Compact complex homogeneous manifolds with large automorphism groups

Let X be a compact complex homogeneous manifold and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. It is well-known that the dimension of Aut(X) is bounded by an integer that depends only on n=dim X. Moreover, if X is K?hler then dimAut (X)≤n(n+2) with equality only when X is complex projective space. In this article examples of non-K?hler compact complex homogeneous manifolds X are given that demonstrate dimAut(X) can depend exponentially on n. Let X be a connected compact complex manifold of dimension n. The group of holomorphic automorphisms of X, Aut(X), is a complex Lie group [3]. For a fixed n>1, the dimension of Aut(X) can be arbitrarily large compared to n. Simple examples are provided by the Hirzebruch surfaces F _m , m∈N, for which dimAut(F _m )=m+5, see, e.g. [2, Example 2.4.2]. If X is homogeneous, that is, any point of X can be mapped to any other point of X under a holomorphic automorphism, then the dimension of the automorphism group of X is bounded by an integer that depends only on n, see [1, 2, 6]. The estimate given in [2, Theorem 3.8.2] is roughly dimAut(X)≤(n+2) ⁿ . For many classes of manifolds, however, the dimension of the automorphism group never exceeds n(n+2). For example, it follows directly from the classification given by Borel and Remmert [4], that if X is a compact homogeneous K?hler manifold, then dimAut(X)≤n(n+2) with equality only when X is complex projective space P ⁿ . It is an old question raised by Remmert, see [2, p. 99], [6], whether this same bound applies to all compact complex homogeneous manifolds. In this note we show that this is not the case by constructing non-K?hler compact complex homogeneous manifolds whose automorphism group has a dimension that depends exponentially on n. The simplest case among these examples has n=3m+1 and dimAut(X)=3m+3 ^m , so the above conjectured bound is exceeded when n≥19. These manifolds have the structure of non-trivial fiber bundles over products of flag manifolds with parallelizable fibers given as the quotient of a solvable group by a discrete subgroup. They are constructed using the original ideas of Otte [6, 7] and are surprisingly similar to examples found there. Generally, a product of manifolds does not result in an automorphism group with a large dimension relative to n. Nevertheless, products are used in an essential way in the construction given here, and it is perhaps this feature that caused such examples to be previously overlooked. Oblatum 13-X-97 & 24-X-1997     

Synthesis of a Helical Bilayer Nanographene

A rigid, inherently chiral bilayer nanographene has been synthesized as both the racemate and enantioenriched M isomer (with 93 % ee) in three steps from established helicenes. This folded nanographene is composed of two hexa‐peri‐hexabenzocoronene layers fused to a [10]helicene, with an interlayer distance of 3.6 Å as determined by X‐ray crystallography. The rigidity of the helicene linker forces the layers to adopt a nearly aligned AA‐stacked conformation, rarely observed in few‐layer graphene. By combining the advantages of nanographenes and helicenes, we have constructed a bilayer system of 30 fused benzene rings that is also chiral, rigid, and remains soluble in common organic solvents. We present this as a molecular model system of bilayer graphene, with properties of interest in a variety of potential applications.     

Electrochemical synthesis of π-indenyl-π-(3)-1,2-dicarbollyliron(III)

Co-electrolysis of potassium 1,2-dicarbadodecahydroundecaborate and indene in 0.1N sodium bromide solution in dimethylsulfoxide using iron electrodes afforded -indenyl--(3)-1,2-dicarbollyliron(III).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 764–765, April, 1993.     

Inhibitors of plasmin that extend into both the S and S' binding sites: cooperative interactions between S1 and S2

A new procedure for the synthesis of cyclohexanone-based inhibitors of serine proteases is reported. In this procedure the reactive ketone functionality is carried through the synthesis in masked form as a TBDMS-protected alcohol. Deprotection followed by oxidation of the alcohol generates the final form of the inhibitor. Two new inhibitors, which interact with the S1-S3 and S2' subsites of plasmin, are synthesized using this procedure. Inhibitors 1 and 2 have IC50 values against plasmin of 20 and 24 microM, respectively. The inhibition studies show that cooperative binding of inhibitors in the S1 and S2 subsites of plasmin is important for determining inhibitor selectivity.     

