Spectroscopic and theoretical studies of optically active porphyrin dimers: a system uninterpretable by exciton coupling theory.

The electronic excited states of a meso-meso beta-beta doubly linked bis-porphyrin are comprehensively investigated by measuring its circular dichroism (CD) and magnetic circular dichroism (MCD) spectra. The observed spectroscopic properties are rationalized by DFT calculations. The frontier molecular orbitals (MOs) are constructed by the linear combinations of the constituent monomers' four MOs. Comparison of a theoretical CD spectrum based on time-dependent DFT (TDDFT) with the experimental spectra resulted in the assignment of the helical conformation of the dimer. This assignment is contrary to the previous assignment based on the point-dipole approximation (exciton coupling theory).     

Polynomially convex hulls of graphs on the sphere

Let be the graph of a continuous map of the unit sphere of into , and the polynomially convex hull of . Several examples of for are given, which have different properties from the known ones for .

     

Beam-size measurement with optical diffraction radiation at KEK accelerator test facility

An experiment on the investigation of optical diffraction radiation (ODR) from a slit target as a possible tool for noninvasive electron beam-size diagnostics has been performed at the KEK accelerator test facility. The experimental setup has been installed at the diagnostics section of the extraction line. We have performed the first incoherent ODR observation from a slit target. The measured angular distributions are in reasonable agreement with the theoretical expectation. The beam-size effect onto the ODR angular pattern has been observed. Moreover, the sensitivity to the beam size as small as 14 microm has been achieved.     

Magnetic circular dichroism study of directly fused porphyrins.

The magnetic circular dichroism (MCD) spectra of doubly and triply linked fused bisporphyrins (2MD and 2MT, M = Ni, Zn, Cu, Pd, and H2) and triply linked higher oligomers (3ZnT and 4ZnT) have been measured, and their Q-bands assigned based on the results of INDO/s calculations. In contrast to the Faraday A term observed for the Q(0,0) band of Ni(II) tetraphenylporphyrin, a single positive Faraday B term was observed for the lowest energy transition of the fused systems. The calculations indicated that the molecular orbitals (MOs) of the directly fused porphyrins consist of linear combinations of the constituent monomeric MOs, and that the effect of lowering the symmetry is always larger on the lowest unoccupied molecular orbital (LUMO) than on the highest occupied molecular orbital (HOMO). On the basis of Michl's perimeter model, these features can be correlated with the observed positive MCD signs in the near infrared region. A weak absorption band at 600-700 nm for the fused dimers can be assigned to a short-axis polarized Q transition.     

Numerical Nahm transform for 2-caloron solutions

A new numerical method for performing the Nahm transform for charge k=2 caloron is presented. The Weyl equations with boundary impurities are solved directly and the determination of the appropriate basis to the linear system is established. The action densities of the 2-calorons with 10 moduli parameters are shown.