Synthesis and structure of the ternary and quaternary strontium nitride halides, Sr2N(X, X′) (X, X′=Cl, Br, I)

A number of new, layered nitride mixed halides have been synthesised in the quaternary phase systems Sr-N-Cl-Br and Sr-N-Br-I. The variation in structure with composition has been investigated by powder X-ray and powder neutron diffraction techniques and the structure of strontium nitride iodide, Sr₂NI, has been determined for the first time (rhombohedral space group R-3m, , , Z=3). A continuous solid solution exists between Sr₂NCl and Sr₂NBr with intermediate compounds adopting the same anti-α-NaFeO₂ structure (rhombohedral space group R-3m) as the ternary end members. A similar smooth and linear relationship between structure and composition is seen from Sr₂NBr to Sr₂NI and hence cubic close packing of metal-nitrogen layers is adopted regardless of halide, X (X′). While nitride and halide anions occupy distinct crystallographic sites, there is no ordering of the halides in the quaternary materials irrespective of stoichiometry or temperature (between 3 and 673 K).     

The vibrational levels of ammonia

A new six-dimensional potential energy function (PEF) of ammonia expressed in internal coordinates is determined by fitting to points evaluated by Density Functional Theory with the B97-1 functional. The C3v and D3h structures are treated on an equal footing. The inversion barrier is 1820 cm(-1), which is in very good agreement with the experimental value of 1834 cm(-1). The minimum 'reaction path' is well defined by the analytic function up to 40 degrees for the umbrella angle. Using this PEF, the vibrational levels are calculated variationally using three different methods. The first employs the internal kinetic energy operator developed for ammonia by Handy, Carter and Colwell (Mol. Phys. 96 (1999) 477). The second uses the code MULTIMODE (J. Chem. Phys. 107 (1997) 10458), which involves the kinetic energy operator as expressed in normal coordinates by Watson. The third uses an implementation of the reaction path hamiltonian (J. Chem. Phys. 72 (1980) 99) within the MULTIMODE code. All three approaches give similar energies for the vibrational energies of ammonia, and these agree with experiment to within 15 cm(-1) for the fundamental vibrations.     

Force driven separation of drops by deterministic lateral displacement

We investigate the separation of drops in force-driven deterministic lateral displacement (f-DLD), a promising high-throughput continuous separation method in microfluidics. We perform scaled-up macroscopic experiments in which drops settle through a square array of cylindrical obstacles. These experiments demonstrate the separation capabilities-and provide insight for the design-of f-DLD for drops of multiple sizes, including drops that are larger than the gaps between cylinders and exhibit substantial deformation as they move through the array. We show that for any orientation of the driving force relative to the array of obstacles, the trajectories of the drops follow selected locking directions in the lattice. We also found that a simple collision model accurately describes the average migration angles of the drops for the entire range of sizes investigated here, and for all forcing directions. In addition, we found a difference of approximately 20° between the critical angles at which the smallest and largest drops first move across a line of obstacles (column) in the array, a promising result in terms of potential size resolution of this method. Finally, we demonstrate that a single line of cylindrical obstacles rotated with respect to the driving force is capable of performing binary separations. The critical angles obtained in such single line experiments, moreover, agree with those obtained using the full array, thus validating the assumption in which the trajectory (and average migration angle) of the drops is calculated from individual obstacle-drop collisions.     

The water hexamer: cage, prism, or both. Full dimensional quantum simulations say both

State-of-the-art quantum simulations on a full-dimensional ab initio potential energy surface are used to characterize the properties of the water hexamer. The relative populations of the different isomers are determined over a wide range of temperatures. While the prism isomer is identified as the global minimum-energy structure, the quantum simulations, which explicitly include zero-point energy and quantum thermal motion, predict that both the cage and prism isomers are present at low temperature down to almost 0 K. This is largely consistent with the available experimental data and, in particular, with very recent measurements of broadband rotational spectra of the water hexamer recorded in supersonic expansions.     

