Derivation of Accurate Kinetic and Potential-energy Functions for Several Simultaneous Large-amplitude Vibrations

A procedure is presented for deriving kinetic and potential-energy functions from experimental data for an arbitrary number of large-amplitude vibrations. As a starting point, the method requires a highquality estimate of the spectroscopic data. We use the previously developed technique of spectrum generation from ab initio calculations to obtain the initial kinetic and potential functions. The present technique minimizes the error between the calculated and experimental energy levels by considering both the kinetic and potential terms. The application to the internal rotation of the methyl group in the So state of acetaldehyde shows that the technique is capable of yielding agreement to the experimental measurements to within 0.0001 cm-'. The joint methyl torsion and aldehyde wagging modes for the T, state of acetaldehyde are also considered. From the twodimensional potential function the barriers to methyl rotation and to inversion of the aldehydic hydrogen are found to be 633.60 and 935.76 cm-', respectively. The equilibrium conformation obtained from the twodimensional potential shows one methyl hydrogen almost eclipsing the aldehydic oxygen (torsion angle 186.40") whereas the aldehydic hydrogen distorts out of the molecular frame by 39.17". These structural results are found to differ from that obtained using one-dimensional models, but they agree very well with the results of ab initio calculations.