Ring Length Research Articles

ADENINE TAUTOMER ELECTRONIC STRUCTURAL SIGNATURES STUDIED USING DUAL SPACE ANALYSIS

Electronic structural signatures of the adenine-7H tautomer in its ground state ( X1A′) have been identified using dual space analysis. The RHF/TZVP and B3LYP/TZVP calculations employed in the present work have shown that proton transfer from N(9)to N(7)makes the purine rings of adenine-7H geometrically closer to purine rather than adenine-9H, at the cost distortion of the amino group local symmetry. The shifts in ring lengths in [Formula: see text] and [Formula: see text], which are proposed in this work as the summation of the bond lengths in the hex- and pentagon-rings, respectively, are [Formula: see text] and [Formula: see text] for adenine-9H and [Formula: see text] and [Formula: see text] for adenine-7H, respectively, from the corresponding rings in purine. We also demonstrate that energetic properties such as the orbital energies are insensitive to tautomerism. However, the N(9)to N(7)proton transfer significantly changes the dipole moments: a large increase from 2.44D (adenine-9H) to 7.49D (adenine-7H) is observed. Finally, four molecular orbitals, 27a′, 25a′, 24a′ and 23a′ are identified in momentum space as bearing the most important structural signatures of the adenine-7H tautomer.

Kondo Screening Cloud Around a Quantum Dot: Large-Scale Numerical Results

Measurements of the persistent current in a ring containing a quantum dot would afford a unique opportunity to finally detect the elusive Kondo screening cloud. We present the first large-scale numerical results on this controversial subject using exact diagonalization and density matrix renormalization group (RG). These extremely challenging numerical calculations confirm RG arguments for weak to strong coupling crossover with varying ring length and give results on the universal scaling functions. We also study, analytically and numerically, the important and surprising effects of particle-hole symmetry breaking.

What is the length of a knot in a polymer?

We give statistical definitions of the length, l, of a loose prime knot tied into a long, fluctuating ring macromolecule. Monte Carlo results for the equilibrium, good solvent regime show that < l > ~ N^t, where N is the ring length and t ~ 0.75 is independent of the knot topology. In the collapsed regime below the theta temperature, length determinations based on the entropic competition of different knots within the same ring show delocalization (t~1).

Controllable All-Optical Switch Using an EDF-Ring Coupled M-Z Interferometer

We propose a new all-optical switch for 1.55-/spl mu/m signal by using an erbium-doped fiber (EDF) ring resonator coupled to one arm of Mach-Zehnder interferometer. Because of the high nonlinearity of EDF and compensating losses in the ring by the gain of EDF amplifier, the switching power-length product is reduced to the order of 10/sup -4/ Wm. When we design the device with the ring length of 0.3 m, and adjust the 980-nm pump power from 14 to 19 mW, the gain changes from 3 to 4 dB, and then the switching power and switching time can be changed from 6 to 11 mW and 22 to 16 ns, respectively.

Single-charge-carrier-type sensing with an insulated Frisch ring CdZnTe semiconductor radiation detector

Performance optimization of an insulated Frisch ring design was investigated for a 3×3×6 mm CdZnTe planar semiconductor detector. The Frisch ring was composed of copper and was insulated from the detector surface with Teflon. Optimization variables included the Frisch ring length and the bias voltage. Optimized overall device performance was found using a 5 mm long Frisch ring extending from the cathode toward the anode, leaving a 1 mm separation between the Frisch ring and the anode. The best energy resolution observed was 1.7% full width at half maximum at 662 keV with the ring extending 4 mm from the cathode toward the anode.

Crystal structures and spectroscopic characterization of radical cations and dications of oligothiophenes stabilized by annelation with bicyclo[2.2.2]octene units: sterically segregated cationic oligothiophenes.

