Twice Q-polynomial distance-regular graphs of diameter 4

It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.     

On the output function in a Ginsburg’s machine

We give the form of the output function in Ginsburg’s machine in which the input and output dictionaries are abelian groups and the transition function is of a special form.     

Theory of chemical bonds in metalloenzymes XXII: a concerted bond-switching mechanism for the oxygen–oxygen bond formation coupled with one electron transfer for water oxidation in the oxygen-evolving complex of photosystem II

ABSTRACT

QM(UB3LYP)/MM(AMBER) calculations were performed for the locations of the transition structure (TS) of the oxygen–oxygen (O–O) bond formation in the S₄ state of the oxygen-evolving complex (OEC) of photosystem II (PSII). The natural orbital (NO) analysis of the broken-symmetry (BS) solutions was also performed to elucidate the nature of the chemical bonds at TS on the basis of several chemical indices defined by the occupation numbers of NO. The computational results revealed a concerted bond switching (CBS) mechanism for the oxygen–oxygen bond formation coupled with the one-electron transfer (OET) for water oxidation in OEC of PSII. The orbital interaction between the σ-HOMO of the Mn(IV)₄–O₍₅₎ bond and the π*-LUMO of the Mn(V)₁=O₍₆₎ bond plays an important role for the concerted O–O bond formation for water oxidation in the CaMn₄O₆ cluster of OEC of PSII. One electron transfer (OET) from the π-HOMO of the Mn(V)₁=O₍₆₎ bond to the σ*-LUMO of the Mn(IV)₄–O₍₅₎ bond occurs for the formation of electron transfer diradical, where the generated anion radical [Mn(IV)₄–O₍₅₎]^-? part is relaxed to the ?Mn(III)₄?…?O₍₅₎^- structure and the cation radical [O₍₆₎=Mn(V)₁]⁺ ? part is relaxed to the ⁺O₍₆₎–Mn(IV)₁? structure because of the charge-spin separation for the electron-and hole-doped Mn–oxo bonds. Therefore, the local spins are responsible for the one-electron reductions of Mn(IV)₄->Mn(III)₄ and Mn(V)₁->Mn(IV)₁. On the other hand, the O₍₅₎^- and O₍₆₎⁺ sites generated undergo the O–O bond formation in the CaMn₄O₆ cluster. The Ca(II) ion in the cubane- skeleton of the CaMn₄O₆ cluster assists the above orbital interactions by the lowering of the orbital energy levels of π*-LUMO of Mn(V)₁=O₍₆₎ and σ*-LUMO of Mn(IV)₄–O₍₅₎, indicating an important role of its Lewis acidity. Present CBS mechanism for the O–O bond formation coupled with one electron reductions of the high-valent Mn ions is different from the conventional radical coupling (RC) and acid-base (AB) mechanisms for water oxidation in artificial and native photosynthesis systems. The proton-coupled electron transfer (PC-OET) mechanism for the O–O bond formation is also touched in relation to the CBS-OET mechanism.     

Triphilic pentablock copolymers with perfluoroalkyl segment in central position

Adding perfluoroalkyl (PF) segments to amphiphilic copolymers yields triphilic copolymers with new application profiles. Usually, PF segments are attached as terminal blocks via Cu(I) catalyzed azide-alkyne cycloaddition (CuAAC). The purpose of the current study is to design new triphilic architectures with a PF segment in central position. The PF segment bearing bifunctional atom transfer radical polymerization (ATRP) initiator is employed for the fabrication of triphilic poly(propylene oxide)-b-poly(glycerol monomethacrylate)-b-PF-b-poly(glycerol monomethacrylate)-b-poly(propylene oxide) PPO-b-PGMA-b-PF-b-PGMA-b-PPO pentablock copolymers by a combined ATRP and CuAAC reaction approach. Differential scanning calorimetry indicates the PF-initiator to undergo a solid–solid phase transition at 63°C before the final crystal melting at 95°C. This is further corroborated by polarized optical microscopy and X-ray diffraction studies. The PF-initiator could successfully polymerize solketal methacrylate (SMA) under typical ATRP conditions producing well-defined Br-PSMA-b-PF-b-PSMA-Br triblock copolymers that are then converted into PPO-b-PSMA-b-PF-b-PSMA-b-PPO pentablock copolymer via CuAAC reaction. Subsequently, acid hydrolysis of the PSMA blocks afforded water soluble well-defined triphilic pentablock copolymers PPO-b-PGMA-b-PF-b-PGMA-b-PPO with fluorophilic central segment, hydrophilic middle blocks, and lipophilic outer blocks. The triphilic block copolymers could self-assemble, depending upon the preparatory protocol, into spherical and filament-like phase-separated nanostructures as revealed by transmission electron microscopy.