Molecular Geometry & Bonding
what the shape decides
Concept

Vibration — where it appears

One normal mode of a molecule: a pattern in which every atom oscillates at a single frequency about the equilibrium geometry. It is a direction in the whole space of atomic displacements rather than the motion of any one bond, and it is what a single line in an infrared or Raman spectrum corresponds to.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

H₂O with 1→D: what each mode is made of. H₂O with 1→D. Each row is one distinct frequency and each column one internal coordinate; the bar is the share of the motion in that coordinate. A mode whose largest share reaches nine tenths is a motion of one bond or one angle and is named for it. 3 of 3 here are.

When a mode becomes a bond stretch

Water's two stretching modes are each exactly half in one O–H bond and half in the other, which is why neither of them belongs to a bond. Change one hydrogen to deuterium and the same force field at the same geometry gives two modes that are 99.5 and 99.7 per cent in a single bond each. Nothing about the bonding changed; a mass did.

spectra · Normal mode The two molecules with a direction no spectrum can see. Methane's fifty-five independent force constants and boron trifluoride's twenty-eight, split into the combinations a spectrum determines and the ones it cannot touch. Both molecules have a redundant coordinate set — methane's six angles at a tetrahedral centre are five coordinates' worth, and boron trifluoride's three angles at a planar centre are two — so both have a flat space, and the smaller molecule's is the larger share of its field.

The second molecule with a blind spot

Methane's fifty-five force constants have ten directions no spectrum can touch, and the forty-five that are fixed were worth a table. Boron trifluoride is the only other molecule here with a redundant coordinate set, and it is not the same case: eight kinds of constant rather than five, a quarter of its field invisible rather than a fifth, and an out-of-plane coordinate the redundancy cannot reach.

spectra · Normal mode

Named alongside it

The objects these essays reach for when they reach for this one.

Force constantInternal coordinateNormal modeClosed formConventionDegeneracyIsotope substitutionLeast-squaresLocalisationModel limitReduced massSymmetry operation

All concepts