The remarkably stable SbF(6)(-) salts of the radical cations of bithiophene 1(2T) and terthiophene 1(3T), completely surrounded by bicyclo[2.2.2]octene (BCO) units, were obtained by one-electron oxidation of the neutral precursors with NO(+)SbF(6)(-), and their solid-state structures were determined by X-ray crystallography. In these radical cations, the presence of quinoidal character was apparent, as shown by the increased planarity and by comparison of the bond lengths with those of the neutral precursors. The shortest intermolecular pi-pi distances in the crystal structure of 1(2T)(*)(+)SbF(6)(-) (distance between two sp(2) carbon atoms, 4.89 A) and 1(3T)(*)(+)SbF(6)(-) (distance between an sp(2) carbon and a sulfur atom, 3.58 A) were found to be longer than the sums of the van der Waals radii of the corresponding atoms. In accord with this, no apparent change was observed in ESR and UV-vis-NIR spectra of solutions of 1(2T)(*)(+) and 1(3T)(*)(+) upon lowering the temperature, indicating that the pi- (or sigma-) dimer formation is inhibited in solution as well as in the solid state. The dications 1(2T)(2+) and 1(3T)(2+) were generated with the stronger oxidant SbF(5) in CH(2)Cl(2) at -40 degrees C and characterized by NMR spectroscopy. In the (1)H NMR spectra, two conformers were observed for each dication of both 1(2T)(2+) (transoid (t) and cisoid (c)) and 1(3T)(2+) (t,t and c,t) at room temperature due to the high rotational barrier around the inter-ring bond(s) between thiophene rings, which was caused by the enhanced double bond character of these bonds following two-electron oxidation. This is supported by DFT calculations (B3LYP/6-31G(d)), which predicted the rotational barriers in the dications of unsubstituted bithiophene and terthiophene to be 27.6 and 22.9 kcal mol(-)(1), respectively. In the case of quaterthiophene and sexithiophene surrounded by BCO frameworks 1(4T) and 1(6T), oxidation with even one molar equivalent of NO(+)SbF(6)(-) afforded the dication salts 1(4T)(2+)2SbF(6)(-) and 1(6T)(2+)2SbF(6)(-), which were isolated as stable single crystals and allowed the X-ray crystallography. In their crystal structures, the cationic pi-systems became planar again due to the great contribution of quinoidal resonance structures, and the pi-systems, which were arrayed in a parallel geometry, were also segregated by the steric effect of BCO units. The degree and tendency of changes in the bond lengths of thiophene rings of 1(4T)(2+) and 1(6T)(2+) as compared with neutral precursors were similar to those of 1(2T)(*)(+)SbF(6)(-) and 1(3T)(*)(+)SbF(6)(-), respectively, implying that the contribution of quinoidal character is modulated by the amount of positive charge per thiophene unit.

Stability and bifurcation in an integral-delay model of cardiac reentry including spatial coupling in repolarization.

We present the bifurcation analysis of a revised version of the integral-delay model [Courtemanche et al., Siam J. Appl. Math. 56, 119 (1996)] of reentry in a one-dimensional ring that includes a spatial coupling in the calculation of the action potential duration. This coupling is meant to reproduce the modulation of repolarization by the diffusive current flowing through the intercellular resistance. We show that coupling modifies the criterion for the stability of the period-1 solution, which is no longer uniquely related to the action potential restitution curve, but depends also on the degree of coupling between cells and on the dispersion relation of the velocity. Coupling also changes the scenario from an infinite-dimension Hopf bifurcation to a finite sequence of Hopf bifurcations that take place at different ring lengths.

Full optical analog to digital (A/D) converter based on Kerr-like nonlinear ring resonator

A new structure for a 4-bit full optical analog to digital converter (A/D) using Kerr-like nonlinear two-port ring resonator will be presented. By controlling the system parameters such as the coupling, the loss coefficients and the ring length, we propose a suitable optical A/D circuit which operates similar to successive approximation method. Our proposed idea can be easily realized by integrated optical circuit techniques (OIC).

Syntheses and structures of silicon analogues of cyclopropabenzenes

The reactions of an overcrowded diaryldilithiosilane, Tbt(Dip)SiLi 2 (Tbt=2,4,6-tris[bis(trimethylsilyl)methyl]phenyl; Dip=2,6-diisopropylphenyl), with o-dibromobenzene and 1,2,4,5-tetrabromobenzene resulted in the synthesis and isolation of the first stable silacyclopropabenzene and bis(silacyclopropa)benzenes (IUPAC name is 4,8-disilatricyclo[5.1.0.0 3,5]octa-1,3(5),6-triene), respectively. The crystallographic analyses and theoretical calculations revealed that the lengths of the juncture carboncarbon bonds of the mono- and bis(silacyclopropa)benzenes were marginally in the range of carboncarbon bond lengths of usual benzene rings. It is shown that this structural feature is attributable to a decrease in the strain energy of silacyclopropabenzenes relative to the corresponding cyclopropabenzenes, and the strain energy is a simple additive function of the number of the fused three-membered rings involving Si atom.

