Spectroscopic fingerprints of toroidal nuclear quantum delocalization via ab initio path integral simulations

We investigate the quantum‐mechanical delocalization of hydrogen in rotational symmetric molecular systems. To this purpose, we perform ab initio path integral molecular dynamics simulations of a methanol molecule to characterize the quantum properties of hydrogen atoms in a representative system by means of their real‐space and momentum‐space densities. In particular, we compute the spherically averaged momentum distribution n(k) and the pseudoangular momentum distribution n(k_θ). We interpret our results by comparing them to path integral samplings of a bare proton in an ideal torus potential. We find that the hydroxyl hydrogen exhibits a toroidal delocalization, which leads to characteristic fingerprints in the line shapes of the momentum distributions. We can describe these specific spectroscopic patterns quantitatively and compute their onset as a function of temperature and potential energy landscape. The delocalization patterns in the projected momentum distribution provide a promising computational tool to address the intriguing phenomenon of quantum delocalization in condensed matter and its spectroscopic characterization. As the momentum distribution n(k) is also accessible through Nuclear Compton Scattering experiments, our results will help to interpret and understand future measurements more thoroughly. © 2012 Wiley Periodicals, Inc.     

Degradation and Dissipation Studies of Isoproturon in a Silty Clay Loam from Norway

Degradation and dissipation studies in laboratory and field were performed with isoproturon (IPU) to produce data for modelling the fate of an autumn applied pesticide in a Gleyic Podzoluvisol in Norway. Transformation rate studies of IPU in the laboratory during 8 weeks displayed a DT 50 of 13 days in topsoil (0-20 cm) and 21 days in subsoil (20-40 cm) at 20°C. In topsoil, a decline in the content of the metabolite monodesmethyl-isoproturon (MMU) was observed along with an initial production of didesmethyl-isoproturon (MU) after 4 weeks. In subsoil, the content of MMU was stabilized and no decrease was observed during the experiment. Only trace amounts of MU were found in the subsoil. Field dissipation of IPU was investigated in a silty clay loam following post-emergence application to winter wheat (September 1999). A bromide tracer was used to monitor the water flow in the soil profile. Soil was sampled from the 0-20, 20-40, 40-60 and 60-80 cm layers after 1, 2, 4, 13, 62, 232 and 371 days. 13 days after herbicide application, the waterfront had reached a depth of 80 cm and as a result an amount of 7 mg IPU m m 3 could be recovered from this depth, representing 2% of the initial amount of herbicide applied. Less than 9% of the herbicide applied could be seen to penetrate below 20 cm soil depth. After 62 days, only 18% of the initial IPU amount applied could be recovered from the profile. Using the results from the laboratory degradation study, a theoretical DT 50 of IPU in the field was estimated to 18-25 days ( Q 10 = 2.2). The theoretical DT 50 corresponded well with the actual dissipation of IPU observed in the field. This indicated that degradation of IPU was the primary contribution to the fast dissipation of IPU in the field, and that the risk of runoff of IPU was negligible. Appearance of the major degradation product MMU in the field was monitored during the entire experimental period, at most representing 11% of the initial herbicide concentration. Field studies showed that MMU was more easily transported below the plough layer than isoproturon. Traces of IPU and MMU could be found in soil one year after application. A second degradation product, MU, could not be recovered in quantifiable amounts in the soil samples.     

Energetics of cyclohexene adsorption and reaction on Pt(111) by low-temperature microcalorimetry

The heat of adsorption and sticking probability of cyclohexene on Pt(111) were measured as a function of coverage using single-crystal adsorption calorimetry in the temperature range from 100 to 300 K. At 100 K, cyclohexene adsorbs as intact di-sigma bonded cyclohexene on Pt(111), and the heat of adsorption is well described by a second-order polynomial (130 - 47 theta - 1250 theta(2)) kJ/mol, yielding a standard enthalpy of formation of di-sigma bonded cyclohexene on Pt(111) at low coverages of -135 kJ/mol and a C-Pt sigma bond strength of 205 kJ/mol. At 281 K, cyclohexene dehydrogenates upon adsorption, forming adsorbed 2-cyclohexenyl (c-C6H(9,a)) and adsorbed hydrogen, and the heat of adsorption is well described by another second-order polynomial (174 - 700 theta + 761 theta(2)) kJ/mol. This yields a standard enthalpy of formation of adsorbed 2-cyclohexenyl on Pt(111) at a low coverage of -143 kJ/mol. At coverages below 0.10 ML, the sticking probability of cyclohexene on Pt(111) is close to unity (>0.95), independent of temperature.     

On extensions of wavelet systems to dual pairs of frames

It is an open problem whether any pair of Bessel sequences with wavelet structure can be extended to a pair of dual frames by adding a pair of singly generated wavelet systems. We consider the particular case where the given wavelet systems are generated by the multiscale setup with trigonometric masks and provide a positive answer under extra assumptions. We also identify a number of conditions that are necessary for the extension to dual (multi-) wavelet frames with any number of generators, and show that they imply that an extension with two pairs of wavelet systems is possible. Along the way we provide examples that demonstrate the extra flexibility in the extension to dual pairs of frames compared with the more popular extensions to tight frames.     

Aromatic hydroxylation in a copper bis(imine) complex mediated by a micro-eta2:eta2 peroxo dicopper core: a mechanistic scenario

Detailed mechanistic studies on the ligand hydroxylation reaction mediated by a copper bis(imine) complex are presented. Starting from a structural analysis of the CuI complex and the CuII product with a hydroxylated ligand, the optical absorption and vibrational spectra of starting material and product are analyzed. Kinetic analysis of the ligand hydroxylation reaction shows that O2 binding is the rate-limiting step. The reaction proceeds much faster in methanol than in acetonitrile. Moreover, an inverse kinetic isotope effect (KIE) is evidenced for the reaction in acetonitrile, which is attributed to a sterically congested transition state leading to the peroxo adduct. In methanol, however, no KIE is observed. A DFT analysis of the oxygenation reaction mediated by the micro-eta2:eta2 peroxo core demonstrates that the major barrier after O2 binding corresponds to electrophilic attack on the arene ring. The relevant orbital interaction occurs between the sigma* orbital of the Cu2O2 unit and the HOMO of the ligand. On the basis of the activation energy for the rate-limiting step (18.3 kcal mol(-1)) this reaction is thermally allowed, in agreement with the experimental observation. The calculations also predict the presence of a stable dienone intermediate which, however, escaped experimental detection so far. Reasons for these findings are considered. The implications of the results for the mechanism of tyrosinase are discussed.     

Perturbation of operators and applications to frame theory

A celebrated classical result states that an operator U on a Banach space is invertible if it is close enough to the identity operator I in the sense that ‖I−U‖<1. Here we show that U actually is invertible under a much weaker condition. As an application we prove new theorems concerning stability offrames (and frame-like decompositions) under perturbation in both Hilbert spaces and Banach spaces. The first named author is partially supported by grants from the U.S. National Science Foundation (grant no. NSF DMS-9201357), the Danish Natural Science Research Council (Grant no. 9401598), and grants from the University of Missouri System Research Board, and the MU Research Council. The second named author thanks the University of Missouri for its hospitality during a visit, where the first draft of the paper was written.