15min:

JAMES K. G. WATSON, Steacie Institute for Molecular Sciences, National Research Council, Ottawa, Ontario, Canada K1A OR6; ARTUR ROYTBURG, Global Travel Computer Services, 7550 Birchmount Road, Markham, Ontario, Canada L3R 6C6; WOLFGANG ULRICH, Abteilung Chemische Physik, Universität Ulm, D-89069 Ulm, Germany.

The zero-point moment of inertia of a linear molecule is I₀=I_e+ ₀, where the vibrational contribution ₀ is a complicated function of degree 1/2 in the atomic masses. The substitution method assumes that ₀ is the same for all isotopomers, but least-squares fits of isotopomeric I₀ values assuming constant ₀ give ₀ values that are approximately half of the correct values. On the other hand, fits using ₀=cI_e^1/2, where c is a constant, give essentially identical fits of the data, but with ₀ values close to the correct values. To allow for vibrational effects of atoms with small coordinates, a second vibrational term is required. Here the formula \beginequation I₀=I_e+cI_e^1/2+d\left(m₁m₂... m_N øverM\right)^1/(2N-2), \endequation where c and d are constants, is tested in fits of both synthetic and experimental data. In general, excellent fits in the parts per million range are obtained. The corresponding bond lengths are called r_m^(2) to indicate the use of two correction terms. The method is readily generalized to non-linear molecules, and special Laurie-type corrections for hydrogen atoms can be incorporated.