Lipophilicity of vinpocetine and related compounds characterized by reversed-phase thin-layer chromatography

A reversed-phase thin-layer chromatographic method was developed and applied to quantitate the lipophilicity of sparingly water-soluble eburnane alkaloids of therapeutic interest. Our method development included calibration, optimization and validation procedures, using also sets of auxiliary compounds. The log P TLC values of five relatively hydrophilic eburnanes were verified by stir-flask studies. The alkaloids were found to have lipophilicity values in the 2.9–4.8 log P TLC range. Conclusions on structure–lipophilicity relationships were drawn in terms of ring anellation, character and length of side chain, conformational preferences and moiety–solvent interactions, also supported by molecular mechanics studies.

The Length of Noetherian Polynomial Rings

We show that if R is a left Noetherian ring, then Here, for a Noetherian left module A, len A is its ordinal valued length as defined by Gulliksen (Gulliksen, (1973). T. H. A theory of length for noetherian modules. J. Pure Appl. Algebra 3:159–170), and ⊗ is the natural product on ordinal numbers.

Persistent currents in mesoscopic rings with a quantum dot

Using the Anderson model in the Kondo regime, we calculate the persistent current j in a ring with an embedded quantum dot (QD) as a function of the Aharonov-Bohm flux $\ensuremath{\Phi}$ for different ring length L, temperature T, and broadening of the conduction states $\ensuremath{\delta}.$ For $T=\ensuremath{\delta}=0$ and $L\ensuremath{\gg}\ensuremath{\xi},$ where $\ensuremath{\xi}$ is the Kondo screening length, $\mathrm{Lj}$ tends to the value for a noninteracting ideal ring, while it is suppressed for a side-coupled QD. For any $L/\ensuremath{\xi},$ $\mathrm{Lj}$ is also suppressed when either T or $\ensuremath{\delta}$ increase above a fraction of the level spacing, which depends on $\ensuremath{\Phi}.$

Infinitesimal extensions of ℙ 1 and their Hilbert schemes

In order to calculate the multiplicity of an isolated rational curve C on a local complete intersection variety X, i.e. the length of the local ring of the Hilbert Scheme of X at [C], it is important to study infinitesimal neighborhoods of the curve in X. This is equivalent to infinitesimal extensions of ℙ1 by locally free sheaves. In this paper we study infinitesimal extensions of ℙ1, determine their structure and obtain upper and lower bounds for the length of the local rings of their Hilbert schemes at [ℙ1].

Dinitro and quinodimethane derivatives of terthiophene that can be both oxidized and reduced. Crystal structures, spectra, and a method for analyzing quinoid contributions to structure.

Two new oligothiophenes, the dinitro compound 3',4'-dibutyl-5,5' '-dinitro-2,2':5',2' '-terthiophene (1) and the quinodimethane 3',4'-dibutyl-5,5' '-bis(dicyanomethylene)-5,5' '-dihydro-2,2':5',2' '-terthiophene (2), have been synthesized and studied with electrochemistry, UV-vis-NIR-IR spectroscopy, ESR, and X-ray crystallography. These compounds, designed to be both electron and hole carriers, show redox properties that are unusual for oligothiophenes. Cyclic voltammetry and spectroelectrochemistry demonstrated that each compound could be oxidized to a cation radical and reduced to an anion radical and dianion. The spectra of 2 and its three redox partners were analyzed in terms of a limiting structure in which the neutral 2 has orbitals corresponding to those of a substituted-terthiophene dication. Compound 1 crystallizes with the thiophene rings held in an unusual nonplanar, cisoid configuration in face-to-face pi-stacks, with a spacing between molecules of 3.65 A. The C-C bond lengths of the outer nitro-substituted rings have quinoid character. Compound 2 crystallizes with the thiophene rings in a planar, transoid configuration. The molecules are held in pi-stacks formed from pi-dimers with a spacing between molecules of 3.47 and 3.63 A. The C-C bond distances of the thiophene rings of 1 and 2 and other oligomers were analyzed by a principal component analysis. The analysis found that 93% of the structural variance resided in one principal component related to the quinoid structure of the oligothiophene moiety. The analysis reliably demonstrated a quinoid contribution to the structure of 1. This method should be applicable to understanding the structure of other conjugated molecules in which quinoid structures contribute.

Formation and Characterization of Aggregates of Merocyanine Dyes in Vacuum-Deposited Thin Film

Thin films of merocyanine (MD) dyes substituted with alkyl chains of various lengths at the benzothiazol ring are prepared by vacuum evaporation. The structure and aggregate formation upon dimethylamine vapor treatment are discussed based on the kind of substituent at the rhodanine ring, crystallinity and alkyl chain length. It is found that the introduction of a carboxymethyl group at the rhodanine ring and the fabrication of amorphous films are very important in aggregate formation. MD-2, -5 and -6 films, which the numbers indicate the number of carbon atoms in the alkyl chain, form H-aggregates, and MD-10 and amorphous MD-18 form J-aggregates. The difference in aggregate structure according to the alkyl chain length positioned at the benzothiazol ring depends on the degree of steric hindrance between alkyl chains. The activation energies of H- and J-aggregate formation are estimated to be 4.46 kJ mol-1 and 11.07 kJ mol-1, respectively.

