Minimum-error method for scattering problems in quantum mechanics: Two stable and efficient implementations

We examine here, by using a simple example, two implementations of the minimum error method (MEM), a least-squares minimization for scattering problems in quantum mechanics, and show that they provide an efficient, numerically stable alternative to Kohn variational principle. MEM defines an error-functional consisting of the sum of the values of (HPsi - EPsi)2 at a set of grid points. The wave function Psi, is forced to satisfy the scattering boundary conditions and is determined by minimizing the least-squares error. We study two implementations of this idea. In one, we represent the wave function as a linear combination of Chebyshev polynomials and minimize the error by varying the coefficients of the expansion and the R-matrix (present in the asymptotic form of Psi). This leads to a linear equation for the coefficients and the R-matrix, which we solve by matrix inversion. In the other implementation, we use a conjugate-gradient procedure to minimize the error with respect to the values of Psi at the grid points and the R-matrix. The use of the Chebyshev polynomials allows an efficient and accurate calculation of the derivative of the wave function, by using Fast Chebyshev Transforms. We find that, unlike KVP, MEM is numerically stable when we use the R-matrix asymptotic condition and gives accurate wave functions in the interaction region.     

Modified rare earth semiconductor oxide as a new nucleotide probe

Recent rapid developments in biological analysis, medical diagnosis, pharmaceutical industry, and environmental control fuel the urgent need for recognition of particular DNA sequences from samples. Currently, DNA detection techniques use radiochemical, enzymatic, fluorescent, or electrochemiluminescent methods; however, these techniques require costly labeled DNA and highly skilled and cumbersome procedure, which prohibit any in-situ monitoring. Here, we report that hybridization of surface-immobilized single-stranded oligonucleotide on praseodymium oxide (evaluated as a biosensor surface for the first time) with complimentary strands in solution provokes a significant shift of electrical impedance curve. This shift is attributed to a change in electrical characteristics through modification of surface charge of the underlying modified praseodymium oxide upon hybridization with the complementary oligonucelotide strand. On the other hand, using a noncomplementary single strand in solution does not create an equivalent change in the impedance value. This result clearly suggests that a new and simple electrochemical technique based on the change in electrical properties of the modified praseodymium oxide semiconductor surface upon recognition and transduction of a biological event without using labeled species is revealed.     

Kinetics of liquid phase semiconductor photoassisted reactions: supporting observations for a pseudo-steady-state model

The kinetics of liquid phase semiconductor photocatalytic and photoassisted reactions are an area of some debate, reignited recently by an article by Ollis(1) in which he proposed a simple pseudo-steady-state model to interpret the Langmuir-Hinshelwood type kinetics, commonly observed in such systems. In the current article, support for this model, over other models, is provided by a reinterpretation of the results of a study, reported initially in 1999,(2) of the photoassisted mineralization of 4-chlorophenol, 4-CP, by titania films and dispersions as a function of incident light intensity, I. On the basis of this model, these results indicate that 4-CP is adsorbed more strongly on P25 TiO2 when it is in a dispersed, rather than a film form, due to a higher rate constant for adsorption, k(1). In addition, the kinetics of 4-CP removal appear to depend on I(beta), where beta = 1 or 0.6 for when the TiO2 is in a film or a dispersed form, respectively. These findings are discussed both in terms of the pseudo-steady-state model and other popular kinetic models.     

Luminescence temperature sensing using poly(vinyl alcohol)-encapsulated Ru(bpy)3 2+ films

The ruthenium(II) diimine complexes, such as ruthenium(II) tris(bipyridyl), Ru(bpy)3 2+, possess highly luminescent excited states that are not only readily quenched by oxygen but also by an increase in temperature. The former effect can be rendered insignificant by encapsulating the complex in an oxygen impermeable polymer, although encapsulation often leads also to a loss of temperature sensitivity. The luminescence properties of Ru(bpy)3 2+ encapsulated in PVA were studied as a function of oxygen concentration and temperature and found to be independent of the former, but still very sensitive towards the latter. The results were fitted to an established Arrhenius-type equation, based on thermal quenching of the emitting state by a slightly higher (DeltaE= 3100 cm(-1))3d-d state that deactivates very rapidly (10(-13) s)via a non-radiative process.     

A Raman spectroscopic study of selected natural jarosites

Raman spectroscopy has been used to characterise the jarosite group of minerals of formula Mn(Fe3+)6(SO4)4(OH)12 where M may be K, (NH4)+, Na, Ag or Pb and where n = 2 for monovalent cations and 1 for the divalent cations. Raman spectroscopy proved useful for mineral identification especially where closely related minerals crystallise out from solutions where paragenetic relationships exist between the minerals. The band position of the SO4(2-) symmetric stretching mode proved to be a function of the ionic radius of the cation. The bending modes show a slight dependence. The spectra of the natural samples can be complex. This complexity is attributed to the incorporation of low levels of other cations into the structure.     

Synthesis and Crystal Structures of Anionic Gallium(II) and Gallium(III) Heterocyclic Compounds Derived from a Gallium(I) N-Heterocyclic Carbene Analogue

Abstract  

The addition of the N–H bond of the formamidine, ArN(H)C=NAr (Ar = C₆H₃Pr₂ⁱ-2,6), to the gallium(I) center of [K(tmeda)][:Ga(Ar-DAB)] (Ar-DAB={(Ar)NC(H)}₂) yields K[(Ar-DAB)Ga^III(H){N(Ar)C=NAr}] 1. The crystal structure of this and two other related anionic compounds, [K(18-crown-6)][(Ar-DAB)Ga^III{N(H)N=Fl}{(H)Fl}] (Fl = fluorendiyl) 2 and [K(OEt₂)₃][(Ar-DAB)Ga^II(CH₂Ph)Ga^II(Ar-DAB)] 3, have been determined. The cell parameters of the compounds are 1: P2₁/c, a = 20.2350(9), b = 14.1760(7), c = 19.6441(10), β = 111.307(1); 2: P2₁/c, a = 13.115(3), b = 21.799(4), c = 22.646(5), β = 90.20(3); 3: P2₁/n, a = 16.783(3), b = 21.635(4), c = 19.814(4), β = 92.34(3). The crystal structures of all complexes exhibit distorted tetrahedral gallium centers, and interactions between anion aryl substituents and the potassium cations.     

Revealing Excited-State Trajectories on Potential Energy Surfaces with Atomic Resolution in Real Time

Photoexcited molecular trajectories on potential energy surfaces (PESs) prior to thermalization are intimately connected to the photochemical reaction outcome. The excited-state trajectories of a diplatinum complex featuring photo-activated metal–metal σ-bond formation and associated Pt−Pt stretching motions were detected in real time using femtosecond wide-angle X-ray solution scattering. The observed motions correspond well with coherent vibrational wavepacket motions detected by femtosecond optical transient absorption. Two key coordinates for intersystem crossing have been identified, the Pt−Pt bond length and the orientation of the ligands coordinated with the platinum centers, along which the excited-state trajectories can be projected onto the calculated PESs of the excited states. This investigation has gleaned novel insight into electronic transitions occurring on the time scales of vibrational motions measured in real time, revealing ultrafast nonadiabatic or non-equilibrium processes along excited-state trajectories involving multiple excited-state PESs.