Molecular inelastic neutron scattering: Computational methods using consistent force fields

Inelastic neutron scattering cross sections for vibrational transitions of molecules are calculated from a knowledge of the eigenvalues and eigenvectors of the vibrational motion which are, in turn, calculated from a knowledge of the molecular potential energy function. In this way, inelastic neutron scattering data may be used as a test of molecular potential energy functions, especially the small nonbonding terms which influence the low frequency motions. In this work the potential energy function of Lifson and Warshel is used in conjunction with the neutron scattering formalism of Zemach and Glauber to calculate neutron scattering spectra for several alkanes. A numerical procedure is used for the orientation averaging. The results are compared to the experiments of Strong and co-workers. It is demonstrated that reliable cross sections and frequencies can be obtained for the low frequency torsional modes of propane, n-butane, and cyclohexane without readjustment of the parameters of the potential function. Reasonable results are also obtained for the branched hydrocarbons isobutane and neopentane which represent an extension of the potential function beyond its original range of applicability. The utility of cross section calculations in vibrational assignments, refinement of the potential function, and prediction of neutron scattering experiments are illustrated. Approximate expressions for the cross sections are given and tested by comparison with the essentially exact numerical methods.