A molecular T-matrix approach to calculating Low-Energy Electron Diffraction intensities for ordered molecular adsorbates

We present a novel approach to calculating Low-Energy Electron Diffraction (LEED) intensities for ordered molecular adsorbates. First, the intra-molecular multiple scattering is computed to obtain a non-diagonal molecular T-matrix. This is then used to represent the entire molecule as a single scattering object in a conventional LEED calculation, where the Layer Doubling technique is applied to assemble the different layers, including the molecular ones. A detailed comparison with conventional layer-type LEED calculations is provided to ascertain the accuracy of this scheme of calculation. Advantages of this scheme for problems involving ordered arrays of molecules adsorbed on surfaces are discussed.     

Selective Ir-catalysed borylation of polycyclic aromatic hydrocarbons: structures of naphthalene-2,6-bis(boronate), pyrene-2,7-bis(boronate) and perylene-2,5,8,11-tetra(boronate) esters

The selectivity of the iridium boryl complex-catalysed reaction of pyrene and perylene with B2(pin)2 (pin = OCMe2CMe2O) has been employed in the synthesis of D(2h)-symmetry pyrene-2,7-(Bpin)2 and D(4h)-symmetry perylene-2,5,8,11-(Bpin)4 providing direct borylation of positions which are otherwise difficult to derivatise.     

Influence of hydrogen bonding on coordination polymer assembly

An extended dipyridyl ligand (L1) capable of hydrogen bonding with guest species via urea functionalities has been designed and synthesised. Assembly of a silver(I) coordination polymer of L1 is dependent on the nature of the hydrogen bond acceptor in a logical extension of the monopyridyl analogue.     

A version of Sharkovskii's theorem for differential equations

We present a version of the Sharkovskii cycle coexistence theorem for differential equations. Our earlier applicable version is extended here to hold with the exception of at most two orbits. This result, which (because of counter-examples) cannot be improved, is then applied to ordinary differential equations and inclusions. In particular, if a time-periodic differential equation has -periodic solutions with , for all , then infinitely many subharmonics coexist.

     

Finitary coding of Markov random fields

Summary There exists a finitary code from any stationary ergodic Markov random field to any i.i.d. random field of strictly lower entropy.     

Non-ohmic conductivity of barely localized electrons in three dimensions

We observe a rapid temperature variation and an electric field dependence of the d.c. conductivity in a carefully characterized sample of P doped Si. These results, combined with measurements of Raman scattering, far-infrared absorption and magnetic susceptibility, indicate a large characteristic electronic length (10⁴ times the donor Bohr radius) at a donor concentration just below the critical density of the metal-insulator transition.     

Direct observation of a large London penetration depth in an organic superconductor

Careful observation of the diamagnetic shielding signal in small fields applied along the a-axis of deuterated (TMTSF)₂ClO₄ crystals reveal a systematic dependence of the diamagnetic susceptibility on the thickness (b- and c-dimensions) of the crystals, which we explain by a macroscopically large value of 0.004 cm for the London penetration depth.