Figure 2. Fingerprinting cluster structure using ¹⁶O¹⁸O mixed oxygen isotope.

a, b, Asymmetrically labelled ¹⁶O¹⁸O can initially bind in two equiprobable orientations, yielding an even mixture of two isotopomers in T or Q (panels a and b, top) exhibiting characteristic vibrations (panels a and b, bottom). Two scenarios are possible for Q, depending on whether two (left) or one (right) O₂-derived atoms (red and blue) are incorporated into the cluster. If only one atom is incorporated, then the second oxygen atom in the core structure would derive from solvent (black). Water and methanol exemplify a departing oxygen atom while other ligands are omitted for simplicity. Since the two isotopomers of T (a) and those of singly labelled Q (b, right) have identical composition as corresponding ¹⁶O₂ and ¹⁸O₂ derivatives, they will exhibit both vibrations simultaneously at half the intensity. Doubly labelled Q (panel b, left) will be different from both symmetrically labelled derivatives and thus, c, will exhibit a new vibration (green), as illustrated by isotope difference spectra (c). The ¹⁶O₂ – ¹⁶O¹⁸O difference (ii) in singly labelled cluster (a, b right) will appear as the ¹⁶O₂ – ¹⁸O₂ difference (i) with reduced intensity. The ¹⁶O¹⁸O derivative will be identical to the average of symmetrical isotopomers, yielding no signal in trace iii, as observed experimentally for T. The new frequency in doubly labelled Q should appear in both difference (ii) and (iii), and can, indeed, be seen in experimental data at 673 cm⁻¹. Spectral superimposition inflates the apparent isotopic shift when frequencies of isotopomers are close (traces (ii) and (iii), right), but not when bands are well separated (trace (i)).