Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Synthesis of 9-arylamino- and (Z)-9-arylimino-9H-pyrrolo[1,2-a]indoles by reactions of 2-(pyrrol-1-yl)benzaldehydes with aryl amines

Heating mixtures of 2-(pyrrol-1-yl)benzaldehydes and aryl amines under argon afforded 9-arylamino-9H-pyrrolo[1,2-a]indoles, via cyclization of the resulting 2-(pyrrol-1-yl)benzaldimine intermediates. Heating in the presence of oxygen afforded (Z)-9-arylimino-9H-pyrrolo[1,2-a]indoles, which were successfully hydrolyzed with hydrochloric acid to give pyrrolo[1,2-a]indol-9-ones.     

Deuterium isotope effects on hydrophobic interactions: the importance of dispersion interactions in the hydrophobic phase

Hydrogen/deuterium isotope effects on hydrophobic binding were examined by means of reversed-phase chromatographic separation of protiated and deuterated isotopologue pairs for a set of 10 nonpolar and low-polarity compounds with 10 stationary phases having alkyl and aryl groups bonded to the silica surface. It was found that protiated compounds bind to nonpolar moieties attached to silica more strongly than deuterated ones, demonstrating that the CH/CD bonds of the solutes are weakened or have less restricted motions when bound in the stationary phase compared with the aqueous solvent (mobile phase). The interactions responsible for binding have been further characterized by studies of the effects of changes in mobile phase composition, temperature dependence of binding, and QSRR (quantitative structure-chromatographic retention relationship) analysis, demonstrating the importance of enthalpic effects in binding and differentiation between the isotopologues. To explain our results showing the active role of the hydrophobic (stationary) phase we propose a plausible model that includes specific contributions from aromatic edge-to-face attractive interactions and attractive interactions of aliphatic groups with the pi clouds of aromatic groups present as the solute or in the stationary phase.     

The Electronic Structure of Azuleno[1,2,3-cd]phenalene and Azuleno[5,6,7-cd]phenalene,a Comparison

The photoelectron (PE.) spectra of azuleno[l, 2, 3-cd]phenalene ( 1 ) and azuleno- [5,6,7-cd]phenalene( 2 ) have been recorded. The first five bands of both compounds could be assigned to transitions corresponding to removal of electrons from 4a₂, 6b₁, 5b₁, 3a₂ and 4b_l orbitals. This assignment is based mainly on a comparison between the observed ionization potentials and orbital energies calculated in a HMO and a PPP model. The UV./VIS. polarized absorption spectrum of 1 in the region 10000–45000 cm^?1 has been measured by means of the stretched film technique. The measurements were performed in polyethylene sheets at 77°K. Several bands could be assigned to π* ← π transitions calculated by a PPP-CI method. A comparison between the electronic structures of 1 and 2 is made by means of a simple HMO diagram.     

Development of chiral pincer palladium complexes bearing a pyrroloimidazolone unit. Catalytic use for asymmetric Michael addition

Novel pincer palladium complexes having chiral hexahydro-1H-pyrrolo[1,2-c]imidazolone groups were designed and prepared. Catalytic asymmetric Michael addition of isopropyl 2-cyanopropionate to ethyl vinyl ketone was catalyzed by the chiral pincer palladium complex to give isopropyl 2-cyano-2-methyl-5-oxoheptanoate with high enantioselectivity (up to 83% ee). [structure: see text]     

Reaction of 3,4-disubstituted 1,2,5-oxadiazole 2-oxides with dipolarophiles : Substituent and solvent effect on the reaction courses

A variety of symmetrically or unsymmetrically 3,4-disubstituttd furoxans such as dicyano, dialkyl, diacyl, bis(phenylsulfonyl), N.N'-dialkyldicarbamoyl, 3(or 4)-methyl-4(or -3)-phenyl(or nitro, ethoxy, phenoxy, phenylthio, pyrrolidinyl, phenylsulfonyl), 3(or 4)-ethyl-4(or -3)phcnyl, and 3(or 4)-ethoxy-4(or -3)-phenylsulfonylruroxan reacted with dipolarophiles in toluene or xylene at the refluxing temperature to give nitrone-type 1,3-dipolar cycloadducts, 5-substituted 1-aza-2,8-dioxabicyclo-[3.3.0]octanes and/or 3-substituted 2-isoxazoline 2-oxides. On the other hand, some of the furoxans gave 2-isoxazolines via nitrile oxide 1,3-dipolar cycloaddition in a toluene (or xylene)-DMF solvent at the refluxing temperature.     

High-performance fluorescent particles prepared via miniemulsion polymerization

Highly fluorescent polymer particles were prepared with Eu beta-diketonates complex as a fluorophore by miniemulsion polymerization technique. Eu beta-diketonates complex has a long decay time, a large Stokes shift, and very narrow emission bands in comparison with other organic fluorescent compounds. Aqueous miniemulsion was prepared by mixing monomer, crosslinker, hydrophobe, and Eu beta-diketonates complex and then putting the mixture into an aqueous solution of surfactant, followed by ultrasonication. An aqueous solution of initiator was added to the miniemulsion to obtain fluorescent polymer particles, which were monodispersed without aggregation. Particle size was decreased to deca-nano scale by increasing the amount of surfactant. Fluorescent intensity was increased by using Eu beta-complex coordinated with additional ligand. Further fluorescence quantum yields and fluorescent properties in the presence of DNA were investigated to the confirm superiority of Eu beta-diketonates complexes in polymer particles.     

