Molecular geometry and symmetry from a differential geometry viewpoint

✍ Scribed by Zbigniew Zimpel; Paul G. Mezey

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 183 KB
• Volume: 64
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1997)64:6<669::aid-qua4>3.0.co;2-u

✦ Synopsis

Relations between an earlier generalization of molecular symmetry called symmorphy and a molecular equivalence based on diffeomorphisms of electron Ž density functional graphs the so-called DFG equivalence introduced in our previous . work are analyzed. Any two DFG-equivalent electron density functions can be derived from one another by a suitable transformation of the spatial coordinates and the electronic charge density 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 the symmorphy group by taking an intersection of a subgroup of the symmorphy group and the group of isometries for a natural choice of the Riemannian metric tensor. The Riemannian metric properties provide a choice 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 densities of molecular conformations.