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Elements. The point group symmetry of a molecule is defined by the presence or absence of 5 types of symmetry element. Symmetry axis: an axis around which a rotation by. 360 ∘ n {\displaystyle {\tfrac {360^ {\circ }} {n}}} results in a molecule indistinguishable from the original. This is also called an n -fold rotational axis and abbreviated Cn.
This lists the character tables for the more common molecular point groups used in the study of molecular symmetry. These tables are based on the group-theoretical treatment of the symmetry operations present in common molecules, and are useful in molecular spectroscopy and quantum chemistry. Information regarding the use of the tables, as well ...
In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension d is then a subgroup of the orthogonal group O (d).
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 ...
O h, (*432) [4,3] =. Icosahedral symmetry. I h, (*532) [5,3] =. In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O (3), the group of all isometries that leave the origin fixed, or ...
Square pyramidal geometry describes the shape of certain chemical compounds with the formula ML5 where L is a ligand. If the ligand atoms were connected, the resulting shape would be that of a pyramid with a square base. The point group symmetry involved is of type C 4v. The geometry is common for certain main group compounds that have a ...
Crystallographic point group. In crystallography, a crystallographic point group is a three dimensional point group whose symmetry operations are compatible with a three dimensional crystallographic lattice. According to the crystallographic restriction it may only contain one-, two-, three-, four- and sixfold rotations or rotoinversions.
The rule of mutual exclusion in molecular spectroscopy relates the observation of molecular vibrations to molecular symmetry. It states that no normal modes can be both Infrared and Raman active in a molecule that possesses a center of symmetry. This is a powerful application of group theory to vibrational spectroscopy, and allows one to easily ...