On the origin of alternating bond distortions and the emergence of chirality in polyoxometalate anions.

Alternating short and long bond length (ABL) distortions observed within the ring structures of molecular metal oxide anions or polyoxometalates (POMs) are reminiscent of the cooperative linear ABL distortions in perovskite d(0) metal oxides. We show herein that these distortions have a common origin: a pseudo Jahn-Teller (PJT) vibronic instability. Four POM structural types with different M(n)O(n) ring sizes are investigated herein using density functional theoretical methods: Lindqvist [M6O19](q-) (n = 4), Keggin alpha-[XM12O40](q-) (n = 6), Wells-Dawson alpha-[X2M18O62](q-) (n = 8), and Preyssler [(Na)P5W30O110](14-) (n = 10), where M = Mo(VI) and W(VI) and X = Si(IV), Ge(IV), P(V), As(V), S(VI), and Se(VI). Chirality is induced within the latter three structural types by the ABL ring distortions. The calculations confirm the PJT vibronic origin of the ABL distortions with good agreement between calculated geometries and published single-crystal X-ray diffraction data. Both theory and experiment show that the vibronic interaction and distortion magnitude increase for (1) molybdates relative to that of tungstates, (2) larger M(n)O(n) ring sizes, (3) increases in negative charge of the internalized fragments (O(2-) or XO4(q-)), and (4) d(0) versus d(n) metal oxidation states. The PJT vibronic coupling model explains these observations in terms of the energy gap between Kohn-Sham frontier molecular orbitals (MOs) concomitant with the propensity for metal-oxygen pi-bonding within the M(n)O(n) rings. The frontier MOs for the undistorted nuclear configurations are largely nonbonding pi-O(p) (occupied) and pi-M(d) (unoccupied) in character, where smaller HOMO-LUMO (H-L) gap energies lead to greater metal-oxygen pi-orbital mixing under the influence of the nuclear distortion. A reduction in pi-bond order decreases the distortion in mixed-valence POMs. Of the tungstates examined, only the Preyssler anion shows pronounced ABL ring distortions, which derive from its large ring size and concomitant small H-L gap.