Fisher Information of Free-Electron Landau States

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.     

Interaction between the end groups and the main chain of conjugated polymers by time-resolved EPR and fluorescence spectroscopy

ABSTRACT

Interaction between a zinc porphyrin (ZnPor) as the end-group and poly(9,9-di-n-octylfluorene-2,7-vinylene) (PFV) as the main chain in a porphyrin end-modified fluorescent conjugated polymer, ZnPFV, was studied by time-resolved electron paramagnetic resonance (EPR) and fluorescence spectroscopy. While fluorescence from the PFV part of ZnPFV showed a spectral profile almost identical to that of a PFV oligomer without end-modification, the emission spectrum of the ZnPor part exhibited a much broader profile compared to that of the reference zinc porphyrin monomer. Based on the analysis of lifetimes and quantum yields, it was found that radiative rate constant of the ZnPor part was enhanced by nearly three times. The observed unusual enhancement in the radiative rate constant was rationalised in terms of a partial π-conjugation between the end group and the main chain, as a result of co-planarisation in fluid solution. On the other hand, the time-resolved EPR spectrum of ZnPFV at 100?K basically showed a similar spectral pattern to that of the reference zinc porphyrin, but with significant differences in zero-field spitting parameters and initial population ratios. The π-system of the excited triplet state is deduced to deviate from D_4h symmetry in the end zinc porphyrin groups. The obtained results show that interaction of the porphyrin end group with the main chain of the polymer significantly influences the excited singlet state properties of the porphyrin, while its triplet state properties were affected to a lesser extent.     

Intramolecular 1,3‐Dipolar Cycloaddition‐Mediated Stereoselective Synthesis of Disubstituted Cyclopentane: A Simple Model for the Cyclopentane Ring System of Polycyclic Oroidine Alkaloids

We present a diastereoselective synthesis of disubstituted cyclopentane 8 having a nitrogen‐containing quaternary carbon center, which is found in axinellamine A ( 5 ) and related compounds. During this work, we found that the 1,3‐dipolar cycloaddition product 24 immediately underwent intramolecular redox reaction at the newly formed morpholin‐2‐one moiety, thus affording disubstituted cyclopentane containing a tertiary amine ( 9 ) stereoselectively in good yield. The amine 9 was successfully converted into guanidine 31 , which corresponds to 8 , through iminium cation–enamine isomerization.     

Sesquifulvalene Trapping as a [12+2] Adduct with Tetracyanoethylene

Sesquifulvalene (1) is a substance of considerable theoretical interest¹ which is expected to have a significant contribution to its structure from the dipolar resonance form 1b,² and hence an exceptionally low bond order for the central double bond. Although a wide variety of annelated and otherwise substituted sesquifulvalenes have been prepared and characterized,³ the parent substance has proved remarkably elusive. Very recently, a preparation of 1 in crystalline form has been reported, based upon elimination of an acetoxy-11,12-dihydrosesquifulvalene derivative.⁴     

A Convenient General Access to α-Sulfenylated Acetophenones and Alkanones

Friedel-Crafts acylation of arenes with methylthio- (1) or phenylthio-acetyl chloride (2) provides ready access to α-methylthio- or α-phenylthio-substituted acetophenones. The acyl chlorides 1 and 2 reacted also with organoaluminum reagents to give α-sulfenylated alkanones.     

Synthesis and Metal Complex Formation of a Bis(terpyridine) Derivative with a Phenylacetylene Framework

A new bis(terpyridine) derivative with a phenylacetylene framework was synthesized via a stepwise terpyridine construction strategy. The addition of ZnCl₂ to a solution of the bis(terpyridine) in chloroform resulted in UV/vis and ¹H NMR spectral changes because of complex formation.     

Novel synthesis of zerumbone-pendant derivatives and their biological activity

Zerumbone 1, having powerful latent reactivity and containing two conjugated double bonds and a double conjugated carbonyl group is the major component of the essential oil of wild ginger, Zingiber zerumbet Smith. The conjugation system plays an important role in the expression of biological activity. N-Bromosuccinimide (NBS) reaction of 1 gave high reactive intermediate 2 with an exo-methylene group, which was obtained from 1 quantitatively. Treatment of 2 with nucleophiles gave various zerumbone-pendant derivatives, including C–H, C–O, C–N, and C–C bond formation, maintaining the conjugation system through S_N2′-type reaction. Almost all zerumbone-pendant derivatives showed a good value of IC₅₀ against the suppressive effect of NO generation. Among them, amine derivative 5, binding with 2 mol of zerumbone, showed the strongest activity (IC₅₀: 0.24 μM).     

Comprehensive characterisation of the E phase of 6-octyl-2-phenylazulene

Molecular dynamics in the soft crystal, E phase of 6-octyl-2-phenylazulene was studied by X-ray diffraction, and dielectric and Fourier transform infrared spectroscopies. Clear dielectric dispersion is observed due to the head-to-tail disordering in a kHz range around 400 K. The CH stretching frequencies exhibit more pronounced shifts at the phase transition point from the high-temperature ordered crystal to the E phase than that at the melting from the E phase to the isotropic liquid. The results are discussed in comparison with a typical E series, 4-n-alkyl-4′-isothiocyanatobiphenyl (n being the number of carbon atoms in the alkyl group).     

Controlling the photochemical reactions of alkenes by light-path length effects of a microchannel reactor

Photoirradiation of Me₂CO–H₂O solution of pent-4-en-1-ol (1a) with a high-pressure mercury lamp in a test tube gave 8-hydroxyoctan-2-one (3a) in 66 % yield along with oxetane (4a) and the isomer (4a′) in 10 % yield. Irradiation of the running Me₂CO–H₂O solution of 1a in the flow system of a microchannel reactor (MCR) gave mainly 4a. The photoreaction of 1,1-diphenylethene (2a) with triethylamine gave a Markovnikov-type adduct (5a) and an anti-Markovnikov-type adduct (6a). The use of the MCR enhanced the production of 5a. These phenomena were explained by the light-path length effects of the MCR.