Z. Zimpel et Pg. Mezey, MOLECULAR-GEOMETRY AND SYMMETRY FROM A DIFFERENTIAL GEOMETRY VIEWPOINT, International journal of quantum chemistry, 64(6), 1997, pp. 669-678
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.