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4.2.2: Other Groups

  • Page ID
    226200
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    D Groups

    The D set of point groups are classified as Dnh, Dnd, or Dn, where n refers to the principal axis of rotation. Overall, the D groups are characterized by the presence of n C2 axes perpendicular to the principal Cn axis. Further classification of a molecule in the D groups depends on the presence of horizontal or vertical/dihedral mirror planes.

    Group Description Example
    Dnh n perpendicular C2 axes, and a horizontal mirror plane (σh) benzene, C6H6 is D6h
    Dnd n perpendicular C2 axes, and a vertical mirror plane (σv) propadiene, C3H4 is D2d
    Dn n perpendicular C2 axes, no mirror planes [Co(en)3]3+ is D3

    C Groups

    The C set of point groups are classified as Cnh, Cnv, or Cn, where n refers to the principal axis of rotation. The C set of groups are characterized by the absence of n C2 axes perpendicular to the principal Cn axis. Further classification of a molecule in the C groups depends on the presence of horizontal or vertical/dihedral mirror planes.

    Group Description Example
    Cnh horizontal mirror plane (σh) perpendicular to the principal Cn axis boric acid, H3BO3 is C3h
    Cnv vertical mirror plane (σv) containing the principal Cn axis ammonia, NH3 is C3v
    Cn no mirror planes P(C6H5)3 is C3

    S Groups

    The S set of point groups are classified as S2n, where n refers to the principal axis of rotation. The S set of groups are characterized by the absence of n C2 axes perpendicular to the principal Cn axis, as well as the absence of horizontal and vertical/dihedral mirror planes. However, there is an improper rotation (or a rotation-reflection) axis collinear with the principal Cn axis.

    Group Description Example
    S2n improper rotation (or a rotation-reflection) axis collinear with the principal Cn axis 12-crown-4 is S4
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