Knowledge Bank

It is shown that Costain's equation $Is=\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}/2(I0+Ie)$ between the substitution, zero-point and equilibrium moments of inertia holds if the isotopic substitution can be treated by first-order perturbation theory. Thus I may be determined from the isotopic variation of the rotational constants, and with enough isotopes an equilibrium structure can be obtained. The disadvantages of the method are: (i) all singly-and a large number of doubly-substituted isotopic molecules are required; (ii) the isotopic changes in moments of inertia must be measured very accurately to give adequate accuracy in the structure. The main advantage is that this method should be less subject to the anomalies that arise in attempts to obtain all the rotation-vibration $\alpha$ constants directly.