Point Groups in Molecular Symmetry

Point Groups Overview

• A point group encapsulates the full symmetry of a molecule.
• Key symmetry elements must be identified to assign a point group.

Regular Shapes

• Regular geometric shapes such as tetrahedra (Td) and octahedra (Oh) can be readily identified without applying detailed rules.

Steps for Assigning Point Groups

• Determine the highest axis of rotational symmetry, denoted as Cn, and establish it as the z-axis.
• If n = 1:
  • Check for a center of symmetry (Ci).
  • Check for a plane of symmetry (Cs).
  • If neither is present, classify the molecule as C1.
• If n ≥ 2:
  • Assess for n C2 axes perpendicular to Cn; if present, classify as dihedral (D).
    • For dihedral:
      • Identify if there is a horizontal plane (Dnh).
      • Check for n vertical planes (Dnd).
  • If not dihedral, check for S2n axis coinciding with Cn (S2n).
  • Check for a horizontal plane (Cnh) or n vertical planes (Cnv) if the molecule is not dihedral.
  • If neither feature exists, classify as Cn.

Examples of Point Group Assignments

• H2O: Analyze the molecule in the xz plane where x, y, and z axes are inequivalent.
• NH3: The x and y axes are equivalent, described as doubly degenerate.
• ClF3: Can be represented in multiple ways, with two types of chemically inequivalent fluorine atoms.
• SF4: Often shows C2v point group characteristics; dynamic interconversion of fluorine types is noted.
• BF3: Assigned systematically following previous steps.

Learning Outcomes

• Ability to identify key symmetry elements effectively.
• Assign the correct point group, reflecting the symmetry of the molecule's ground state.
• Recognize the implications of degeneracy in symmetry axes where x, y, and z may be the same or different.