Finding the point group template

Decision flowchart from "linear?" to the point group, with a table of point groups, their symmetry elements and examples.

What the template shows

• Answer each question for the molecule in 3D; "yes" goes right or left, "no" goes down
• Linear molecule?
• Inversion centre i?
• HCN, HCl
• Two or more Cn with n ≥ 3?
• Any proper axis Cn?
• Mirror plane σ?
• HOCl, CH₂ClBr
• meso anti conformer
• Take the highest-order Cn as the principal axis
• Horizontal plane σh?
• n dihedral planes σd?
• allene, staggered ethane
• B(OH)₃, trans-ClCH=CHCl
• n vertical planes σv?
• S₂n axis along Cn?
• tetramethyl-COT (S₄)
• Common point groups
• Point group Symmetry elements Examples C1 E CHFClBr Cs E, σ HOCl, SOCl₂ Ci E, i meso-CHClBr–CHClBr (anti) C2 E, C₂ H₂O₂ C2v E, C₂, 2σv H₂O, SF₄, CH₂Cl₂ C3v E, 2C₃, 3σv NH₃, CHCl₃ C4v E, 2C₄, C₂, 2σv, 2σd BrF₅ C∞v E, C∞, ∞σv HCN, CO C2h E, C₂, i, σh trans-ClCH=CHCl C3h E, C₃, σh, S₃ B(OH)₃ D3 E, 2C₃, 3C₂ [Co(en)₃]³⁺ D2h E, 3C₂, i, 3σ ethene, naphthalene D3h E, 2C₃, 3C₂, σh, 2S₃, 3σv BF₃, PCl₅ D4h E, C₄, 4C₂, i, σh, 2σv, 2σd, S₄ XeF₄, [PtCl₄]²⁻ D6h E, C₆, 6C₂, i, σh, 3σv, 3σd … benzene D∞h E, C∞, ∞C₂, i, σh, ∞σv CO₂, H₂ D2d E, 2S₄, C₂, 2C₂′, 2σd allene D3d E, 2C₃, 3C₂, i, 2S₆, 3σd staggered ethane S4 E, S₄, C₂, S₄³ 1,3,5,7-tetramethyl-COT Td E, 8C₃, 3C₂, 6S₄, 6σd CH₄, P₄, adamantane Oh E, 8C₃, 6C₂, 6C₄, 3C₂, i, 6S₄, 8S₆, 3σh, 6σd SF₆, cubane Ih 120 operations: 6C₅, 10C₃, 15C₂, i … C₆₀, [B₁₂H₁₂]²⁻
• Principal axis: the Cn with the highest n. n in Dnh, Cnv … is its order.
• Td, Oh, Ih: check for 4 C₃ axes (tetrahedron, octahedron/cube) or 6 C₅ axes (icosahedron); T, Th, O, I are rarer.

Drawn with 105 shapes – every one editable in MolDraw.

Sources

• Housecroft & Sharpe, Inorganic Chemistry, 5th ed., Pearson 2018, ch. 3 Textbook
• Atkins, de Paula & Keeler, Atkins' Physical Chemistry, 11th ed., OUP 2018 Textbook