Molecular Geometry & Bonding
what the shape decides
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The thread: Taught confidently, and wrong

This subject has an unusual number of explanations that are memorable, widespread and false. Each is stated fairly here and then tested against a computation rather than an opinion.
2pzencloses 90% of the densitycontour at |ψ| = 9.48e-30 radial nodes1 angular nodecontour solved for by integrating the density1 shell · one electron Orbitals

What an orbital is

Not a region the electron occupies, not a path it follows, and for any atom but hydrogen not an exact anything. An orbital is a one-electron wavefunction, and almost every difficulty in this subject comes from forgetting that.

 tetrahedral109.47° × 6repulsion minimised, angles measured off the result4 sites Where the atoms go

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.

 FFFSFFFOhprincipal axis C49 mirror planeshas an inversion centrecannot be polarcannot be chiralgroup recovered from the coordinates7 atoms Beyond the octet

Hypervalency without d orbitals

Sulfur hexafluoride is not d²sp³ hybridised. The d orbitals are far too high in energy to contribute meaningfully, the bonding is three-centre four-electron, and the textbook account has been known to be wrong for fifty years.

 HHCHHTdprincipal axis C36 mirror planesno inversion centrecannot be polarcannot be chiralgroup recovered from the coordinates5 atoms What is taught wrongly

Hybridisation does not explain

Methane's photoelectron spectrum has two bands, not one. Four equivalent sp³ bonding orbitals cannot produce that, and the resolution is that hybridisation was never a claim about what a measurement would find.

 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 What symmetry decides

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.

 HHCCHCCHCCHHD6hprincipal axis C67 mirror planeshas an inversion centrecannot be polarcannot be chiralgroup recovered from the coordinates12 atoms Beyond the octet

Delocalisation

Benzene does not alternate between two structures. It has one structure, and the two Kekulé forms are basis functions in a description of it — which is a different and much less exciting claim than the one usually made.

 one scale across the plate1s0 radial · 0 angular2s1 radial · 0 angular2pz0 radial · 1 angulareach level solved for separately90% · one electron What is taught wrongly

Orbitals are not where the electron is

A many-electron atom has no exact orbitals at all. The orbital picture is a basis for an approximation — an extremely good one — and treating it as a description of reality is the source of most of the confusion in this subject.

 HHOC2vprincipal axis C22 mirror planesno inversion centremay be polarcannot be chiralgroup recovered from the coordinates3 atoms Where the atoms go

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.

 BrClCHFC1no rotation axis0 mirror planesno inversion centremay be polarmay be chiralgroup recovered from the coordinates5 atoms What symmetry decides

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.

 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 What is taught wrongly

The dipole is not a sum of bonds

Adding bond dipoles as vectors gets the easy cases right and rests on a quantity with several incompatible definitions. The symmetry argument is exact, needs no electronegativities, and says when the answer must be zero.

 most probable radius 1.00 a₀R(r)and 4πr²R²r / bohrmeasured off the computed function0 radial nodes · one electron Orbitals

Where the electron is

The wavefunction is largest at the nucleus, the electron is most likely to be found a bohr out, and the ninety-per-cent contour is at 2.66. Three numbers, all correct, all answering different questions.

 1s-1sσ overlapS = 0.39002pz-2pzσ overlapS = 0.45852px-2pxπ overlapS = 0.75291s-2pxsymmetry forbids itS = 0 exactlyno splittingoverlaps computed at 2.8 bohr, levels in proportionone electron Bonding models

Molecular orbital and valence bond

Two frameworks, taught as rivals, describing the same molecules. One starts from delocalised orbitals and localises; the other starts from localised bonds and delocalises. Pushed far enough they meet.

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