Atmospheric chemistry of diazomethane – an experimental and theoretical study

The kinetics of the O₃, OH and NO₃ radical reactions with diazomethane were studied in smog chamber experiments employing long-path FTIR and PTR-ToF-MS detection. The rate coefficients were determined to be k _CH2NN+O3?=?(3.2?±?0.4)?×?10^?17 and k _CH2NN+OH?=?(1.68?±?0.12)?×?10^?10 cm³ molecule^?1 s^?1 at 295?±?3?K and 1013?±?30 hPa, whereas the CH₂NN?+?NO₃ reaction was too fast to be determined in the static smog chamber experiments. Formaldehyde was the sole product observed in all the reactions. The experimental results are supported by CCSD(T*)-F12a/aug-cc-pVTZ//M062X/aug-cc-pVTZ calculations showing the reactions to proceed exclusively via addition to the carbon atom. The atmospheric fate of diazomethane is discussed.     

Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Design and Cold Tests of Asymmetric Quasioptical Resonators

This paper presents the design and test of asymmetric quasioptical resonators for gyrotron applications, where most of the diffraction output coupling comes from the smaller of two mirrors. A computer code based on scalar diffraction theory is used to calculate the resonator losses and the electric field near the mirrors. Resonators with mirror separations approaching confocal have reduced side lobes in the diffraction patterns, which should allow for better power transmission and focusing. Cold tests have been performed at 94 and 141 GHz to measure the quality factor of the asymmetric resonators as a function of mirror separation and mirror misalignment. Typical resonator parameters include 65 cm mirror separation, 1-3% output coupling and 85% of the losses from the small mirror. A half-symmetric resonator with one flat and one curved mirror has also been investigated. The calculated values of Q are in reasonably good agreement with the cold test measurements.     

Planting in his Neighbor's Garden: David Hilbert and Early Göttingen Quantum Physics

David Hilbert (1862-1943) played an important role in establishing quantum physics in Göttingen. I analyze the ways in which his influence was decisive by comparison with Woldemar Voigt (1850-1919). Voigt was the leading Göttingen theoretical physicist before the arrival of Peter Debye (1884-1966), who was appointed to a new professorship in 1914 at Hilbert's instigation. I portray the Göttingen mathematicians, above all Hermann Minkowski (1864-1909) and David Hilbert, as planting the seeds for the blossoming of quantum physics under their student Max Born (1882-1970) in the 1920s.     

Mapping properties of wave and scattering operators for two-body Schrödinger operators

The modified wave and scattering operators are shown to be bounded between weighted L ²-spaces for two-body Schrödinger operators with long range potentials.     

Kinetic determination of magnesium and calcium by stopped-flow injection analysis

A kinetic method for the simultaneous determination of magnesium and calcium ions in solution is described. The method is based on the dissociation reactions of cryptand (2.2.2) complexes; a stopped-flow injection technique is used with spectrophotometric monitoring of the phthalein complexone complexes of the released metal ions. Analyses were done at a rate of 80 h^?1, with injected sample volumes of 80 μl. A microcomputer system for data acquisition and control of the system is described.     

Molecular structure of gaseous vanadyl(V) fluoride as studied by electron diffraction,and its modified valence force field

The molecular structure of gaseous OVF₃ has been determined by electron diffraction to be: r_g(V-O) = 1.570(5) Å, r_g(V-F) = 1.729(2) Å and ∠_α(OVF) = 107.5(4)°. A modified force field has been fitted to results from spectroscopic as well as diffractional studies. A similar attempt to determine the force field for OVCl₃ was not as successful as for OVF₃, probably because the Coriolis constants are less accurately determined for that molecule.     

Calculation of photoionization cross sections of Na2–8 and K2–8 clusters

Analysis of free metal clusters studied with photoionization mass spectrometry or photoelectron spectroscopy requires theoretical predictions of the photoionization cross sections to gain a deeper physical understanding. Calculated energy-dependent photoionization cross sections of Na_2–8 and K_2–8 clusters are presented in this study. The ground state electronic structure of the clusters are calculated using the Local Spin Density method (LSD) which is also the starting point for the cross section calculation with the continuum multiple scattering method. A basic analysis of the photoionization process is given within the independent electron picture. Strong resonances are predicted in the UV cross sections (5–10 eV) of K_3–8 but not for Na_3–8, interpreted as shape resonances, i.e. quasibound states in which electrons are trapped by a potential barrier. Unfortunately experimental data are only known close to the ionization threshold and a comparison between our values and experimental data in a broad energy range is not possible.     

Copper(II) Complexes of ω‐Hydroxy‐Functionalized N‐Salicylidenehydrazides show pH‐Controlled Switching between Dicationic Dimers and Neutral One‐Dimensional Coordination Polymers

New copper(II) complexes of the hydrazone ligands H₂salhyhb, H₂salhyhp, and H₂salhyhh, derived from salicylaldehyde and ω‐hydroxy carbonic acid hydrazides, have been synthesized and physically characterized. Two fundamental structures were found in solid state depending on the pH‐value of the reaction solution. Acidic conditions lead to the formation of the di‐μ‐phenoxo‐bridged dicationic complex dimers [{Cu(Hsalhyhb)}₂]²⁺ ( 1a ), [{Cu(Hsalhyhp)}₂]²⁺ ( 2a ), and [{Cu(Hsalhyhh)}₂]²⁺ ( 3a ), isolated as perchlorate salts. The dimeric complexes show strong antiferromagnetic coupling with J = ?399 ( 1a ), ?410 ( 2a ), and ?311 cm^?1 ( 3a ). Higher pH‐values resulted in the aggregation of neutral copper ligand fragments to the one‐dimensional coordination polymers [{Cu(salhyhb)}_n] ( 1b ), [{Cu(salhyhp)}_n] ( 2b ), and [{Cu(salhyhh)}_n] ( 3b ). 3b has been examined by means of X‐ray crystallography and represents the first example of a structurally characterized neutral copper(II) N‐salicylidenehydrazide complex without additional ligands. The magnetic interactions in the polymers are also antiferromagnetic with J = ?125 ( 1b ), ?136 ( 2b ), and ?148 cm^?1 ( 3b ), but strongly reduced compared to the corresponding dimeric complexes. The two basic structure types can be reversibly interconverted simply by pH‐control.     

Basis-independent potential energy curves for the neutral diatomics of Li,Na and K evaluated by means of Hartree-Fock and different density functional potentials

Summary The solution of the Schrödinger equation for diatomic molecules when the finite element method is used gives the possibility to evaluate highly accurate basis-independent potential energy curves. In this work such types of numerically accurate potential energy curves on the HF level have been evaluated for Li₂, Na₂ and K₂ and could be used as benchmarks in the optimization of basis sets. A comparison between recent LCAO HF calculations in which extended basis sets are used and the accurate values determined in this work show that there is a difference in total energy of 4×10^–5 and 10^–3 a.u. for Li, Li₂, and Na, Na₂, respectively. Evaluated dissociation energies are, however, due to the cancellation of numerical errors in much better agreement. Further, it is found that different exchange correlation potentials for the heavier molecules such as those given by von Barth-Hedin and Vosko, Wilk and Nusair reproduce experimental properties such as dissociation energies, vibrational frequencies almost as well as those achieved with advanced CI methods. TheX potential gives accurate bond lengths for Na₂ and K₂, whereas the dissociation energies are too small.