Ground-state calculations isotopomer structures

The simplest structural procedure is to use ground state (v = 0) effective moments via equations of the form of Eqs. (2), (8) or (10). Such structures are commonly known as r or effective structures since they utilize only Aq. Bq, Cq values. For most polyatomic molecules it is customarily assumed that the interatomic distances are isotopicalfy invariant, even though this is true only for a rigid, non-vibrating or equilibrium molecule. Therefore, data from several isotopic species can be invoked. Thus, for OCS, if Bq is determined for each of the isotopes 16-12-32 and 16-13-32, the two Bq values pamit determination of the C-0 and C-S distances from two equations with the form of Eq. (10). Indeed, various isotopomer combinations are possible, as summarized in Table 2. It is seen that the ro structure parameters vary rather widely (far outside experimental error), depending upon which pair is selected for the calculation. This is a clear example of the deleterious effects of uncorrected zero-point vibration terms (a or s), along with the assumption of isotopic invariance. 

A calculation of the vibration frequencies for the transition and the ground state structures of a reacting system provides for a correct solution of one more important problem of chemical kinetics, namely, a theoretical assessment of the change in reaction rates during isotopic substitution, i.e., the calculation of the kinetic isotopic effect. This effect arises owing to changes in the entropies of activation and in the zero vibration energy of the reactants as a consequence of the difference in masses of individual atoms in isotopomers which affects the values of the force constants and the vibration frequencies [see Eq. (1.8)]. 

Values estimated for the rotational constants Aq of H NNN and HNN N were used in determining the structural parameters a later evaluation of microwave spectra confirmed these constants and the structure deduced therefrom [2]. The structure is consistent with the vibrational data, chemical reactivity [1], and the geometry predicted by earlier ab initio calculations [3, 4]. A planar HN3 is indicated by very small inertial defects of HN3 and the N end-labeled isotopomers [5]. The results of ab initio calculations on the geometries and energies of HN3 in the ground state until 1988 are summarized in [6] and more recently reviewed in [7]. 

The low value of the activation barrier accounts also for the ambiguity in interpretations of experimental results for XI by the methods of electron diffraction, IR spectroscopy, and even X-ray structural analysis. The most accurate experimental data on the structure of cis-enol of malonaldehyde were obtained by studying a microwave spectrum of a series of its isotopomers [64]. Consistently with theoretical predictions, the molecule has symmetry. Experimental geometry parameters [64] are given below together with calcul-ational data [62] on the ground (CJ and the transition (C2v) state. 

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