Molecular Geometry & Bonding
what the shape decides
Ladder

Aromaticity — the ladder

2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. ringlevel pattern (degeneracies, lowest first)shellπ energyC33 e⁻open1 unpaired3α + 3.000βC44 e⁻open2 unpaired4α + 4.000βC55 e⁻open1 unpaired5α + 5.854βC66 e⁻closed4n+2 (n = 1)6α + 8.000βC77 e⁻open1 unpaired7α + 8.543βC88 e⁻open2 unpaired8α + 9.657βfilled and then asked, not matched against a ruleamber = non-bonding

    Aromaticity as a computed shell closure

    Hückel's 4n+2 rule is not a rule. It is what comes out when every ring size is filled and asked whether its highest occupied shell came out full — and the machinery that answers does not know the phrase.

    rung 1 · bonding
  2. αα + 2.000βα + 0.000β×2α − 2.000βethenecyclobutadiene · 4 π electronstotal π energy 4α + 4.0000βagainst 2 isolated double bonds: 4βdelocalisation +0.0000β — none at all2 unpaired electrons — a tripleteigenvalues of the adjacency matrixHückel, no repulsion

    Delocalisation is stabilising, and other things that are false in general

    Spreading electrons over more centres is supposed to lower their energy. Cyclobutadiene is delocalised in exactly the same sense as benzene, gains exactly nothing by it, and the arithmetic says so before any experiment does.

    rung 2 · wrong

All ladders