Synchronization of coupled oscillators on small-world networks

We investigate the synchronous dynamics of Kuramoto oscillators and van der Pol oscillators on Watts-Strogatz type small-world networks. The order parameters to characterize macroscopic synchronization are calculated by numerical integration. We focus on the difference between frequency synchronization and phase synchronization. In both oscillator systems, the critical coupling strength of the phase order is larger than that of the frequency order for the small-world networks. The critical coupling strength for the phase and frequency synchronization diverges as the network structure approaches the regular one. For the Kuramoto oscillators, the behavior can be described by a power-law function and the exponents are obtained for the two synchronizations. The separation of the critical point between the phase and frequency synchronizations is found only for small-world networks in the theoretical models studied.     

Hydrogen-bonded assemblies of two-electron reduced mixed-valence [XMo12O40] (X = P and Si) with p-phenylenediamines

Hydrogen-bonded assemblies of the two-electron reduced mixed-valence Keggin clusters [PMo(12)O(40)](5-) and [SiMo(12)O(40)](6-) were obtained by the one-pot electron-transfer reactions between p-phenylenediamine (PPD) or 2,3,5,6-tetramethyl-PPD (TMPPD) (donors) and H(+)(3)[PMo(12)O(40)](3-) or H(+)(4)[SiMo(12)O(40)](4-) (acceptors) in CH(3)CN. The redox states of the [PMo(12)O(40)](5-) and [SiMo(12)O(40)](6-) clusters were confirmed by the redox titrations and electronic absorption measurements. In (HPPD(+))(3)(H(+))(2)[PMo(12)O(40)](5-)(CH(3)CN)(3-6) (1), the N-H ~ O hydrogen-bonded interactions between the monoprotonated HPPD(+) (or diprotonated H2PPD(2+)) and the [PMo(12)O(40)](5-) resulted in a windmill-like assembly and hydrophilic one-dimensional channels are formed with a cross-sectional area of 0.065 nm(2), and these are filled by the CH(3)CN molecules. Also, the CH(3)CN molecules in salt 1 were removed by immersing the single crystals of 1 into H(2)O, CH(3)OH, and C(2)H(5)OH solvents. In the compound, (HTMPPD(+))(6)[SiMo(12)O(40)](6-)(CH(3)CN)(6) (2), the N-H ~ O hydrogen-bonded interactions between the monoprotonated HTMPPD(+) molecules and the [SiMo(12)O(40)](6-) formed a "Saturn-ring"-like assembly. Each Saturn-ring was arranged into an hexagonally packed array via hydrogen-bonded and π-stacking interactions of HTMPPD(+), while the CH(3)CN solvent present in salt 2 are only found in the zero-dimensional isolated cavities.     

A Structurally Robust Chiral Borate Ion: Molecular Design,Synthesis, and Asymmetric Catalysis

Catalysis by chiral weakly-coordinating anions (WCAs) remains underdeveloped due to the lack of a molecular design strategy for exploiting their characteristics, such as the non-nucleophilic nature. Here, we report the development of a chiral borate ion comprising an O,N,N,O-tetradentate backbone, which ensures hitherto unattainable structural robustness. Upon pairing with a proton, the hydrogen borate acts as an effective catalyst for the asymmetric Prins-type cyclization of vinyl ethers, providing access to structurally and stereochemically defined dihydropyrans. The key to selectivity control is the distinct ability of the borate ion to discriminate the prochiral faces of the acyclic oxonium ion intermediate and dictate the regiochemical outcome. We anticipate that this study paves the way for exploring the untapped potential of WCA catalysis for selective chemical synthesis.     

Syntheses and electronic structures of one-electron-oxidized group 10 metal(II)-(disalicylidene)diamine complexes (metal = Ni, Pd, Pt)

Group 10 metal(II) complexes of H2tbu-salen (H2tbu-salen = N,N'-bis(3',5'-di-tert-butylsalicylidene)ethylenediamine) and H2tbu-salcn (H2tbu-salcn = N,N'-bis(3',5'-di-tert-butylsalicylidene)-1,2-cyclohexanediamine) containing two 2,4-di(tert-butyl)phenol moieties, [Ni(tbu-salen)] (1a), [Ni(tbu-salcn)] (1b), [Pd(tbu-salen)] (2a), [Pd(tbu-salcn)] (2b), and [Pt(tbu-salen)] (3), were prepared and structurally characterized by X-ray diffraction, and the electronic structures of their one-electron-oxidized species were established by spectroscopic and electrochemical methods. All the complexes have a mononuclear structure with two phenolate oxygens coordinated in a very similar square-planar geometry. These complexes exhibited similar absorption spectra in CH2Cl2, indicating that they all have a similar structure in solution. Cyclic voltammograms of the complexes showed a quasi-reversible redox wave at E1/2 = 0.82-1.05 V (vs Ag/AgCl), corresponding to formation of the relatively stable one-electron-oxidized species. The electrochemically oxidized or Ce(IV)-oxidized species of 1a, 2a, and 3 displayed a first-order decay with a half-life of 83, 20, and 148 min at -20 degrees C, respectively. Ni(II) complexes 1a and 1b were converted to the phenoxyl radicals upon one-electron oxidation in CH2Cl2 above -80 degrees C and to the Ni(III)-phenolate species below -120 degrees C. The temperature-dependent conversion was reversible with the Ni(III)-phenolate ground state and was found to be a valence tautomerism governed by the solvent. One-electron-oxidized 1b was isolated as [Ni(tbu-salcn)]NO3 (4) having the Ni(II)-phenoxyl radical ground state. One-electron-oxidized species of the Pd(II) complexes 2a and 2b were different from those of the Ni(II) complexes, the Pd(II)-phenoxyl radical species being the ground state in CH2Cl2 in the range 5-300 K. The one-electron-oxidized form of 2b, [Pd(tbu-salcn)]NO3 (5), which was isolated as a dark green powder, was found to be a Pd(II)-phenoxyl radical complex. On the other hand, the ESR spectrum of the one-electron-oxidized species of Pt(II) complex 3 exhibited a temperature-independent large g anisotropy in CH2Cl2 below -80 degrees C, while its resonance Raman spectrum at -60 degrees C displayed nu8a of the phenoxyl radical band at 1600 cm-1. These results indicated that the ground state of the Pt(II)-phenoxyl radical species has a large distribution of the radical electron spin at the Pt center. One-electron oxidation of 3 gave [Pt(tbu-salen)]NO3 (6) as a solid, where the oxidation state of the Pt center was determined to be ca. +2.5 from the XPS and XANES measurements.