Overtone-induced dissociation and isomerization dynamics of the hydroxymethyl radical (CH2OH and CD2OH). I. A theoretical study

The dissociation of the hydroxymethyl radical, CH(2)OH, and its isotopolog, CD(2)OH, following the excitation of high OH stretch overtones is studied by quasi-classical molecular dynamics calculations using a global potential energy surface (PES) fitted to ab initio calculations. The PES includes CH(2)OH and CH(3)O minima, dissociation products, and all relevant barriers. Its analysis shows that the transition states for OH bond fission and isomerization are both very close in energy to the excited vibrational levels reached in recent experiments and involve significant geometry changes relative to the CH(2)OH equilibrium structure. The energies of key stationary points are refined using high-level electronic structure calculations. Vibrational energies and wavefunctions are computed by coupled anharmonic vibrational calculations. They show that high OH-stretch overtones are mixed with other modes. Consequently, trajectory calculations carried out at energies about ~3000 cm(-1) above the barriers reveal that despite initial excitation of the OH stretch, the direct OH bond fission is relatively slow (10 ps) and a considerable fraction of the radicals undergoes isomerization to the methoxy radical. The computed dissociation energies are: D(0)(CH(2)OH → CH(2)O + H) = 10,188 cm(-1), D(0)(CD(2)OH → CD(2)O + H) = 10,167 cm(-1), D(0)(CD(2)OH → CHDO + D) = 10,787 cm(-1). All are in excellent agreement with the experimental results. For CH(2)OH, the barriers for the direct OH bond fission and isomerization are: 14,205 and 13,839 cm(-1), respectively.     

Due Date-Based Metrics for Activity Importance in Stochastic Activity Networks

A metric pair for assessing the importance of activities in stochastic activity networks based on completing a project on time (or reaching other project milestones) is presented. The metric pair is recommended as a supplement to other metrics of activity importance that have been suggested for use with Monte Carlo simulation. The differences in behavior of the various metrics are analyzed to help understand the additional types of insights that would be available by including the new metrics in simulation-based analyses.     

Kinetics of thiol–ene and thiol–acrylate photopolymerizations with real‐time fourier transform infrared

We used real‐time Fourier transform infrared to monitor the conversion of both thiol and ene (vinyl) functional groups independently during photoinduced thiol–ene photopolymerizations. From these results, the stoichiometry of various thiol–ene and thiol–acrylate polymerizations was determined. For thiol–ene polymerizations, the conversion of ene functional groups was up to 15% greater than the conversion of thiol functional groups. For stoichiometric thiol–acrylate polymerizations, the conversion of the acrylate functional groups was roughly twice that of the thiol functional groups. With kinetic expressions for thiol–acrylate polymerizations, the acrylate propagation kinetic constant was found to be 1.5 times greater than the rate constant for hydrogen abstraction from the thiol. Conversions of thiol–acrylate systems of various initial stoichiometries were successfully predicted with this ratio of propagation and chain‐transfer kinetic constants. Thiol–acrylate systems with different initial stoichiometries exhibited diverse network properties. Thiol–ene systems were initiated with benzophenone and 2,2‐dimethoxy‐2‐phenylacetophenone as initiators and were also polymerized without a photoinitiator. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3311–3319, 2001     

Bounds for integrals using segments

For certain integrals, with one-signed integrands, bounds depending on a parameter can be constructed. Sharpness of the bounds can be improved by fragmentation of the interval; this device is the basis of most quadrature formulas.     

A reinforcement-depletion urn model: A contiguity case

Summary An urn contains balls ofs different colors. The problem of the reinforcement of a specified color and random depletion of balls has been considered by Bernard (1977,Bull. Math. Biol.,39, 463–470) and Shenton (1981,Bull. Math. Biol.,43, 327–340), (1983,Bull. Math. Biol.,45, 1–9). Here we consider a special relation between a reinforcement and depletion, leading to a hypergeometric distribution. Research sponsored in part by the Applied Mathematical Sciences Research Program, Office of Energy Research, U.S. Department of Energy under contract DE-AC05-840R21400 with the Martin Marietta Energy Systems, Inc.