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Molecular geometry and symmetry from a differential geometry viewpoint
Author(s) -
Zimpel Zbigniew,
Mezey Paul G.
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)64:6<669::aid-qua4>3.0.co;2-u
Subject(s) - symmetry group , symmetry (geometry) , electron density , differential geometry , physics , equivalence (formal languages) , group (periodic table) , geometry , mathematics , electron , pure mathematics , quantum mechanics
Relations between an earlier generalization of molecular symmetry called symmorphy and a molecular equivalence based on diffeomorphisms of electron 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. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 669–678, 1997