Geometric phase within the complex quantum Hamilton-Jacobi formalism

We derive a geometric phase using the quantum kinematic approach within the complex quantum Hamilton-Jacobi formalism. The single valuedness of the wave function implies that the geometric phase along an arbitrary path in the complex plane must be equal to an integer multiple of 2π. The nonzero geometric phase indicates that we travel along the path through the branch cut of the phase function from one Riemann sheet to another.     

Quenching of IR luminescence of erbium, neodymium, and ytterbium beta-diketonate complexes by ligand C-H and C-D bonds

The effect of CH and CD quenching on the luminescence lifetime of Er(3+) Nd(3+) and Yb(3+) in the Cs[Ln(HFA)(4)] system has been quantified, and we have shown that for Er(3+) ions the quenching is dominated by the nearest neighbor CH oscillators, whereas for Nd(3+) ions the roles of more distant CH oscillators and nearest neighbor CD oscillators are important.     

A Semple-type approach to a problem of Goursat: The multi-flag case

We consider the problem of classifying the orbits within a tower of fibrations with fibers diffeomorphic to projective planes and we generalize the tower of fiber bundles due to J. Semple. This tower, which was rediscovered by Montgomery and Zhitomirskii in the context of subriemannian geometry, admits a natural action of the diffeomorphism group of affine 3-space, and these orbits correspond to classes of Goursat multi-flags. We demonstrate that it is possible to classify many of these orbits by elementary means by appealing to some basic tools in projective geometry, and the combinatorics of spatial curves.     

A Directly Patternable,Click‐Active Polymer Film via Initiated Chemical Vapor Deposition

Click‐active surfaces patterned at 200 nm resolution are demonstrated using the dual functional polymeric film, poly(propargyl methacrylate) (PPMA). The commercially available monomer of propargyl methacrylate (PMA) is polymerized in a single step by initiated chemical vapor deposition (iCVD). FT‐IR and X‐ray photoelectron spectroscopy confirm retention of the click‐active acetylene functional group in the bulk and surface of the iCVD film, respectively. Treating substrates with silane coupling agents prior to deposition results in grafting of iCVD PPMA polymers onto various inorganic surfaces. This grafting technique provides the chemical and mechanical stability required for the PPMA layer to survive the subsequent wet chemical steps used for click functionalization. Successful attachment of an azido‐functionalized coumarin dye is demonstrated. Moreover, the PPMA film displays direct positive‐tone sensitivity to e‐beam irradiation, which enables e‐beam patterning without the use of a resist layer. Direct e‐beam exposure of the multifunctional PPMA iCVD layer results in a 200 nm pattern to which quantum dot nanoparticles are selectively conjugated on the substrates by click chemistry.

     

Near IR luminescent rare earth 3,4,5,6-tetrafluoro-2-nitrophenoxide complexes: Synthesis,X-ray crystallography and spectroscopy

3,4,5,6-Tetrafluoro-2-nitrophenoxide (L⁻) forms complexes with rare earth M³⁺ ions. X-ray crystal structures of substances with the stoichiometry Cs₂ML₅ · mEt₂O (M = Er, m = 0; M = Er, m = 1; M = Y, m = 1.5; M = Yb, m = 1) have been determined. Each M³⁺ ion is coordinated to two bidentate and three monodentate L⁻ ions; Et₂O does not coordinate to M³⁺. The complexes absorb both visible and ultraviolet light. The solid Er³⁺ and Yb³⁺ complexes have unusually long lifetimes (τ = 20.2 μs and 142 μs, respectively) for the decay of their luminescence in the near-infrared region following photoexcitation; this is attributed to the lack of C–H bonds and other high frequency oscillators that could cause vibrational quenching.     

Characterisation of organometallic and coordination compounds by solvent-free matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry

Insoluble or low solubility organometallic and coordination compounds have been characterised by matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry, with solvent-free sample preparation being the key step toward successful analysis.     

