Asymptotic Expansions of Posterior Distributions in Nonregular Cases

We study the asymptotic behaviour of the posterior distributions for a one-parameter family of discontinuous densities. It is shown that a suitably centered and normalized posterior converges almost surely to an exponential limit in the total variation norm. Further, asymptotic expansions for the density, distribution function, moments and quantiles of the posterior are also obtained. It is to be noted that, in view of the results of Ghosh et al. (1994, Statistical Decision Theory and Related Topics V, 183-199, Springer, New York) and Ghosal et al. (1995, Ann. Statist., 23, 2145-2152), the nonregular cases considered here are essentially the only ones for which the posterior distributions converge. The results obtained here are also supported by a simulation experiment.     

Current-less photoreactivity catalyzed by functionalized AFM tips

A spatially confined photocatalytic oxidation of a thin film of synthetic textile azo dye (Procion Red MX-5B) using TiO2-functionalized AFM probes is described.     

Studies on the exchange characteristics of [Co(NH3)6]3+ in amberlite IRC-50

Summary The exchange of Co(NH₃)₆]³⁺-ions on amberlite IRC-50 resin has been studied at room temperature. For this exchange process the cations are effective in the order: Cs⁺<Rb⁺<K⁺<Na⁺<Li⁺<NH₄ ⁺<Mg²⁺ <Ca²⁺<H⁺ and (C₂H₅)₄N<(CH₃)₄N⁺ ≪Cetyltrimethylammonium-ion <Cetylpyridinium-ion. The logarithm of the selectivity coefficient gives linear graphs when plotted against the radius of the hydrated ions or the reciprocals of theDebye-Hückel parameter?.     

Conformational effects on vibronic spectra and excited state dynamics of 3-fluorobenzoic acid dimer

Two conformational isomers of 3-fluorobenzoic acid dimer (3-FBA(2)) have been identified in a supersonic jet expansion by use of laser-induced fluorescence excitation (FE), UV-UV hole-burning, and dispersed fluorescence (DF) spectroscopic methods. In the FE spectrum, the S(1) origins of the two isomeric species appear at a frequency gap of only 24 cm(-1), and the vibronic intensities of the redshifted dimer (dimer I) are about two times weaker than those of dimer II. However, ab initio quantum chemistry calculations at the MP2/6-31G(**) level of theory predict that all the isomeric species of 3-FBA(2) have almost the same binding energy (approximately 17 kcal/mol) in the ground state. Furthermore, unlike benzoic acid dimer, the present system shows intense activity for a low-frequency mode in both the FE and DF spectra. With the aid of DFT (B3LYP/6-311G(**)) predicted normal mode frequencies, we have assigned the mode to the in-plane gear (cogwheel) vibration of the cyclic hydrogen-bonded frame of the dimer. The Franck-Condon profiles for vibronic excitation of the mode indicate that the distortion of the cyclic hydrogen bond frame as a result of S(1)<--S(0) excitation is larger for dimer I than dimer II. Moreover, the fluorescence lifetime at the S(1) zero-point level of the former is also significantly smaller than the latter. Using the predictions of configuration interaction singles calculations, we have proposed that the spectral and dynamical differences between the two isomeric species observed in this study are manifestations of the different characteristics of their S(1) surfaces. By measuring FE, DF, and hole-burning spectra of a mixed dimer between 3-fluobenzoic acid and benzoic acid we have shown that the isomeric features in the homodimer spectra are due to two locally excited rotamers of the 3-fluorobenzoic acid moiety.     

Impact of extended pi conjugation on methyl rotor-induced IVR in aromatic molecules

Laser-induced fluorescence excitation and resolved fluorescence spectra following excitations of the single vibronic levels (SVL) of p-vinyltoluene (p-VT) and p-vinylfluorobenzene (p-VFB) have been measured in a seeded supersonic free-jet expansion. A complete vibronic assignment of the fluorescence spectrum measured following excitation of the 0(0)0-band of p-VT has been presented. Normal vibrational modes in the S0 and S1 states of the molecule have been calculated by CASSCF method, and the correlation between the two set of modes is made by expressing the excited-state normal modes in terms of those of the ground state. The calculations predict that in the excited state methyl and vinyl torsional motions of p-VT are extensively mixed with many of the out-of-plane modes of the aromatic ring. Our resolved fluorescence spectral data measured following SVL excitations essentially agree with such predictions. In the excited state, the molecule exhibits a dramatically low threshold for the rotor-induced IVR in a supersonic jet expansion. Several mechanisms have been discussed to explain the phenomenon.     

Is there any three-center CBC bond in 1, 5-C2B3H5 and 1,5-C2B3H3?

