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Chemistry LibreTexts

4.2.1: Groups of Low and High Symmetry

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    226199
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    Low Symmetry Point Groups

    Low symmetry point groups include the C1, Cs, and Ci groups

    Group Description Example
    C1 only the identity operation (E) CHFClBr
    Cs only the identity operation (E) and one mirror plane C2H2ClBr
    Ci only the identity operation (E) and a center of inversion (i) C2H2Cl2Br

    High Symmetry Point Groups

    High symmetry point groups include the Td, Oh, Ih, C∞v, and D∞h groups. The table below describes their characteristic symmetry operations. The full set of symmetry operations included in the point group is described in the corresponding character table.

    Group Description Example
    C∞v linear molecule with an infinite number of rotation axes and vertical mirror planes (σv) HBr
    D∞h linear molecule with an infinite number of rotation axes, vertical mirror planes (σv), perpendicular C2 axes, a horizontal mirror plane (σh), and an inversion center (i) CO2
    Td typically have tetrahedral geometry, with 4 C4 axes, 3 C2 axes, 3 S4 axes, and 6 dihedral mirror planes (σd) CH4
    Oh typically have octahedral geometry, with 3 C4 axes, 4 C3 axes, and an inversion center (i) as characteristic symmetry operations SF6
    Ih typically have an icosahedral structure, with 6 C5 axes as characteristic symmetry operations B12H122-
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