Initiated chemical vapor deposition of alternating copolymers of styrene and maleic anhydride

Initiated chemical vapor deposition (iCVD) of alternating copolymer thin films has been achieved for the first time. Copolymerization is desirable for maleic anhydride (Ma) since this monomer does not homopolymerize to an appreciable extent. At conditions where the observed deposition rates for styrene (S) and Ma homopolymers were only 0 and 5.5 nm/min, respectively, combining the two monomers resulted in a much higher deposition rate of 75.4 nm/min. iCVD processes utilize low energy (<30 W) to generate peroxy radicals from initiator molecules while avoiding degradation of functional groups in the monomers. Indeed, full retention of the anhydride functionality from the Ma monomer and avoidance of undesirable side reactions was observed in iCVD of poly(styrene-alt-maleic anhydride) (PSMa) copolymer films. Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and 13C nuclear magnetic resonance (NMR) conclusively demonstrate that all of the copolymer films contain 50% styrene and 50% Ma (within experimental error), irrespective of gas feed ratios employed during the deposition. The 13C NMR signal in the 136-140 ppm region from the quaternary carbon in styrene and additional distortionless enhancement polarization transfer experiments confirmed that the copolymers are strictly alternating. Varying the gas feed ratio of Ma to styrene provided control over deposition rates and number-average molecular weights. Number-average molecular weights varied from 1380 to 4680 g/mol, and deposition rates varied from 6.3 to 75.4 nm/min.     

Torsional eigenvalues of the water trimer on several ab initio potential surfaces

Eigenvalues corresponding to the three torsional degrees of freedom were calculated for the water trimer and its deuterated isotopomer in four sets of calculations involving different potential energy surfaces. The four potential surfaces were developed in this work by reparametrization of the CKL function against four sets of ab initio energies calculated with and without counterpoise correction. Transition frequencies corresponding to the low-frequency torsional motions of the trimer were calculated and then compared with those found from experiment to assess the accuracy of each potential energy surface. Although reparametrization of the CKL function to a set of counterpoise-corrected energies yielded transition energies that are in qualitative agreement with those from experiment, reparametrization to another set of counterpoise-corrected energies resulted in highly inaccurate values of the transition energy. As a consequence, our results demonstrate that caution must be exercised in the implementation of the counterpoise method as it does not always lead to more accurate ab initio calculations. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 233–252, 1998     

Computational method for the quantum Hamilton-Jacobi equation: bound states in one dimension

An accurate computational method for the one-dimensional quantum Hamilton-Jacobi equation is presented. The Mobius propagation scheme, which can accurately pass through singularities, is used to numerically integrate the quantum Hamilton-Jacobi equation for the quantum momentum function. Bound state wave functions are then synthesized from the phase integral using the antithetic cancellation technique. Through this procedure, not only the quantum momentum functions but also the wave functions are accurately obtained. This computational approach is demonstrated through two solvable examples: the harmonic oscillator and the Morse potential. The excellent agreement between the computational and the exact analytical results shows that the method proposed here may be useful for solving similar quantum mechanical problems.     

Stereoselective synthesis of (E)-mannosylidene derivatives using the Wittig reaction

Stabilized ylides Bu(3)P=CH(EWG), where EWG is an ester or nitrile group, react with 2,3,4,6-tetra-O-benzylmannono-1,5-lactone giving high yields of mannosylidene derivatives; in contrast to the glucose and galactose analogues, the (E)-mannosylidenes are predominant (E:Z > 9:1), thus minimizing dipole-dipole repulsions in the Wittig reactions. NMR indicates chair-like conformations for solutions of the (E)-mannopyranosylidenes, but not for those (Z)-isomers where data are available (EWG = CN or CO(2)Et). X-ray crystallography shows an approximately twist-boat conformation for the tetra-O-benzyl-protected (Z)-mannosylideneacetonitrile.