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.

Cluster geometry optimizations were performed as follows. Our Si 21 H 20 and Si 9 H 12 geometries were B3LYP/6-311++G(3df,2pd) optimized without constraints, while Si 6 H 12 and Si 2 H 4 geometries were obtained from the optimized Si 21 H 20 . The Si 21 H 20 center dimer was isolated and modified into the Si 6 H 12 cluster. The Si 6 H 12 bare cluster was obtained from the bare Si 21 H 20 cluster. The complex, transition state guess and product geometries were obtained analogously. The 6-silicon atoms in the following geometry optimizations and transition state searches were kept frozen (other coordinates unconstrained) to retain the geometric orientation about the dimer bond modeling the silicon surface. The bare Si 2 H 4 cluster was also obtained from the Si 21 H 20 center dimer by replacing the four second-layer silicon atoms with hydrogen atoms. The complex, transition state guess and product geometries were obtained analogously. The two-silicon dimer atoms in the following geometry optimizations and transition state searches were kept frozen. Four dihedral and two angles were also frozen as listed (by the optimized coordinates) retaining the geometric orientation about the dimer bond.Tables I-IV compares selected geometric parameters from our B3LYP/6-311++G(3df,2pd) calculations to previous literature. Results are reported for an isolated silicon cluster ("bare cluster"), NH 3 adsorbed onto the cluster ("complex"), "transition structure" and "product" for dissociated ammonia chemisorbed NH * 3 → NH * 2 + H * (asterisks denoting surface bound species). Cartesian coordinates for the series of clusters and atom numbering are reported in Supporting Information II. Tables report distances inÅ and angles in degrees.To calculate the tilt angle θ tilt , a plane is first defined by the four-silicon atoms (in the secondlayer) bonded to the two-silicon dimer atoms in the Si 21 H 20 and Si 9 H 12 clusters (through constraints Si 6 H 12 is equivalent to Si 21 H 20 ). The Si 2 H 4 plane is defined by the four-hydrogen atoms in the second-layer; and the Si(100)-2x2 slab plane is defined by the two-translation vectors. The θ tilt is then the angle adjacent to the plane resulting from the vertical separation ('z ' direction) in the coordinates of the silicon 'up' and 'down' atoms.The B3LYP Si 9 H 12 geometries from Surface Science, 2000 469, 9 (in Table II) used a mixed basis set: 6-311++G(2d,p) on chemically active atoms, 6-31G(d) on subsurface Si and terminating

Density functional theory calculations on the title compounds indicate that metal−olefin bond strengths follow the trend for cyclic olefin strain energies. It was found, however, that the proportionality between metal−olefin bond energy and strain energy is not evenly distributed throughout the olefin series. For instance, cyclopropene and cyclobutene are expected to bind to the metal much more weakly than would be anticipated on the basis of their strain energies. A bond energy decomposition analysis reveals that the metal−olefin interaction is responsible for strain relief in the cycloolefins by means of the rehybridization of the olefinic carbons. However, the geometrical changes accompanying this rehybridization, namely CC elongation and olefin pyramidalization, involve an energetic cost that is paid at the expense of the bonding interaction energy. Nonpyramidalized strained olefins such as cyclopropene and cyclobutene undergo large conformational changes, to the detriment of their large attractive interaction energies. It was found that a cyclic olefin that is already deformed, such as trans-cyclooctene, interacts strongly with a metal to relieve strain but does not suffer much energy-costly reorganizations. This, thus, constitutes an energy benefit to the metal−trans-cyclooctene bond strength.