Asymmetric isotopomers

Because of the reduced number of coupling elements in the symmetric isotopomers, we have assumed that the symmetric isotopomers have less energy redistribution of the energy of the newly formed chemical bond among the other coordinates than do the asymmetric isotopomers ("less statistical") [15]. Thereby, this O3 occupies less "phase space" (as depicted schematically in Figure 2.7) and. 

This assumption of less energy redistribution in the symmetric isotopomers, compared with asymmetric isotopomers, remains to be tested by ah initio quantum mechanical calculations, and as well as by a more direct experiment, as discussed later. Such fundamental quantum mechanical calculations would yield an a priori value of t]. In principle, p can also be inferred from the more direct but more difficult experiment. 

In summary, because of a dynamical consequence of symmetry in this model, the vibrationally excited asymmetric isotopomers, such as QOO, have approximately equal lifetimes that are longer than that of the symmetric isotopomers, such as 000 and OQO, Q being or At low pressures they have thereby an improved chance of being deactivated by a collision and so of forming a stable... 

Experimental studies permit some tests of these ideas. For example, the universality of the effect among all types of ozone isotopomers is seen in oxygen mixtures heavily enriched in and [18] and compared with theory in Figure 2.3 [12,13]. It is also seen in Figure 2.4, the points at AZPE = 0 being about 18% lower than those for the asymmetric cases. The effect of pressure on the MIF from 10 to 10 bar [16,17] has been measured and the theory tested by comparison with the data [12,13]. We note that at higher pressures all of the O3 formed is collisionally deactivated to form O3 and so the anomaly reflected in the differences in lifetimes of the symmetric and asymmetric isotopomers of O3 disappears and so the MIF disappears, experimentally and theoretically. 

The exact mechanism arises in the process of inverse pre-dissociation, as discussed in detail by Herzberg (1966). During an atom-molecule collision, the reactants interact with one another subject to the relevant potential energy surface. The lifetime of this excited intermediate is on the order of molecular vibrational periods, or 10 s. The lifetime is a complex function of the chemical reaction dynamics, which in turn depends on the number of available states. In this specific instance, there is a state dependence for the isotopically substimted species. Ozone of pure has a Cav symmetry and has half the rotational complement of the asymmetric isotopomers. As a result, it was suggested that the extended lifetime for the asymmetric species leads to a greater probability of stabilization. While these assumptions are valid for a gas phase molecular reaction, they do not sufficiently account for the totality of the experimental ozone isotopic observations. Reviews by Weston (1999) and Thiemens (1999) have detailed the physical-chemical reasons. 

Rajamaki T, Miani A, Halonen L (2003) Vibrational energy levels for symmetric and asymmetric isotopomers of ammonia with an exact kinetic energy operator and new potential energy surfaces. J Chem Phys 118 2003... 

Fig. 14.6 Experimental and calculated enrichments or depletions of all possible ozone iso-topomers. The labels 6, 7 and 8 represent lsO, 170, and lsO respectively. Ozone (gray bars) was produced in well scrambled oxygen mixtures at about 90 mbar and room temperature (Mauersberger et al. Adv. Atomic Mol. Opt. Phys. 50, 1 (2005)). The calculated values (vide infra) are those of Gao, Y. Q. and Marcus, R. A., J. Chem. Phys. 116, 137 (2002) setting the parameter r = 1.18 (black bars) or r = 1.0 (white bars). A typical symbol, such as 668, denotes an ozone with the isotopic composition 160160180 and consists of a mixture of symmetric (160180160) and asymmetric (160160180) isotopomers (After Gao, Y. Q. and Marcus, R. A., Science 293, 259 (2001))...

Typke has introduced the rs-fit method [7] where Kraitchman s basic principles are retained. A system of equations is set up for all available isotopomers of a parent (not necessarily singly substituted) and is solved by least-squares methods for the Cartesian coordinates (referred to the PAS of the parent) of all atomic positions that have been substituted on at least one of the isotopomers The positions of unsubstituted atoms need not be known and cannot be determined. The method is presented here with two recent improvements true derivatives are used for the Jacobian matrix X, and the problem of the observations and theircovariances, which is rather elaborate, is fully worked out. The equations are always given for the general asymmetric rotor, noting that simplifications occur in more symmetric situations, e.g. for linear molecules, which could nonetheless be treated within the framework presented. 

As mentioned in the introductory section, N2O is an asymmetrical molecule and therefore it is possible to distinguish so-caUed isotopomers according to the position of N within the N2O molecule (the corresponding 6 notation is given in parenthesis 14N15NO ((5i5]sf ) and Ni NO (Toyoda and Yoshida, 1999). The... 

In Tables 1 and 2, values are given for 17 for a selection of asymmetric and symmetric tops, respectively. In cases where the higher order parameters have been determined, these are given in the Comments column. Where appropriate, this column also indicates the specific top, isomer, state, and/or isotopomer that has been studied. For ethane, three symmetric top isotopomer are listed to illustrate the isotopic dependence of 17 and 17. In aU other cases, only one isotopomer is listed, even if several have been studied. In aU but one of these cases, the isotopomer reported is the one with the highest natural abundance. However, CH OCDO is listed because the results obtained are more precise than for CH OCHO. The molecules are listed alphabetically in Hill order according to the molecular formula. 

MHD2 would, in its turn produce HD. The only way in which HD formation from MHD2 could be avoided would be if the trihydride were in a sense asymmetric, with one M-H bond chemically distinct from the other two and hence unable to reductively-eliminate H2 with either of the other M-H bonds. It is not difficult to envisage such a situation brought about by stereochemical restrictions. However, such a species is without precedent in simple chemical systems. It seems more likely that the observations with the various dihydrogen isotopomers dictate that only a dihydridic state is produced. Point (ii) demonstrates that any metal hydride is not involved in a protolytic equilibrium as shown in Equation (15), or at least that this exchange process is slow. 

Kawasaki, T Soai, K. Asymmetric Induction Arising from Enantiomerically Enriched Carbon-13 Isotopomers and Highly Selective Chiral Discrimination by Asymmetric Autocatalysis. Bull. Chem. Soc. Jpn. 2011,84, 879-892. 

Nevertheless, progress in these directions has been extremely promising based on approximate three particle variational calculations with suitably modified potentials and effective non-Born Oppenheimer kinetic energy terms in the Hamiltonian. Indeed, predictions based on this ah initio procedure now reproduce existing experimental data for Hg to nearly spectroscopic levels of precision, i.e., within a few hundredths of a cm By virtue of the additional non-Born-Oppenheimer terms in the Hamiltonian, a particularly stringent test is provided by the asymmetrically substituted isotopomers, which prior to these studies had not been observed beyond the fundamental manifold. 

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