Ab initio investigation of the HCO and COH molecule-ions: Structure and potential surfaces for dissociation in ground and excited states

Ab initio SCF calculations are reported for the potential surfaces of the HCO⁺ and COH⁺ molecular ions in both ground and low-lying excited states. An analysis of the bonding characteristics of the two systems is undertaken, from which it is noted that the 5σ and 1π orbital energy levels in HCO⁺ are inverted relative to the order found in both COH⁺ and also in CO itself. This fact leads to a situation in which the (1π, 2π) excited states of HCO⁺ as well as the ground state are more stable than their COH⁺ counterparts, whereas the opposite relationship is observed for (5σ, 2π) species. In addition it is pointed out that those states which populate the 7a' in-plane component of the 2π MO in either molecule-ion are characterized both by bent equilibrium structures and also by dissociation into CO⁺ + H, whereas all other low-lying species, including the ground state, prefer linear structures which dissociate via a CO + H⁺ channel.     

The electronic spectrum of linear HC9H

Large-scale ab initio multi-reference configuration interaction (MRD-CI) calculations are carried out to determine the vertical electronic spectrum of HC₉H. The calculated energy for the first dipole-allowed ³Σ_u⁻←X ³Σ_g⁻ transition of 2.38 eV is in reasonable agreement with recent measurements of 582 nm (2.13 eV) in neon matrix. The oscillator strength is computed with f=0.007. In addition a second very strong (f=4.7) ³Σ_u⁻←X ³Σ_g⁻ transition is predicted by the calculations to be located near 6 eV.     

Effective potentials for spectator groups in molecular systems I. Potential curves and binding energies

Summary A method for representing inactive groups, i.e. spectator groups, in a molecular system by an effective potential is presented. The matrix elements for the spectator's short-range Hartree-Fock potential is stored in an intermediate AO basis, from which it can be transferred into the user basis for the active part of the molecular system. The longer-range of the potential is transferred via a (distributed) multipole expansion. The method is illustrated for the NH₃·X (X=NH₃, H₂O, HF) complexes: binding energies could be reproduced to within 5% by employing the effective NH₃ potential (whereby the lone pair was included in the active system), the entire NH₃·HF potential curve with a depth of 50 kJ/mol is reproduced within 2 kJ/mol if various intermediate basis sets are chosen. Technical details are discussed; the effective potential can directly be introduced in CI calculations.     

Novel Lipophilic Fluorophores with Highly Acidity-Dependent Two-Photon Response

Lipophilic fluorophores are widely implemented in nonlinear microscopy; however, few existing membrane-specific probes combine the high brightness of two-photon excited fluorescence (2PEF) with pH sensitivity. Herein we describe four novel two-photon excited fluorophores, based on a coumarin 151 core structure, where lipophilicity is induced by a covalently attached phosphazene moiety. Changing the environmental acidity using trifluoromethanesulfonic (triflic) acid leads to profound changes in the linear fluorescence and 2PEF characteristics, due to chromophores’ switching between neutral- and protonated forms. We characterize this dependence by measuring the two-photon absorption (2PA) spectra over the region λ_2PA=550–1000 nm, observing 2PA cross sections of σ_2PA=10–20 GM, with an associated 2PEF brightness of 10–13 GM, in neutral solutions of both acetonitrile and n-octanol. Although quantum chemical modelling and NMR measurements show that, at high chromophore concentrations, protonation may be accompanied by a dimerization process, these dimers likely do not form at the lower concentrations used in optical spectroscopy.     

The bottleneck transportation problem with auxiliary resources

In this paper, we introduce a new extension of the bottleneck transportation problem where additionally auxiliary resources are needed to support the transports. A single commodity has to be sent from supply to demand nodes such that the total demand is satisfied and the time at which all units of the commodity have arrived at the demand nodes is minimized. We show that already the problem with a single demand node and a single auxiliary resource is NP-hard and consider some polynomially solvable special cases.     

In and Ex Situ Studies of the Formation of Layered Microspherical Hydrozincite as Precursor for ZnO

Layered ZnO microspheric particles were prepared by the thermal decomposition of layered hydrozincite (LZnHC), which was synthesized from zinc nitrate and urea in a water/PEG400 mixture. The influence of the starting reagents, their concentrations, and the amount of PEG in the water/PEG400 mixture on the particle growth was observed. The chemical aspect of the particle growth was proposed in the frame of the partial charge model (PCM), and the formation of [Zn(OH)₂(OH₂)₄]⁰ and [Zn(OH)(HCO₃)(OH₂)₃]⁰ was predicted for the solid phase. The assumed growth mechanism, which follows the “nonclassical crystallization” concept of a self‐assembling mechanism, was observed in situ by small‐angle X‐ray scattering (SAXS) and predicts the rapid formation of approximately 6 nm sized building units. The size of these nano building units, stable only in the reaction medium, remains nearly constant during the synthesis, as the concentration of the nano building units increases throughout the reaction. The nano building units connect into leaves of LZnHC with a thickness of 20 nm. These leaves of LZnHC are further agglomerated into porous, microsphere‐like particles with sizes up to 4 μm.     

Structure preserving simulation of muscle actuated movements

Biomechanical simulation of human locomotion is commonly done via dynamical simulations of multibody systems. The actuation of the system is thereby often represented via muscle models that create a force depending on muscle length and activation level. We show a comparison of such a simulation using a structure preserving integration framework to MATLAB/Simulink results. The conclusion is that structure preservation is important to represent such systems correctly, in particular concerning energy and angular momentum evolutions. We introduce a method for structure preserving simulation of muscle actuated movements. Additionally we show examples of a simple arm movement including only one muscle as well as a finger movement including up to six muscles as an example for more complex biomechanical systems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Epistemological beliefs concerning the nature of mathematics among teacher educators and teacher education students in mathematics

Beliefs constitute a central part of a person’s professional competences as beliefs are crucial to the perception of situations and as they influence our choice of actions. The present article focuses on epistemological beliefs about the nature of mathematics among future teachers and their educators at university and post-university teacher-training institutions in Germany. The data reported are part of a larger sample originating from the MT21 study [supported by the National Science Foundation through a grant to W. S. Schmidt and M. T. Tatto (REC-0231886). MT21 started in 2003] which explores and compares mathematics teacher education in Bulgaria, Germany, Mexico, South Korea, Taiwan, and the United States. In this article, we examine the structure and level of beliefs concerning the nature of mathematics for teacher education students in Germany both at the beginning (n = 368) and the end of their education (n = 286) as well as their educators (n = 77) in three academic disciplines (mathematics, mathematics pedagogy and general pedagogy). In the first part of the article, the literature on epistemological beliefs and their structure will be reviewed. In the empirical part, analyses on the level and the structure of beliefs for our samples and subsamples will be presented. Relations between educators’ and students’ beliefs will be explored.