Molecular Geometry & Bonding
what the shape decides
Concept

Franck–Condon principle — where it appears

The principle that a molecule's nuclei do not move while an electron leaves or a transition occurs, so the new state is reached at the old geometry. The intensities of the vibrational lines that follow are squared overlaps of vibrational wavefunctions, and their spread measures how far the geometry changed.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

Where the d–d band falls, and where the eye is. Nine ligands' measured splittings as wavelengths, on a logarithmic scale, with the visible range shaded. Three fall inside it; the halides sit in the near infrared and carbon monoxide in the ultraviolet. The splitting decides where the band is and does not decide what is seen.

Where a d–d band falls

A splitting is an energy and an energy is a wavelength, so the ligand field fixes where a complex absorbs. Only three of nine common ligands put that band inside the visible range at all — and the most intensely coloured transition-metal compound in the cupboard has no d electrons to excite.

applied · Ligand field Three bands of one spectrum, and the bond length behind each. Nitrogen's three photoelectron bands, drawn as the vibrational intensity distributions computed from the measured bond lengths and vibrational constants of the three states of the ion. Each band's lines add to one. The middle band is spread over five lines because the electron removed came out of a strongly bonding orbital and the bond lengthened by 77.22 thousandths of an ångström; the outer two keep 92 and 88 per cent of their strength in a single line.

The width of a band is a bond length

Nitrogen's three photoelectron bands are one sharp line, a progression of five, and a line with a shoulder. Computed from the measured bond lengths of the three states of the ion, the intensities come out at 0.917, 0.263 and 0.880 in the first line of each — because removing a weakly bonding electron lengthens the bond by 18.7 thousandths of an ångström, a strongly bonding one by 77.2, and an antibonding one shortens it by 23.7.

spectra · Photoelectron A photoelectron band is a filter, and the group chooses the filter. The Huang–Rhys factor of every vibration of five molecules under a change of geometry that lengthens every bond alike — which is what removing an electron from a non-degenerate orbital does. On a logarithmic scale spanning sixteen decades, eight modes carry the whole of it and the rest sit on the floor at arithmetic noise. Which ones is decided by the point group: only a totally symmetric vibration can appear, whatever the size of the change.

A band is a filter on the modes

A photoelectron band's vibrational structure reports the frequencies of a few of the ion's vibrations and is silent about the rest, and which few is decided by the point group before any geometry is known. Under a change of shape that lengthens every bond alike, methane's totally symmetric stretch gets a Huang–Rhys factor of 0.905 and its other eight modes get between 10⁻²⁸ and 10⁻³⁵.

spectra · Photoelectron

Named alongside it

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

Bond lengthModel limitPhotoelectron spectrumSelection rulesVibrational modesAbsorptionAntibondingBondingCharge transferClosed formD d transitiond orbitals

All concepts