Ladder

Vsepr — the ladder

5 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. tetrahedral109.47° × 6repulsion minimised, angles measured off the result4 sites

    VSEPR, computed

    The tetrahedral angle is not 109.5 degrees because a textbook says so. It is arccos(−1/3), and it falls out of minimising the repulsion of four points on a sphere without ever being written down.

    rung 1 · shape
  2. axial — 2 sitesneighbours at 90°, 90°, 90°, 180°equatorial — 3 sitesneighbours at 90°, 90°, 120°, 120°the two are not equivalentneighbour angles measured, not assumed5 sites

    Five sites are not alike

    Every other common arrangement has one or two distinct angles. Five has three, because two of its positions are on an axis and three are round an equator — and a molecule built that way does something about it.

    rung 2 · shape
  3. HHOC2vprincipal axis C22 mirror planesno inversion centremay be polarcannot be chiralgroup recovered from the coordinates3 atoms

    Why water is bent

    The standard answer is lone pair repulsion, it predicts the right direction, and it cannot predict the magnitude. A better rule can, and the heavier hydrides show where both accounts run out.

    rung 3 · shape
  4. cubesquare antiprismenergy 19.740774energy 19.6752883 distinct angles4 distinct anglesthe antiprism is lower by 0.065486 — about one part in 301both energies computed, neither assumed8 points

    The shapes above six coordination

    Eight points on a sphere do not arrange themselves in a cube. They twist one face by forty-five degrees, and above six the arrangements stop being the ones anybody would name and start being the ones a minimisation finds.

    rung 3 · shape
  5. sp3109.471°between every pair4 hybridsworst off-diagonal 0e+0an orthogonal transformation of the atomic orbitalsone electron

    Bent's rule, against the substituent series

    More electronegative substituents get more p character, so the angle between them shrinks. The rule predicts a trend, the trend is observed, and the quantity it depends on turns out not to be one quantity.

    rung 4 · shape

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