Accurate inertias for large-amplitude motions: Improvements on prevailing approximations

We present a simple yet accurate method for the calculation of effective moments of inertia for large-amplitude low-frequency internal motions in molecules. Our technique makes use of the quantum-mechanical kinetic energy operator developed within the internal coordinate path Hamiltonian formalism, with the imposition of Eckart conditions on the molecular frame to separate the internal motion from overall molecular rotation. Numerical results are presented for several molecules possessing internal large-amplitude motions. These results are compared with those obtained from approximate analytic formulas proposed by Pitzer. We also give detailed examples where the conventional approximations in the current literature are not applicable for describing a single large-amplitude motion. Our straightforward algorithm yields results more accurate than those of Pitzer's method, especially for molecules with asymmetric internal rotors.