidin.

Rotational spectra provide measurement of the moments of inertia of a chemical species. Bond angles and bond lengths can be derived by making isotopic substitutions and measuring the resulting changes in the moments of inertia. A major drawback of rotational spectroscopies is the limited information contained in a measurement of the moment of inertia. Consequently, while quite precise, it is generally limited to smaller molecules. It is the chief technique used to identify molecules in outer space, such as the components of interstellar gas clouds. 

Garret, B. C. and Truhlar, D. G. Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules and isotopically substituted hydrogen molecules, JPhys.Chem., 83 (1979), 1079-1112... 

When molecules are heavy, isotope substitution will not alter the masses to any considerable extent and (pi/p)l/2 will tend to unity. 

---