Group Theory
Group Theory
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Group theory is the mathematical study of groups and their properties. One fundamental family of groups are point groups. Point groups are defined by a set of symmetry operations related to the symmetry elements that an object such as a molecule contains. Since all molecules belong to a point group, group theory underpins a wide variety of chemical properties such as bonding, dipole moments and spectra.
Molecules with no symmetry elements belong to the point group, which has no symmetry elements.
C
Consider the unsymmetric molecule bromochlorofluoromethane:
moleculeBrClFCH=Molecule["Bromo(chloro)fluoromethane"]
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Molecule
Compute the point group:
moleculeBrClFCH["PointGroupDisplay"]
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C
1
Compute the symmetry elements:
moleculeBrClFCH["SymmetryElements"]
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{}
Symmetric molecules belong to a variety of point groups and can have many symmetry elements.
Compute the point group of water:
moleculeWater=Molecule;moleculeWater["PointGroup"]
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C2v
Compute the symmetry elements of water:
Dataset[moleculeWater["SymmetryElements"],ItemDisplayFunction("Name"(Style[#,ShowStringCharactersFalse]&))]
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Visualizing symmetry elements is easy with the Wolfram Function Repository function MoleculeSymmetryPlot3D.
Display the symmetry elements for water:
ResourceFunction["MoleculeSymmetryPlot3D"][moleculeWater]
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Display the symmetry elements for sulfur hexafluoride:
ResourceFunction["MoleculeSymmetryPlot3D"]
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