Broken orbital symmetry and the description of valence hole states in the tetrahedral [CrO4]2− anion

The localization of ligand-based valence holes in the tetrahedral complex ion [CrO₄]^2? in a crystalline environment is studied by SCF calculations on the hole states, with progressively less restrictions on the spatial symmetry of the molecular orbitals. The final wavefunctions are obtained by constructing, from the symmetry broken SCF solutions, wavefunctions that exhibit again the proper transformation properties under the operations of T _d . The crystal environment of the [CrO₄]^2? anion is represented by a point charge model. In contrast with the situation for core hole states, the projection afterwards into T _d symmetry is important. The final ionization energies, which are obtained from projected C _3v adapted SCF solutions, are reduced considerably (?3 eV) with respect to the T _d ΔSCF results, but the ordering of the states has not changed essentially. The calculated ionization energies compare favourably with results of XPS experiments on Na₂CrO₄. The evaluation of the energies of projected symmetry broken SCF solutions requires the calculation of hamiltonian matrix elements between determinantal wavefunctions built from mutually non-orthogonal orbital sets. An efficient method for the calculation of such matrix elements is presented.     

Unfoldings of quasi-periodic tori in reversible systems

A general KAM-theory for reversible systems is given. The cases of both maximal and lower-dimensional tori are covered. In some cases parameters are needed for persistence, therefore an unfolding theory is developed.     

Geometric Desingularization of a Cusp Singularity in Slow–Fast Systems with Applications to Zeeman’s Examples

The cusp singularity—a point at which two curves of fold points meet—is a prototypical example in Takens’ classification of singularities in constrained equations, which also includes folds, folded saddles, folded nodes, among others. In this article, we study cusp singularities in singularly perturbed systems for sufficiently small values of the perturbation parameter, in the regime in which these systems exhibit fast and slow dynamics. Our main result is an analysis of the cusp point using the method of geometric desingularization, also known as the blow-up method, from the field of geometric singular perturbation theory. Our analysis of the cusp singularity was inspired by the nerve impulse example of Zeeman, and we also apply our main theorem to it. Finally, a brief review of geometric singular perturbation theory for the two elementary singularities from the Takens’ classification occurring for the nerve impulse example—folds and folded saddles—is included to make this article self-contained.     

The thermal metal-insulator phase transition in (EDO-TTF)2PF6

ABSTRACT

The thermal metal-insulator phase transition in the π-stacked (EDO-TTF)₂PF₆ charge transfer salt is of the Peierls type. It is related to geometrical reorganisations and charge ordering phenomena. We report that dimerising displacements are involved in the mechanism of this transition. By using periodic quantum chemical calculations, we find a double well potential in which dimerisation and charge localisation become manifest. By analysing the nuclear wavefunctions we discuss the mechanism of the phase transition in terms of thermal fluctuations.     

Light‐Induced Demixing of Hole or Electron Transporting Moieties

Summary: This paper describes the synthesis of two triphenylamine monomers (hole conducting) and one triazine monomer (electron conducting) which differ in their copolymerization parameters because of their styrene and vinyl ester nature. A blend of triphenylamine monomer and poly(ethylene glycol) and mixtures of both types of monomers (triphenylamine and triazine) were illuminated through a line mask, creating laterally modulated radicals, thus leading to lateral demixing. The experiments with mixtures of triphenylamine and triazine monomers show that the concentration of p‐ or n‐type polymers can be modulated laterally in a controlled way.

AFM measurement of line pattern formed by illuminating a mixture of monomer 2 and 3 showing the height difference between illuminated and non‐illuminated areas.