MOLECULAR-GEOMETRY AND SYMMETRY FROM A DIFFERENTIAL GEOMETRY VIEWPOINT

Relations between an earlier generalization of molecular symmetry call ed symmorphy and a molecular equivalence based on diffeomorphisms of e lectron density functional graphs (the so-called DFG equivalence intro duced in our previous work) are analyzed. Any two DFG-equivalent elect ron density functions can be derived from one another by a suitable tr ansformation of the spatial coordinates and the electronic charge dens ity scale; the classes of DFG equivalence are the orbits of a group of Linear operators operating in the space of electron density functions . Within the symmorphy framework, the symmetry group is derived from t he symmorphy group by taking an intersection of a subgroup of the symm orphy group and the group of isometries for a natural choice of the Ri emannian metric tenser. The Riemannian metric properties provide a cho ice for a suitable reference electron density function for each class of equivalent densities. Such reference densities serve as tools for a systematic classification of the infinite family of electron densitie s of molecular conformations. (C) 1997 John Wiley & Sons, Inc.