Graphical description of the symmetries of potential energy surfaces.

Shapes of the potential energy surfaces (PES) of ‘‘floppy’’ molecules can be represented by graphs in which vertices denote global minima and edges connecting the vertices describe energetically accessible paths connecting such global minima. Such graphical representations of PESs are characterized by (i) the number of vertices; (ii) edges that connect (or do not) various vertices; and (iii) the symmetry of the PES, which may be obtained from the graphical figure. These characteristics are shown in this paper to be reflected in the vibration–rotation wave function’s symmetry. Such a symmetry analysis reduces to that provided by the conventional point group for rigid molecules, but provides a useful tool for characterizing vibrations of floppy molecules. In particular, it is shown that for so-called connected graphs, the nonrigid group of the molecule is its full permutation-inversion group. PESs with connected graphs having three and six global minima are examined as examples, and relevant character tables are provided. PESs with disconnected graphs (which characterize species containing some inaccessible barriers), are also considered. The flexible molecules ArH3+, C2H3+, CH4+, and LiBH4 are considered as examples of the tools presented here. [ABSTRACT FROM AUTHOR]