Adsorption of molecular SiO2 on a clean Si(1 0 0) surface

We have investigated the adsorption of molecular (gaseous) SiO₂ on a clean Si(1 0 0) p(2 × 2) reconstructed surface using density functional theory based methods. The SiO₂ molecule is found to be chemisorbed on various sites on the Si surface and the most energetically favourable structure is on top of the dimers. The minimum energy pathways for the various adsorption channels indicate that the reaction is barrierless in all cases. The corresponding vibrational spectrum is also calculated and the adsorbed molecules are, as expected, found to have red-shifted vibrational frequencies. The energetically favourable adsorption sites and adsorption energies are comparable to the results found for SiO.     

Geometric Counting on Wavefront Real Spherical Spaces

We provide L~p-versus L~∞-bounds for eigenfunctions on a real spherical space Z of wavefront type. It is shown that these bounds imply a non-trivial error term estimate for lattice counting on Z. The paper also serves as an introduction to geometric counting on spaces of the mentioned type.     

Compact operator semigroups applied to dynamical systems

A right chain ordered semigroup is an ordered semigroup whose right ideals form a chain. In this paper we study the ideal theory of right chain ordered semigroups in terms of prime ideals, completely prime ideals and prime segments, extending to these semigroups results on right chain semigroups proved in Ferrero et al. (J Algebra 292:574–584, 2005).     

Algebras that satisfy Auslander’s condition on vanishing of cohomology

Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of cohomology of finitely generated modules. The failure of this conjecture—by a 2003 counterexample due to Jorgensen and Şega—motivates the consideration of the class of rings that do satisfy Auslander’s condition. We call them AC rings and show that an AC Artin algebra that is left-Gorenstein is also right-Gorenstein. Furthermore, the Auslander–Reiten Conjecture is proved for AC rings, and Auslander’s G-dimension is shown to be functorial for AC rings that are commutative or have a dualizing complex.     

Van Vleck’s functional equation for the sine

We solve Van Vleck’s functional equation on semigroups with an involution in terms of multiplicative functions.     

Towards Solar Energy Storage in the Photochromic Dihydroazulene–Vinylheptafulvene System

One key challenge in the field of exploitation of solar energy is to store the energy and make it available on demand. One possibility is to use photochromic molecules that undergo light‐induced isomerization to metastable isomers. Here we present efforts to develop solar thermal energy storage systems based on the dihydroazulene (DHA)/vinylheptafulvene (VHF) photo/thermoswitch. New DHA derivatives with one electron‐withdrawing cyano group at position 1 and one or two phenyl substituents in the five‐membered ring were prepared by using different synthetic routes. In particular, a diastereoselective reductive removal of one cyano group from DHAs incorporating two cyano groups at position 1 turned out to be most effective. Quantum chemical calculations reveal that the structural modifications provide two benefits relative to DHAs with two cyano groups at position 1: 1) The DHA–VHF energy difference is increased (i.e., higher energy capacity of metastable VHF isomer); 2) the Gibbs free energy of activation is increased for the energy‐releasing VHF to DHA back‐reaction. In fact, experimentally, these new derivatives were so reluctant to undergo the back‐reaction at room temperature that they practically behaved as DHA to VHF one‐way switches. Although lifetimes of years are at first attractive, which offers the ultimate control of energy release, for a real device it must of course be possible to trigger the back‐reaction, which calls for further iterations in the future.     

The 6,6‐Dicyanopentafulvene Core: A Template for the Design of Electron‐Acceptor Compounds

The electron‐accepting ability of 6,6‐dicyanopentafulvenes (DCFs) can be varied extensively through substitution on the five‐membered ring. The reduction potentials for a set of 2,3,4,5‐tetraphenyl‐substituted DCFs, with varying substituents at the para‐position of the phenyl rings, strongly correlate with their Hammett σ_p‐parameters. By combining cyclic voltammetry with DFT calculations ((U)B3LYP/6‐311+G(d)), using the conductor‐like polarizable continuum model (CPCM) for implicit solvation, the absolute reduction potentials of a set of twenty DCFs were reproduced with a mean absolute deviation of 0.10 eV and a maximum deviation of 0.19 eV. Our experimentally investigated DCFs have reduction potentials within 3.67–4.41 eV, however, the computations reveal that DCFs with experimental reduction potentials as high as 5.3 eV could be achieved, higher than that of F₄‐TCNQ (5.02 eV). Thus, the DCF core is a template that allows variation in the reduction potentials by about 1.6 eV.