Effect of Anharmonic Vibrations on the Bond Lengths of Polyatomic Molecules. I. Model of Force Field and Application to Water

Abstract

The detailed information on molecular force fields required for precise determinations of molecular structure is only rarely available for polyatomic molecules. A model of the force field is therefore proposed from which the cubic potential constants may be estimated from commonly available data. The potential energy is represented by a modified, anharmonic Urey‐Bradley field in which the stretching and nonbonded potentials are assumed to have the Lippincott and Buckingham forms, respectively, and in which stretch‐stretch interactions are included. The model is applied to H₂O and D₂O, for which exceptionally complete spectroscopic data are available for comparison, and is found to give cubic constants in satisfactory agreement with experiment. The cubic constants thus estimated are used to evaluate the effect of zero‐point vibrations on the internuclear distances and rotational constants of water by a first‐order perturbation treatment. The resultant mean distances and mean amplitudes are in good agreement with those of Reitan's second‐order treatment using the experimental cubic constants, and the rotation‐vibration constants α agree satisfactorily with Benedict's experimental values.