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.     

Aligned carbon cones in free‐standing UV‐Curable polymer composite

A concept where an alternating electric field (dielectrophoresis) is used to assemble and align carbon nanocone particles (CNCs) into microscopic wires in self‐supporting polymer films is demonstrated. The particle fraction is kept low (one‐tenth of the percolation threshold of isotropic mixture), which allows uniform dispersion and efficient UV curing. The alignment leads to the conductivity enhancement of three to four orders of magnitude (from ～10^?7 to ～10^?3 S/m) in the alignment direction. It does not require passing current so the material can be isolated from the alignment electrodes. This prevents electrodes attaching to the film, if the film is adhesive in nature. The alignment can be done using either in‐plane or out‐of‐plane geometries. It is proposed that this concept could be applied in areas such as electrostatic discharge applications where inexpensive conductive or dissipative materials and macroscopic uniformity are prerequisites. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Iridium Catalyzed Carbocyclizations: Efficient (5+2) Cycloadditions of Vinylcyclopropanes and Alkynes

Third‐row transition metal catalysts remain a largely untapped resource in cycloaddition reactions for the formation of medium‐sized rings. Herein, we report the first examples of iridium‐catalyzed inter‐ and intramolecular vinylcyclopropane (VCP)–alkyne (5+2) cycloadditions. DFT modeling suggests that catalysis by iridium(I) proceeds through a mechanism similar to that previously reported for rhodium(I)‐catalyzed VCP–alkyne cycloadditions, but a smaller free energy span for iridium enables substantially faster catalysis under favorable conditions. The system is characterized by up to quantitative yields and is amenable to an array of disubstituted alkynes and vinylcyclopropanes.     

Hydrogenation of Esters to Alcohols with a Well‐Defined Iron Complex

We present the first base‐free Fe‐catalyzed ester reduction applying molecular hydrogen. Without any additives, a variety of carboxylic acid esters and lactones were hydrogenated with high efficiency. Computations reveal an outer‐sphere mechanism involving simultaneous hydrogen transfer from the iron center and the ligand. This assumption is supported by NMR experiments.