Molecular Geometry & Bonding
what the shape decides
Ladder

Overlap — the ladder

2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. 1s · 1sS = 0.38997sigma interactionseparation 2.8 bohrcontours at 50% of each densitythe signed product integrated over all spaceone electron

    Overlap decides

    Two orbitals interact in proportion to how much they overlap, and the sign of the overlap decides which of the two combinations is the lower in energy. It is one integral, and almost everything about bonding follows from it.

    rung 1 · bonding
  2. 1s · 2pxS = 0 exactlycomputed -9.6e-17 — arithmetic noiseseparation 2.8 bohrcontours at 50% of each densitythe contributions cancel in pairs, so the integral vanishesone electron

    Exactly zero

    Where symmetry forbids an interaction the overlap is not small. It is zero — and computing it and finding arithmetic noise is a different kind of statement from computing it and finding a small number.

    rung 2 · bonding

All ladders