An ab initio molecular orbital study of the grignard reagents CH3MgCl and [CH3MgCl]2: The Schlenk equilibrium

Ab initio molecular orbital calculations are used to study the modified Schlenk equilibrium: 2RMgCl (RMgCl)² MgR₂ + MgCl₂ Mg(Cl₂)MgR₂ with R=H and CH₃. In the absence of any solvents, calculations indicate that the formation of the various possible bridged dimers (RMgCl)₂ is substantially exothermic. However, using dimethylether as a model solvent, we show that the formation of the dimer (Me₂O)(CH₃)Mg(Cl₂)Mg(CH₃)(OMe₂) is exothermic only when entropic effects are included.     

Lower Bounds for the Lp-Norm in Terms of the Mellin Transform

Given a measurable function f on (0, ) with Mellin transformF(s), let |f|_p denote the L^p-norm of f with respect to the measuredx/x. We prove that under certain assumptions, for instanceif f is real and non-negative and F() converges for in an openinterval and F() 0, then wherec_p (2e)^–1. We derive similar inequalities for complex-valuedf, for the L^p-norm of the derivative of f, and for the supremumof real-valued f and of its derivative. The lower bounds areeminently applicable when f is a convolution product.     

Binding of the two-valence-electron metal ions Sc(+), Ti(2+), and V(3+) to the second-row hydrides BeH(2), BH(3), NH(3), OH(2), and FH: a computational study

We report results from a computational study of the binding in complexes formed from one of the transition-metal ions Sc(+), Ti(2+), or V(3+), each of which has two valence electrons outside an argon core, and one of the second-row hydrides FH, OH(2), NH(3), BH(3), or BeH(2). The complexes that involve the electron-rich ligands FH, OH(2), and NH(3) have strong ion-dipole components to their binding. There are large stabilization energies for sigma-interactions that transfer charge from occupied lone-pair natural bond orbitals on the F, O, or N atom of the (idealized) Lewis structure into empty non-Lewis orbitals on the metal ions; these interactions effectively increase electron density in the bonding region between the metal ion and liganded atom, and the metal ions in these complexes act in the capacity of Lewis acids. The complexes formed from the electron-poor hydrides BH(3) and BeH(2) consistently incorporate bridging hydrogen atoms to support binding, and there are large stabilization energies for interactions that transfer charge from the Be-H or B-H bonds into the region between the metal ion and liganded atom. The metal ions in Sc(+)-BeH(2), Ti(2+)-BeH(2), Ti(2+)-BH(3), and V(3+)-BH(3) act in the capacity of Lewis acids, whereas the scandium ion in Sc(+)-BH(3) acts as a Lewis base.