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Point groups are used to describe the symmetries of geometric figures and physical objects such as molecules. 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 ...
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 results in a molecule indistinguishable from the original.
These groups are characterized by an n-fold improper rotation axis S n, where n is necessarily even. The S 2 group is the same as the C i group in the nonaxial groups section. S n groups with an odd value of n are identical to C nh groups of same n and are therefore not considered here (in particular, S 1 is identical to C s).
For example, a common case is a tetrahedral carbon bonded to four distinct groups a, b, c, and d (Cabcd), where swapping any two groups (e.g., Cbacd) leads to a stereoisomer of the original, so the central C is a stereocenter. Many chiral molecules have point chirality, namely a single chiral stereogenic center that coincides with an atom.
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 ...
When all three atoms at the corners are identical, the molecule belongs to point group C 3v. Some molecules and ions with trigonal pyramidal geometry are the pnictogen hydrides (XH 3), xenon trioxide (XeO 3), the chlorate ion, ClO − 3, and the sulfite ion, SO 2− 3.
A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system. Of the 32 point groups that exist in three dimensions, most are assigned to only one lattice system, in which case the crystal system and lattice system both have the same name.
Such species belong to the point group D 3h. Molecules where the three ligands are not identical, such as H 2 CO, deviate from this idealized geometry. Examples of molecules with trigonal planar geometry include boron trifluoride (BF 3), formaldehyde (H 2 CO), phosgene (COCl 2), and sulfur trioxide (SO 3).