Electronic molecule-like spectrum of quantum wells in crossed fields

We show that an electron confined to a single finite parabolic quantum well in crossed electric and magnetic fields can behave as a double quantum well system. The magnetic field is parallel to the heterostructure layers and the electric field is perpendicular to those. For a suitable choice of both fields and quantum well width, the electron can be confined to a double quantum well effective potential that is very similar to the electronic potential model for diatomic molecules. The double quantum well spectrum is calculated using a numerical algorithm based on semiclassical methods. A physical interpretation of this quantum system is given based on the analogy to the electrons bound to diatomic molecules.     

More compact invariant manifolds appearing in the non-linear coupling of oscillators

Near partially elliptic rest points of generic families of vector fields or transformations, many types of normally hyperbolic invariant compact manifolds can appear, diffeomorphic to intersections of quadrics. To cite this article: M. Chaperon et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Deformations of incompressible bodies with free boundaries

Communicated by C. Dafermos     

Monitoring photopolymerization reactions with optical pyrometry

This article describes the development of optical pyrometry (OP) as a new analytical technique for the continuous monitoring of the progress of both free‐radical and cationic photopolymerizations. The method is rapid, reproducible, and very easy to implement. A temperature profile of a photopolymerization can be obtained. Preliminary studies have shown that the temperatures of some polymerizing monomers can easily reach temperatures in excess of 250 °C. The effects of the mass and reactivity of the monomer, light intensity, structures, and concentrations of the photoinitiators and monomers as well as the presence or absence of oxygen on various free‐radical and cationic photopolymerizations were examined with this method. Coupling of real‐time infrared spectroscopy with OP provides a convenient method for simultaneously monitoring both the chemical conversion and the temperature of a photopolymerization. This combined technique affords new insights into the effects of temperature‐induced autoacceleration on the course of photopolymerizations. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 579–596, 2003     

Comprehensive study of the methyl effect on the solvolysis rates of bridgehead derivatives

The effect of a bridgehead methyl group on the hydride ion affinity in the gas phase of bicyclo[1.1.1]pent-1-yl (1+), 1-norbornyl (3+), cubyl (5+), 1-adamantyl (7+), bicyclo[2.2.2]oct-1-yl (9+),and bicyclo[3.1.1]hept-1-yl (11+) cations has been studied using density functional theory and ab initio methods. It is concluded that the methyl group always increases the stability of the substituted cations. The effect of the solvent on the stability of methyl-substituted cations in relation to the unsubstituted cations has been studied using the polarizable continuum model of the self-consistent reaction field theory. In the case of rearranging cations, the nucleophilic assistance of the solvent is determined by means of the interaction energy of the corresponding water complexes. It is concluded that the solvent causes the relative stabilization of the parent cations. As a consequence, most of the methyl-substituted bridgehead derivatives show a lower solvolysis rate than the corresponding unsubstituted compounds. A nonqualitative explanation of the methyl effect on the relative stability of bridgehead cations in both gas phase and solution is given for the first time. The ratios of solvolysis products in the case of rearranging bridgehead cations have also been computed from the relative stability of the intermediate water complexes.     

A new insight on the structural changes of linear quadrupole liquids

Molecular-dynamics simulations for linear quadrupole liquids are presented. The study is carried out for two different molecular lengths at constant density and a number of temperatures and quadrupole moments. All the simulated thermodynamic states correspond to the condensed phases and some of them show typical features of a solid structure. Furthermore, a change on the preferred intermolecular orientation in the liquid phase is observed from a shifted parallel molecular arrangement to a perpendicular orientation as the quadrupole raises. This change depends on the quadrupole moment as well as on the molecular length and is put in relation with the solid structure of different "diatomic" molecules such as nitrogen, ethane, and acetylene. The appearance of a plastic solid phase at low quadrupole moment and density is also justified. A thoroughly discussion about the availability of classical perturbation theories for this kind of systems is presented.     

Continuous chirality measures in transition metal chemistry

The definition of the continuous chirality measure(CCM) is provided and its applications are summarized in this tutorial review, with special emphasis on the field of transition metal complexes. The CCM approach, developed in recent years, provides a quantitative parameter that evaluates the degree of chirality of a given molecule. Many quantitative structural correlations with chirality have been identified for most of the important families of metal complexes. Our recent research has shown that one can associate the chirality measures with, e.g., enantioselectivity in asymmetric catalysis. We also explore a fragment approach to chirality in which we investigate which part of a molecule is responsible for the chirality-associated properties of a given family of compounds.     

E- and Z-isomerism of 2-acetylthiophene oximes

A study on the oximation of a number of 2-acetylthiophenes in order to ascertain the validity of contradictory results previously described is reported. The fact that the steric hindrance is smaller in 2-acetylthiophenes unsubstituted at position-3 than in acetylbenzenes allows in these cases the formation of Z oximes, which even can predominate on the E oximes in the case of a + M substitution at position-5. In the paper is also shown that the E/Z ratio of 2-acetylthiophene oximes can be deduced from the ¹H-nmr spectrum of the crude oxime mixture.     

Thermal and photochemical rearrangement of bicyclo[3.1.0]hex-3-en-2-one to the ketonic tautomer of phenol. Computational evidence for the formation of a diradical rather than a zwitterionic intermediate

The ground state (S(0)) and lowest-energy triplet state (T(1)) potential energy surfaces (PESs) concerning the thermal and photochemical rearrangement of bicyclo[3.1.0]hex-3-en-2-one (8) to the ketonic tautomer of phenol (11) have been extensively explored using ab initio CASSCF and CASPT2 calculations with several basis sets. State T(1) is predicted to be a triplet pipi lying 66.5 kcal/mol above the energy of the S(0) state. On the S(0) PES, the rearrangement of 8 to 11 is predicted to occur via a two-step mechanism where the internal cyclopropane C-C bond is broken first through a high energy transition structure (TS1-S(0)()), leading to a singlet intermediate (10-S(0)()) lying 25.0 kcal/mol above the ground state of 8. Subsequently, this intermediate undergoes a 1,2-hydrogen shift to yield 11 by surmounting an energy barrier of only 2.7 kcal/mol at 0 K. The rate-determining step of the global rearrangement is the opening of the three-membered ring in 8, which involves an energy barrier of 41.2 kcal/mol at 0 K. This high energy barrier is consistent with the fact that the thermal rearrangement of umbellulone to thymol is carried out by heating at 280 degrees C. Regarding the photochemical rearangement, our results suggest that the most efficient route from the T(1) state of 8 to ground state 11 is the essentially barrierless cleavage of the internal cyclopropane C-C bond followed by radiationless decay to the S(0) state PES via intersystem crossing (ISC) at a crossing point (S(0)()/T(1)()-1) located at almost the same geometry as TS1-S(0)(), leading to the formation of 10-S(0)() and the subsequent low-barrier 1,2-hydrogen shift. The computed small spin-orbit coupling between the T(1) and S(0) PESs at S(0)()/T(1)()-1 (1.2 cm(-)(1)) suggests that the ISC between these PESs is the rate-determining step of the photochemical rearrangement 8 --> 11. Finally, computational evidence indicates that singlet intermediate 10-S(0)() should not be drawn as a zwitterion, but rather as a diradical having a polarized C=O bond.