Symmetry constraints on the configurational properties of non-linear molecules

Abstract

Symmetry constraints on coefficients in the generalized spherical harmonic expansions of configurational properties are derived for pairs of non-linear molecules. Constraints are also obtained for the coefficients in the expansion of the time dependent reorientational distribution function for a non-linear molecule. In addition to invariance under the operations of the molecular point group, these properties must be invariant to interchange (for pairs of identical molecules) and to changes in the ‘handedness’ of the coordinate axes (for optically inactive molecules). Specific results are given for the configurational properties of tetrahedra, but other simple non-linear point groups are briefly considered. In the time dependent case, several types of molecular symmetry are discussed (including tetrahedral), and the relationship between point group constraints and the results for anisotropic rotational diffusion models is clarified.

Notes

This work supported in part by a grant from the National Science Foundation.