Recent advances in metal catalysts with hybrid ligands

This review summarises some recent developments of the metal complexes of hetero-functional hybrid ligands of C-, N-, O-, P- and S-donors. It highlights the ligand designs, synthetic pathways, structural motifs and catalytic prowess of these complexes.     

A sharper uncertainty principle

The work strengthens the result established by L. Cohen on uncertainty principle involving phase derivative. We propose stronger uncertainty principles not only in the classical setting for Fourier transform, but also for self-adjoint operators. We also deduce the conditions that give rise to the equal relation of the uncertainty principle. Examples are provided to show that the new uncertainty principle is truly sharper than the existing ones in literature.     

A justification for the use of approximate transition amplitudes in semiclassical surface hopping

Recent work has shown that a certain surface hopping form of the wave function is capable of obtaining highly accurate transition probabilities for nonadiabatic problems. It has also been found that it is necessary to include hops in classically forbidden regions in order to obtain this level of accuracy at low energies. The amplitude for the hops in this surface hopping expansion of the wave function has the typical p^?1/2 semiclassical divergence at the turning points in the classical motion. While this singularity is an integrable divergence, the divergent behavior complicates the numerical evaluation of the integrals over hopping points that is present in the surface hopping expressions. Numerical evidence has shown that only small errors are incurred at most energies if these singular hopping amplitudes are replaced with a nonsingular approximation. This agreement is surprising, since the exact and approximate amplitudes differ greatly in the turning point region, and this region is expected to make important contributions to the transition probability at low energies. A numerical analysis is presented in this work that provides a justification as to why this numerically useful approximation works as well as it does.     

Electron transfer reactions between vinylmagnesium bromide and phenyl-substituted methyl chlorides

The reaction of vinylmagnesium bromide ( 1 ) with trityl chloride ( 2 ) was investigated and the products were identified as triphenylmethane ( 3 ) (81 %), acetylene ( 4 ) (74%), trityl peroxide ( 6 ) (4%), and minute amounts of triphenylpropene ( 7 ) and p-diphenylmethyltetraphenylmethane ( 8 ). The results indicate that 1 possesses reducing property. The reaction mixture showed an ESR spectrum identical with that for trityl radical and the CIDNP of enhanced absorption for 4-H of l-diphenylmethylene-4-trityl-2,5-cyclohexadiene ( 9 ). Trapping experiment with styrene decreased the amount of 3 but had no effect on the formation of 4. The reducing property of 1 is discussed and one electron transfer mechanism for the reaction of 1 with 2 is proposed. S-T₀ mixing between trityl and·MgBr occurred and the coupling of polarized trityl radical with another trityl radical resulted in the formation of polarized dimeric product. The different character between the reaction of 1 and 2 and that of 1 and diphenylmethyl chloride ( 10 ) may be rationalized by the different electron-accepting abilities between 2 and 10. The origin of CIDNP effect shown by the product tetraphenylethane ( 11 ) for the reaction of 1 with 10 is also explained according to Kaptein's sign rule.