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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. This reduces the number of ...
In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type. Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions:
Each point group can be represented as sets of orthogonal matrices M that transform point x into point y according to y = Mx. Each element of a point group is either a rotation (determinant of M = 1), or it is a reflection or improper rotation (determinant of M = −1). The geometric symmetries of crystals are described by space groups, which ...
The point group of 18-crown-6 is S 6. The dipole moment of 18-crown-6 is solvent- and temperature-dependent. Below 25 °C, the dipole moment of 18-crown-6 is 2.76 ± 0.06 D in cyclohexane and 2.73 ± 0.02 in benzene. [2] The synthesis of the crown ethers led to the awarding of the Nobel Prize in Chemistry to Charles J. Pedersen.
A construct in chemistry is molecular symmetry, as embodied in Group theory. Inorganic compounds display a particularly diverse symmetries, so it is logical that Group Theory is intimately associated with inorganic chemistry. [14] Group theory provides the language to describe the shapes of molecules according to their point group symmetry ...
This group is called the point group of that molecule, because the set of symmetry operations leave at least one point fixed (though for some symmetries an entire axis or an entire plane remains fixed). In other words, a point group is a group that summarises all symmetry operations that all molecules in that category have. [8]
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