Sigma trans promotion effect in transition metal complexes: a manifestation of the composite nature of binding energy

It is well known that intra-fragment electronic reorganization is one among several important components of the binding energy (bond dissociation energy) for two fragments forming an adduct. An interesting manifestation of this notion is proposed: a counterintuitive trend in binding energies that shall be commonly observed for a series of particular open shell transition metal containing complexes binding a small molecule at an empty coordination site. The prediction is that stronger σ interaction between the metal and the ligand trans to the empty site will result in a larger magnitude of binding energy and, possibly, a lower substrate coordination barrier. This trend, which we call the ‘trans promotion effect’ (TPE), is exemplified with a case study of dinitrogen binding by tri- and four-coordinated Mo(III) complexes. It is demonstrated that a trans amine ligand significantly increases the magnitude of dinitrogen binding energy. Orbital analysis and decomposition of the binding energy show that substrate coordination is favoured by stronger interaction of Mo with the trans ligand due to the d_z2 orbital of Mo that is occupied in the complex but vacant in the dinitrogen adduct.     

Duality for hypergeometric functions and invariant Gauss-Manin systems

We present some basic identities for hypergeometric functions associatedwith the integrals of Euler type. We give a geometrical proof for formulaesuch as the identity between the single and double integrals expressingAppell's hypergeometric series F1 (a, b, b' c; x, y).     

Ibuprofen-Cyclodextrin Inclusion Complex Formation using Supercritical Carbon Dioxide

Supercritical carbon dioxide (SC-CO₂) processing was performed with mixtures of cyclodextrins (CDs) and ibuprofen (IBP) to create inclusion complexes of ibuprofen and CD. Mixtures of IBP and trimethyl-β-CD showed new powder X-ray diffraction peaks after SC-CO₂ processing, although samples after processing with β-CD showed identical X-ray diffraction patterns with the physical mixture. The differential scanning calorimetry curves of samples after processing with trimethyl-β-CD showed no fusion peak of IBP and a new melting peak at around 185 °C. The physicochemical properties are similar to the co-precipitated samples of IBP and trimethyl-β-CD. Therefore, inclusion complex between IBP and trimethyl-β-CD was successfully prepared using SC-CO₂ technique. No inclusion formation was found when nitrogen was used as the supercritical fluid. Complexation of IBP and CD would not occur only on a high-pressure condition. The solubility of cyclodextrin into SC-CO₂ might play an important role in the formation of the inclusion complex.