Experimental and Computational Studies of Anti‐Bredt Amidinium Salts

Experimental and computational investigations of anti‐Bredt amidinium salts are presented. Calculations show that the pyramidalization of an amino group can significantly destabilize the formal carbocation center of amidiniums, due to the decreased π donation. In some cases, the unfavorable ‐I effect of nitrogen surpasses its beneficial +M effect, and amidiniums become less stable than iminiums. It is shown that although 1‐aza‐3‐azonia[3.3.1]bicyclo‐non‐2‐enes can be isolated, they feature a nonclassical reactivity, which is more typical for iminium than amidinium salts, such as pronounced electrophilicity and azomethineylide instead of carbene formation.     

An Effective Mass Theorem for the Bidimensional Electron Gas in a Strong Magnetic Field

We study the limiting behavior of a singularly perturbed Schr?dinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane (x, y) and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr?dinger equations in the plane (x, y), coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator.