A simplified group vibration method for calculating normal vibrations of large molecules

Abstract

An earlier formulation of the group vibration method by the author divided a molecule into groups and used coordinates defined in terms of 3 n displacements of the atoms relative to axes within the groups, together with 6 K coordinates associated with the translational and rotational motions of the K groups. These coordinates provided a convenient basis for guiding the selection of linearly independent symmetry coordinates, and they were well suited to calculations aimed at studying interactions of skeletal and intragroup motions, or vibrations characteristic of special structural units. However, the work of setting up a calculation was complicated because the transformation relating changes in bond distances and interbond angles to the 6 K skeletal coordinates was cumbersome to obtain, and the relation between the Cartesian displacements and the symmetry coordinates was rather complicated. This adds to the work of applying the results of normal coordinate analyses to such problem as the calculation of slow neutron scattering by molecules. These complicating features can be avoided by using as coordinates only the 3 n Cartesian displacements of the atoms. However, to retain the group vibration approach the proper recipes for choosing the skeletal symmetry coordinates are needed. This paper shows how to express these coordinates in terms of the 3 n Cartesian displacements, and shows how the work of setting up a calculation can be simplified further by admitting the use of non-orthogonal symmetry coordinates. As in the earlier work, the method is adapted to selecting linearly independent symmetry coordinates and this eliminates problems arising from redundancies.