Localized molecular orbitals, two- and three-center bond indices of 1,5-dicarba-closo-pentaborane ( 5 ) and 1,5-dicarba-closo-pentaborane ( 3 ) and their hydrocarbon analogs bicyclo [1,1,1]-pentane and [1,1,1] propellane, respectively, have been calculated using a suitable basis set. No previously reported three-center CBC bond has been found. However, a new three-center BCB bond has been observed in 1,5-dicarba-closo-pentaborane ( 5 ). © 1995 John Wiley & Sons, Inc.     

Sequential cross-metathesis/phosphorus-based olefination: stereoselective synthesis of 2,4-dienoates

A variety of stereodefined 2,4-dienoates have been prepared in a stereoselective manner by sequencing olefin cross-metathesis (CM) with phosphorus-based olefination reactions (Wittig and Horner-Wadsworth-Emmons) in good yield using commercially available reagents.     

Controlling diffusion in sol-gel derived monoliths

Redox probes were trapped within a silica monolith prepared in part with organoalkoxysilanes containing a quaternary ammonium functional group. The diffusion coefficients of the entrapped molecules were measured as the gels were slowly dried using chronoamperometry and cyclic voltammetry with ultramicroelectrodes. Gel-entrapped cobalt(II) tris(bipyridine) (Co(bpy)(3)(2+)) diffuses at rates similar to that measured in the sols by incorporating a small amount of the positively charged functional group in the matrix. In comparison, the diffusion coefficient of gel-entrapped ferricyanide (Fe(CN)(6)(3-)) drops an order of magnitude relative to its value in the sol soon after gelation. These results demonstrate the ease at which diffusion in hydrated gels can be easily controlled by simply changing the charge on the walls of the silica host.     

Synchrotron radiation circular dichroism spectroscopy of ribose and deoxyribose sugars, adenosine, AMP and dAMP nucleotides.

Synchrotron radiation circular dichroism (SRCD) spectra of ribose and deoxyribose sugars, adenosine, AMP and dAMP nucleotides and cyclic derivatives were measured in the vacuum ultraviolet region (down to 168 nm for sugars and 175 nm for adenine derivatives) and at different pH values (3, 6-7, 9-10) and temperatures (between 5 and 45 degrees C). The information content in the VUV region is important since the CD bands strongly depend on the chemical structure of the sugar, the presence and orientation of a phosphate group and the protonation state of adenine. On the other hand, single or double deprotonation of the phosphoric acid group has no influence on the spectra. We assign the vacuum ultraviolet (VUV) CD bands of the nucleoside and nucleotides to be due mainly to n-->pi* transitions in the adenine nucleobase based on a comparison with the absorption spectra. The CD bands of the sugars are due to n(O -->sigma*) transitions and are much smaller than the CD signal from the nucleotides in the VUV region. Bands are assigned to both pyranose and open-chain forms.     

A study on the electronic effect of <Emphasis Type="Italic">para</Emphasis> substituents in the aryloxy ring of the hydrazone ligands on the vanadium centre in a family of mixed-ligand [V<Superscript>V</Superscript>O(ONO)(OO)] complexes

[V^IVO(acac)₂] reacts with the methanolic solutions of tridentate dibasic ONO donor hydrazone ligands derived from the condensation of benzoyl hydrazine with either 2-hydroxyacetophenone (H₂L¹) or its para-substituted derivatives (H₂L^2–4) (general abbreviation H₂L), in the presence of vanillin (Hvan) in equimolar ratio under aerobic conditions generating the mixed-ligand oxovanadium(V) complexes of the type [V^VO(L)(van)], (1)–(4) in good yield. All the complexes are diamagnetic and exhibit only ligand-to-metal charge transfer (l.m.c.t.) band near 510 nm in addition to intra-ligand (π → π*) transition band near 330 nm in CH₂Cl₂ solution. ¹H-n.m.r. spectra of the complexes in CDCl₃ solution indicate the presence of two isomeric forms [(1A), (1B); (2A), (2B); (3A), (3B) and (4A), (4B)] in different ratios, which is explained by the interchange of the two binding sites of van⁻ motif between its coordinated equatorial and axial positions. Complexes display two quasi-reversible one electron reduction peaks near +0.10 V and near +0.30 V versus s.c.e. in CH₂Cl₂ solution which are attributed to the successive reduction of V^V→ V^IV and the V^IV→ V^III motifs, respectively. λ_max (for l.m.c.t. transition), and the two reduction potential values (E _1/2)^I (average of the first step anodic and first step cathodic peak potentials) and (E _1/2)^II (average of the second step anodic and second step cathodic peak potentials) of the complexes, are found to be linearly related to the Hammett constants (σ) of the substituents in the aryloxy ring of the hydrazone ligands. λ_max, (E _1/2)^I and (E _1/2)^II values show large dependence: dλ_max/dσ = 37.29 nm, d(E _1/2)^I/dσ = 0.21 V and d(E _1/2)^II/dσ = 0.21 V, respectively, on σ.