Molecular Geometry & Bonding
what the shape decides
Ladder

Point group — the ladder

3 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. HHHNC3vprincipal axis C33 mirror planesno inversion centremay be polarcannot be chiralgroup recovered from the coordinates4 atoms

    Point groups from coordinates

    A molecule's symmetry is not a label to be looked up. It is decidable from the atom positions by searching for the operations that permute them, and the search either finds an operation or it does not.

    rung 1 · symmetry
  2. moleculegroupmay be polarmay be chiralwaterC2vyesno2 σcarbon dioxideD∞hnonohas iammoniaC3vyesno3 σmethaneTdnono6 σboron trifluorideD3hnono4 σhydrogen peroxideC2yesyes—bromochlorofluoromethaneC1yesyes—both columns derived from the symbol, not from the bonds

    Symmetry forbids a dipole

    Whether a molecule can have a dipole moment follows from its point group alone. The usual argument — adding up bond vectors — gets the right answer for easy cases by a route that does not generalise.

    rung 2 · symmetry
  3. BrClCHFC1no rotation axis0 mirror planesno inversion centremay be polarmay be chiralgroup recovered from the coordinates5 atoms

    Chirality is a symmetry statement

    A molecule is chiral when its group contains no improper operation at all. The four-different-groups rule is a useful special case that misses molecules with no stereocentre and wrongly condemns some that have several.

    rung 3 · symmetry

All ladders