Prediction of heptagonal bipyramidal nonacoordination in highly viable [OB-M©B7O7-BO]− (M = Fe, Ru, Os) complexes

Non-spherical distributions of ligand atoms in coordination complexes are generally unfavorable due to higher repulsion than for spherical distributions. To the best of our knowledge, non-spherical heptagonal bipyramidal nonacoordination is hitherto unreported, because of extremely high repulsion among seven equatorial ligand atoms. Herein, we report the computational prediction of such nonacoordination, which is constructed by the synergetic coordination of an equatorial hepta-dentate centripetal ligand (B7O7) and two axial mono-dentate ligands (-BO) in the gear-like mono-anionic complexes [OB-M©B7O7-BO]– (M = Fe, Ru, Os). The high repulsion among seven equatorial ligand B atoms has been compensated by the strong B–O bonding. These complexes are the dynamically stable (up to 1500 K) global energy minima with the HOMO-LUMO gaps of 7.15 to 7.42 eV and first vertical detachment energies of 6.14 to 6.66 eV (being very high for anions), suggesting their high probability for experimental realization in both gas-phase and condensed phases. The high stability stems geometrically from the surrounded outer-shell oxygen atoms and electronically from meeting the 18e rule as well as possessing the σ + π + δ triple aromaticity. Remarkably, the ligand-metal interactions are governed not by the familiar donation and backdonation interactions, but by the electrostatic interactions and electron-sharing bonding.

Spherical Distributions Used in Evolutionary Algorithms

Performance of evolutionary algorithms in real space is evaluated by local measures such as success probability and expected progress. In high-dimensional landscapes, most algorithms rely on the normal multi-variate, easy to assemble from independent, identically distributed components. This paper analyzes a different distribution, also spherical, yet with dependent components and compact support: uniform in the sphere. Under a simple setting of the parameters, two algorithms are compared on a quadratic fitness function. The success probability and the expected progress of the algorithm with uniform distribution are proved to dominate their normal mutation counterparts by order n!!.

Modelling with star-shaped distributions

We prove and describe in great detail a general method for constructing a wide range of multivariate probability density functions. We introduce probabilistic models for a large variety of clouds of multivariate data points. In the present paper, the focus is on star-shaped distributions of an arbitrary dimension, where in case of spherical distributions dependence is modeled by a non-Gaussian density generating function.