The estimation of equilibrium molecular structures from zero-point rotational constants

The approximate equation I_e = 2I₈ - I₀, where I_e, I₈, and I₀ are, respectively, the equilibrium, substitution and zero-point moments of inertia of a molecule, can be derived from a first order treatment of isotope effects, and is valid for linear, symmetric or asymmetric tops. By means of this equation it is possible to estimate the equilibrium structure of a molecule from the zero-point rotational constants of several isotopes. The advantage of this “mass-dependence” (r_m) method over the conventional r_e method is that it is insensitive to the perturbations and resonances that frequently affect excited vibrational states. The main disadvantages are that a large number of isotopic molecules may be necessary and that the above equation is not sufficiently accurate for hydrogen-deuterium isotope effects.A detailed comparison between r_m and r_e of CO shows that the slight difference of about 2 × 10^?4Å between the two bond lengths is due mainly to the difference in the contributions of the electrons. The r_m method has also been applied to the triatomic molecules N₂O, OCS, SO₂ and HCN. For N₂O and SO₂ the results are in excellent agreement with the most recent r_e structures. For OCS there is a significant difference between the r_m structure and the present r_e structure. This difference is as yet unexplained. The poor results for HCN confirm the general expectation that the r_m method cannot be applied to hydrides without further modification.