Phosphahelicenes with (Thio)Phosphinic Acid and Ester Functions by the Oxidative Photocyclisation Approach

Phosphahelicenes with thiophosphinic acid and ester functions have been obtained by the oxidative photocyclisation of olefins bearing both a benzophenanthrene and a benzophosphole unit. When the method has been extended to olefins bearing a partially saturated benzophospholene unit, a divergent regioselectivity of the photocyclisation step has been observed, leading to new helicenes in which the phosphorus function is located on the external rim of the helical backbone. The observed regioselectivity correlates well with the free-valence numbers of the atoms involved in the photocyclisation reaction (DFT calculations).     

Ruthenium-vinylhelicenes: remote metal-based enhancement and redox switching of the chiroptical properties of a helicene core

Introducing metal-vinyl ruthenium moieties onto [6]helicene results in a significant enhancement of the chiroptical properties due to strong metal-ligand electronic interactions. The electro-active Ru centers allow the achievement of the first purely helicene-based redox-triggered chiroptical switches. A combination of electrochemical, spectroscopic, and theoretical techniques reveals that the helicene moiety is a noninnocent ligand bearing a significant spin density.     

Influence of hydrogen bonding on excitonic coupling and hierarchal structure of a light-harvesting porphyrin aggregate

Helical porphyrin nanotubes of tetrakis(4-sulfonatophenyl)porphyrin (TSPP) were examined in DCl/D(2)O solution using resonance Raman and resonance light scattering spectroscopy to probe the influence of hydrogen bonding on the excitonic states. Atomic force microscopy reveals similar morphology for aggregates deposited from DCl/D(2)O and from HCl/H(2)O solution. Deuteration results in subtle changes to the aggregate absorption spectrum but large changes in the relative intensities of Raman modes in the J-band excited resonance Raman spectra, revealing relatively more reorganization along lower-frequency vibrational modes in the protiated aggregate. Depolarization ratio dispersion and changes in the relative Raman intensities for excitation wavelengths spanning the J-band demonstrate interference from overlapping excitonic transitions. Distinctly different Raman excitation profiles for the protiated and deuterated aggregates reveal that isotopic substitution influences the excitonic structure of the J-band. The deuterated aggregate exhibits a nearly two-fold increase in intensity of resonance light scattering as a result of an increase in the coherence number, attributed to decreased exciton-phonon scattering. We propose that strongly coupled cyclic N-mers, roughly independent of isotopic substitution, largely decide the optical absorption spectrum, while water-mediated hydrogen bonding influences the further coherent coupling among them when they are assembled into nanotubes. The results show that, similar to natural light-harvesting complexes such as chlorosomes, hydrogen bonding can have a critical influence on exciton dynamics.     

Diastereo‐ and Enantioselective Synthesis of Organometallic Bis(helicene)s by a Combination of C?H Activation and Dynamic Isomerization

Homochiral and heterochiral cis‐bis‐cycloplatinated‐[6]helicene derivatives 1 b^{1, 2} , as representative examples of platina[6]helicenes that share a common platinum center, have been prepared. A diastereo‐ and enantioselective synthesis, which combines CH activation and dynamic isomerization from heterochiral structure 1 b² into homochiral structure 1 b¹ , is also described. Overall, this isomerization process results in the transfer of chiral information from one helicene moiety to the other one. The chiroptical properties of homochiral (P)‐ and (M)‐ 1 b¹ were greatly modified upon oxidation into their corresponding (P)‐ and (M)‐diiodo‐Pt^IV complexes ( 5 ). The changes were also analyzed by performing theoretical calculations. C? H activation in the synthesis of organometallic helicenes is further demonstrated by the preparation of cis‐bis‐cycloplatinated‐[8]helicene 1 c .