Evidence that naphthocyclobutene, phenanthrodicyclobutene, and anthrodicyclobutene derivatives are not contaminated by their cyclobutene ring-opened isomers

It has not been directly proven that the title cyclobutene derivatives which have an extremely long C sp 3C sp 3 bond length of the cyclobutene ring, are not contaminated by their cyclobutene ring-opened isomers. In order to clarify the uncertainties, NO addition experiments were carried out. When the cyclobutene ring is cleaved easily, NO may react with the cyclobutene ring. Although NO did not react with naphthocyclobutene and anthrodicyclobutene derivatives, NO reacted with anthrodicyclobutene derivatives at their central benzene nuclei instead of their cyclobutene rings. These results clearly show that all the cyclobutene derivatives do not exist in an equilibrium with any cyclobutene ring-opened isomer.

Persistent current and Drude weight inone-dimensional rings with substitution potentials

Persistent currents and Drude weights are investigated using thetight-binding approximation to one-dimensional rings threaded by amagnetic flux and with the potential given by some almost-periodicsubstitution sequences with different degrees of randomness, and forvarious potential strengths. The Drude weight D distinguishescorrectly conductors and insulators, in accordance with the resultsindicated by the currents. In the case of insulators the decay ofD(N) for large ring lengths N provides an estimate for thelocalization length of the system. It is shown that a more randomsequence does not imply reduced conduction. This discrepancybetween the hierarchy of disorder of the sequences and the capacityfor conduction of the system is explained by the gaps in the energyspectra.

Structure and dynamics of amorphous silica surfaces

We use molecular dynamics computer simulations to study the equilibrium properties of the surface of amorphous silica. Two types of geometries are investigated: (i) clusters with different diameters (13.5, 19, and 26.5 Å) and (ii) a thin film with thickness 29 Å. We find that the shape of the clusters is independent of temperature and that it becomes more spherical with increasing size. The surface energy is in qualitative agreement with the experimental value for the surface tension. The density distribution function shows a small peak just below the surface, the origin of which is traced back to a local chemical ordering at the surface. Close to the surface the partial radial distribution functions as well as the distributions of the bond–bond angles show features which are not observed in the interior of the systems. By calculating the distribution of the length of the Si–O rings we can show that these additional features are related to the presence of two-membered rings at the surface. The surface density of these structures is around 0.6/nm2, in good agreement with experimental estimates. From the behavior of the mean-squared displacement at low temperatures, we conclude that at the surface the cage of the particles is larger than the one in the bulk. Close to the surface the diffusion constant is somewhat larger than the one in the bulk and with decreasing temperature the relative difference grows. The total vibrational density of states at the surface is similar to the one in the bulk. However, if only the one for the silicon atoms is considered, significant differences are found.

Length Approximations for Independently Generated Ideals

We study ideals primary to the maximal ideal of a commutative Noetherian local ring. When such an ideal is generated by elements which are independent in the sense of C. Lech, we prove a lower bound on the length of the quotient ring in terms of the orders of the generators. As a corollary we obtain a substantial partial result on Lech's conjecture on the multiplicities of a flat couple of local rings.

Molecular structure and ring distortions of 1,3-dicyanobenzene in the gas phase and in the crystal

The crystals of 1,3-dicyanobenzene have been obtained by a sublimation method. 1,3-Dicyanobenzene crystallizes in the monoclinic system. The X-ray geometry of the 1,3-dicyanobenzene molecule has been compared with the ab initio (HF/6-31+G(d) basis sets level) calculated structure in the gas-phase. The difference between equivalent parameters obtained by these methods is a consequence of the intermolecular interactions present in the crystal. The distortion of the benzene ring from the D6h symmetry is consistent with the substitution effect caused by two highly polar groups. The distortion of the benzene ring in 1,3-dicyanonbenzene has been compared and discussed in relation to the o- and p-isomers of dicyanobenzene. The differences in the C–C bond lengths of the phenyl ring in the gas-phase have been analyzed in terms of the distribution of the charge density. The calculated charge density and its Laplacian function were analyzed in term of the topological properties at the (3,-1) critical points. Some comments on the crystal packing and intermolecular interactions present in the crystals of o-, m- and p-dicyanobenzene and their melting points have also been presented.