Space Groups and Crystalline Structures

Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 153)


Molecules consist of positively charged nuclei and negatively charged electrons moving around them. If the translations and rotations of a molecule as a whole are excluded, then the motion of the nuclei, except for some special cases, consists of small vibrations about their equilibrium positions. Orthogonal operations (rotations through symmetry axes, reflections in symmetry planes and their combinations) that transform the equilibrium configuration of the nuclei of a molecule into itself are called the symmetry operations of the molecule. They form a group F of molecular symmetry. Molecules represent systems from finite (sometimes very large) numbers of atoms, and their symmetry is described by so-called point groups of symmetry. In a molecule it is always possible to so choose the origin of coordinates that it remains fixed under all operations of symmetry. All the symmetry elements (axes, planes, inversion center) are supposed to intersect in the origin chosen. The point symmetry of a molecule is defined by the symmetry of an arrangement of atoms forming it but the origin of coordinates chosen is not necessarily occupied by an atom.


Point Group Lattice Vector Point Symmetry Translation Vector Primitive Cell 
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© Springer-Verlag Berlin Heidelberg 2007

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