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In chemistry and crystallography, a symmetry element is a point, line, or plane about which symmetry operations can take place. In particular, a symmetry element can be a mirror plane , an axis of rotation (either proper and improper), or a center of inversion .
In chemistry, molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain many of a molecule's chemical properties , such as whether or not it has a dipole moment , as well ...
Each symmetry operation is performed with respect to some symmetry element (a point, line or plane). [1] In the context of molecular symmetry, a symmetry operation is a permutation of atoms such that the molecule or crystal is transformed into a state indistinguishable from the starting state. Two basic facts follow from this definition, which ...
D nd has, in addition to the elements of D n, mirror planes parallel to the n-fold axis. The letter T (for tetrahedron) indicates that the group has the symmetry of a tetrahedron. T d includes improper rotation operations, T excludes improper rotation operations, and T h is T with the addition of an inversion.
The defining property of a crystal is its inherent symmetry. Performing certain symmetry operations on the crystal lattice leaves it unchanged. All crystals have translational symmetry in three directions, but some have other symmetry elements as well. For example, rotating the crystal 180° about a certain axis may result in an atomic ...
The modern definition of the law of symmetry is based on symmetry elements, and is more in the German dynamistic [1] crystallographic tradition of Christian Samuel Weiss, Moritz Ludwig Frankenheim and Johann F. C. Hessel. Weiss and his followers studied the external symmetry of crystals rather than their internal structure.
Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in the application of quantum mechanics in physics and chemistry, for example, it can be used to predict or explain many of a molecule's properties, such as its dipole moment and its allowed ...
Crystal chemistry is the study of the principles of chemistry behind crystals and their use in ... Miller Indices, symmetry elements, bond lengths and radii ...