Synthesis of 12-deoxyroyleanone, cryptoquinone, 11,14-dihydroxy-8,11,13-abietatrien-7-one, and related derivatives from dehydroabietic acid

Naturally occurring abietane quinones and hydroquinone, namely, 12-deoxyroyleanone (1a), cryptoquinone (4a), and 11,14-dihydroxyabieta-8,11,13-trien-7-one (5a), together with the epimers of tryptoquinones D (2) and F (3), were first synthesized from dehydroabietic acid (6).     

Photoinduced Molecular Transformations. Part 142. One-step syntheses of 1H-benz[f]indole-4,9-diones and 1H-indole-4,7-diones by a new regioselective photoaddition of 2-amino-1,4-naphthoquinones and 2-amino-1,4-benzoquinones with alkenes

The 2,3-dihydro-1H-benz[f]indole-4,9-diones 3a–d , h were formed in a one-step reaction in 13–82% yield by an unprecedented [3 + 2] regioselective photoaddition of 2-amino-1,4-naphthoquinone ( 1 ) with various electronrich alkenes 2 (Scheme 1, Table). The [3 + 2] photoadducts derived from 1 with vinyl ethers and vinyl acetate gave 1H-benz[f]indole-4,9-diones 4e , f , i , in 33–72% yield, by spontaneous loss of the corresponding alcohol or AcOH from the resulting adducts; 4i has a kinamycin skeleton. The [3 + 2] photoaddition also took place on irradiation of the differently substituted amino-1,4-benzoquinones 6 , 7 , and 12 and excess alkenes 2 in benzene, giving 1H-indole-4,7-dione derivatives 13 and 14 (Scheme 3), 15a and 16 (Scheme 4), and 18 (Scheme 4), respectively. The initial products in these photoadditions were proved to be hydroquinones, the air oxidation of which yielded the heterocyclic quinones; 2,3-dihydro-2-methoxy-2-methyl-5-phenyl-1H-indole-1,4,7-triyl triacetate ( 19 ) was isolated after treatment of the crude photoaddition mixture obtained from 2-amino-5-phenyl-1,4-benzoquinone ( 7 ) and 2-methoxyprop-1-ene ( 2f ) with Ac₂O and pyridine under N₂. A pathway leading to the annelated hydroquinones involving ionic intermediates arising from an electron transfer in these photoadditions is proposed (Scheme 5).     

Xenophilic complexes bearing a Tp(R) Ligand, [Tp(R)M--M'Ln] [Tp(R) = Tp(iPr2), Tp(#) (Tp(Me2,4-Br)); M=Ni, Co, Fe, Mn; M'Ln = Co(CO)4, Co(CO)3(PPh3), RuCp(CO)2]: the two metal centers are held together not by covalent interaction but by electrostatic attraction

A series of dinuclear complexes, [Tp(R)M--M'L(n)] [Tp(iPr(2) )M--Co(CO)(4) (1; M=Ni, Co, Fe, Mn); Tp(#)M--Co(CO)(4) (1'; M=Ni, Co); Tp(#)Ni--RuCp(CO)(2) (3')] (Tp(iPr(2) )=hydrotris(3,5-diisopropylpyrazolyl)borato; Tp(#) (Tp(Me(2),4-Br))=hydrotris(3,5-dimethyl-4-bromopyrazolyl)borato), has been prepared by treatment of the cationic complexes [Tp(iPr(2) )M(NCMe)(3)]PF(6) or the halo complexes [Tp(#)M--X] with the appropriate metalates. Spectroscopic and crystallographic characterization of 1-3' reveals that the tetrahedral, high-spin Tp(R)M fragment and the coordinatively saturated carbonyl-metal fragment (M'L(n)) are connected only by a metal-metal interaction and, thus, the dinuclear complexes belong to a unique class of xenophilic complexes. The metal-metal interaction in the xenophilic complexes is polarized, as revealed by their nu(CO) vibrations and structural features, which fall between those of reference complexes: covalently bonded species [R--M'L(n)] and ionic species [M'L(n)](-). Unrestricted DFT calculations for the model complexes [Tp(H(2) )Ni--Co(CO)(4)], [Tp(H(2) )Ni--Co(CO)(3)(PH(3))], and [Tp(H(2) )Ni--RuCp(CO)(2)] prove that the two metal centers are held together not by covalent interactions, but by electrostatic attractions. In other words, the obtained xenophilic complexes can be regarded as carbonylmetalates, in which the cationic counterpart interacts with the metal center rather than the oxygen atom of the carbonyl ligand. The xenophilic complexes show divergent reactivity dependent on the properties of donor molecules. Hard (N and O donors) and soft donors (P and C donors) attack the Tp(R)M part and the ML(n) moiety, respectively. The selectivity has been interpreted in terms of the hard-soft theory, and the reactions of the high-spin species 1-3' with singlet donor molecules should involve a spin-crossover process.