Q8(b). Fluxional molecules and their detection by NMR

Fluxional molecules

1. A molecule is fluxional when its atoms exchange positions between two or more chemically equivalent structures (same energy, different labelling) by a low-energy, intramolecular process, usually without breaking bonds.
2. Each instant the molecule has a definite structure; but the exchange is so fast at room temperature that some methods see only the time average. Diffraction, IR and Raman, with much shorter time scales, see the rigid structure; NMR (time scale near milliseconds) may see the average.
3. Examples: PF₅ and Fe(CO)₅ (Berry pseudorotation exchanges axial and equatorial groups); SF₄ (axial and equatorial F exchange; two ¹⁹F signals appear only at low temperature); (C₅H₅)₄Ti and (η¹-C₅H₅) complexes (ring whizzing by 1,2-shifts); IF₇.

How NMR detects it

1. Two nuclei in different environments give lines Δν (Hz) apart. If the exchange rate k≪Δν, two separate lines are seen (slow exchange); if k≫Δν, one line at the weighted mean position (fast exchange).
2. Variable-temperature NMR: cooling slows the exchange. The single line broadens, flattens at the coalescence temperature T_c, then splits into the separate lines of the frozen structure (panel). The low-temperature spectrum gives the true structure; the way the lines merge identifies the motion.
3. At coalescence (two equal lines): k_c=(π Δν)/(√2)=2.22 Δν; for Δν=100 Hz, k_c=222 s⁻¹. With the Eyring equation, k_c at T_c gives the activation barrier Δ G° of the exchange.
4. Coupling is the proof of intramolecular exchange: if spin–spin splitting to a third nucleus survives in the averaged line, the atoms never left the molecule.

Example: PF₅

RIGID2 Fₐₓ + 3 F_(eq): two signals 2: 3OBSERVEDone doublet, ¹J(P–F)PROCESSBerry pseudorotation

1. A rigid trigonal bipyramid would give two ¹⁹F signals (2 axial: 3 equatorial). Observed: one fluorine signal, a doublet from coupling to ³¹P (I=12), even at -100°C.
2. In Berry pseudorotation one equatorial F stays as pivot; the axial pair closes from 180° to 120° while two equatorial F open to 180°, through a square-pyramidal transition state. Axial and equatorial F exchange; the P–F doublet is kept, so the exchange is intramolecular.
3. Fe(CO)₅ likewise gives one ¹³C line at all accessible temperatures. In (η¹-C₅H₅) complexes the σ-bonded ring gives one ¹H line at room temperature but three (1: 2: 2) at low temperature.

Application. variable-temperature NMR is the standard method for measuring small rearrangement barriers in organometallic and main-group compounds; the same line-shape analysis gives rates of proton exchange and ring inversion.