Evaluating the third and fourth derivatives of spectral data

The problem of differentiating spectral data to yield the third and fourth derivatives is converted into one of solving an integral equation of the first kind. This equation is solved by Tikhonov regularization. The method of General Cross Validation is used to guide the choice of the regularization parameter that keeps noise amplification under control. The performance of this route to third and fourth derivative spectra is demonstrated by applying it to a number of published spectra. A computational problem associated with General Cross Validation has been identified.     

Preparation and structural study of a novel nonlinear molecular material: the -histidinum dihydrogenarsenate orthoarsenic acid crystal

-Histidinium dihydrogenarsenate orthoarsenic acid (LHA) crystal ;

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belongs to P2₁ space group of the monoclinic system, Z=2, a=9.264(2) Å, b=8.929(2) Å, c=8.874(2) Å, β=108.61(3)°. The crystal is isomorphous to

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(LHP) crystal. The H₂AsO₄⁻ anions and H₃AsO₄ molecules are joined into layers parallel to the (100) crystallographic planes by the O–HO type hydrogen bonds. The histidinium cations occupy the space between the layers. The histidinium cation posses the carboxylic COO⁻ group. The positive charges appear in the ring (the proton is attached to the =N(3)– nitrogen) and in the ammonium group. The differential scanning calorimetric (DSC) diagram does not show any phase transition till 100 K. The infrared spectrum fully confirms the X-ray crystal structure. The LHA crystal is a good second harmonic generator (0.46 relative to KDP)     

A study of the reactivity of elemental Cr/Se/Te thin multilayers using X-ray reflectometry, in situ X-ray diffraction and X-ray absorption spectroscopy

The reactivity of [Cr/Se/Te] multilayers under annealing was investigated using X-ray reflectometry, in situ X-ray diffraction, X-ray absorption fine structure (XAFS) measurements and transmission electron microscopy. For all samples, interdiffusion was complete at temperatures between 100 and 300 °C, depending on the repeating tri-layer thickness. A crystalline phase nucleated approximately 20 °C above the temperature where interdiffusion was finished. The first crystalline phase in a binary Cr/Te sample was layered CrTe₃ nucleating at 230 °C. In ternary samples (Se:Te=0.6-1.2), the low-temperature nucleation of such a layered CrQ₃ (Q=Se, Te) phase is suppressed and instead the phase Cr₂Q₃ nucleates first. Interestingly, this phase decomposes around 500 °C into layered CrQ₃. In contrast, binary Cr/Se samples form stable amorphous alloys after interdiffusion and Cr₃Se₄ nucleates around 500 °C as the only crystalline phase. Evaluation of the XAFS data of annealed samples yield Se-Cr distances of 2.568(1) and 2.552(1) Å for Cr₂Q₃ and CrQ₃, respectively. In the latter sample, higher coordination shells around Se are seen accounting for the Se-Te contacts in the structure.     

Cyclodextrin and modified cyclodextrin complexes of E-4-tert-butylphenyl-4'-oxyazobenzene: UV-visible, 1H NMR and ab initio studies

alpha-Cyclodextrin, beta-cyclodextrin, N-(6(A)-deoxy-alpha-cyclodextrin-6(A)-yl)-N'6(A)-deoxy-beta-cyclodextrin-6(A)-yl)urea and N,N-bis(6(A)-deoxy-beta-cyclodextrin-6(A)-yl)urea (alphaCD, betaCD, 1 and 2) form inclusion complexes with E-4-tert-butylphenyl-4'-oxyazobenzene, E-3(-). In aqueous solution at pH 10.0, 298.2 K and I = 0.10 mol dm(-3)(NaClO(4)) spectrophotometric UV-visible studies yield the sequential formation constants: K(11) = (2.83 +/- 0.28) x 10(5) dm(3) mol(-1) for alphaCD.E-(-), K(21) = (6.93 +/- 0.06) x 10(3) dm(3) mol(-1) for (alphaCD)(2).E-3(-), K(11) = (1.24 +/- 0.12) x 10(5) dm(3) mol(-1) for betaCD.E-(-), K(21) = (1.22 +/- 0.06) x 10(4) dm(3) mol(-1) for (betaCD)(2).E-(-), K(11) = (3.08 +/- 0.03) x 10(5) dm(3) mol(-1) for .E-3(-), K(11) = (8.05 +/- 0.63) x 10(4) dm(3) mol(-1) for .E-3(-) and K(12) = (2.42 +/- 0.53) x 10(4) dm(3) mol(-1) for .(E-3(-))(2). (1)H ROESY NMR studies show that complexation of E-3(-) in the annuli of alphaCD, betaCD, 1 and 2 occurs. A variable-temperature (1)H NMR study yields k(298 K)= 6.7 +/- 0.5 and 5.7 +/- 0.5 s(-1), DeltaH = 61.7 +/- 2.7 and 88.1 +/- 4.2 kJ mol(-1) and DeltaS = -22.2 +/- 8.7 and 65 +/- 13 J K(-1) mol(-1) for the interconversion of the dominant includomers (complexes with different orientations of alphaCD) of alphaCD.E-3(-) and (alphaCD)(2).E-3(-), respectively. The existence of E-3(-) as the sole isomer was investigated through an ab initio study.     

Vibrational effects in laser-driven molecular wires

The influence of an electron-vibrational coupling on the laser control of electron transport through a molecular wire that is attached to several electronic leads is investigated. These molecular vibrational modes induce an effective electron-electron interaction. In the regime where the wire electrons couple weakly to both the external leads and the vibrational modes, we derive within a Hartree-Fock approximation a nonlinear set of quantum kinetic equations. The quantum kinetic theory is then used to evaluate the laser driven, time-averaged electron current through the wire-leads contacts. This formalism is applied to two archetypical situations in the presence of electron-vibrational effects, namely, (i) the generation of a ratchet or pump current in a symmetrical molecule by a harmonic mixing field and (ii) the laser switching of the current through the molecule.     

Duality for full crossed products of -algebras by non-amenable groups

Let be a cosystem and be a dynamical system. We examine the extent to which induction and restriction of ideals commute, generalizing some of the results of Gootman and Lazar (1989) to full crossed products by non-amenable groups. We obtain short, new proofs of Katayama and Imai-Takai duality, the faithfulness of the induced regular representation for full coactions and actions by amenable groups. We also give a short proof that the space of dual-invariant ideals in the crossed product is homeomorphic to the space of invariant ideals in the algebra, and give conditions under which the restriction mapping is open.