B3LYP calculations on bishomoaromaticity in substituted semibullvalenes*

B3LYP/6‐31G* calculations on the degenerate rearrangements of substituted semibullvalenes spuriously predict the relative enthalpies of the bishomoaromatic TSs to be lower than the experimental values. However, the calculations do make the useful and experimentally testable prediction that the two cyano and two phenyl substituents in 2,6‐dicyano‐4,8‐diphenylsemibullvalene ( 9d ) are more likely than four cyano substituents in 2,4,6,8‐tetracyanosemibullvalene ( 9f ) or the four phenyl substituents in 2,4,6,8‐tetraphenylsemibullvalene ( 9g ) to produce a semibullvalene that has a bishomoaromatic equilibrium geometry in the gas phase. The major reason for the surprising finding that 9d is more likely to be bishomoaromatic than 9g is shown to be steric interactions between the phenyl groups at C‐2 and C‐8 and at C‐4 and C‐6 in bishomoaromatic structure 10g . These interactions inhibit the conjugative stabilization of 10g ; but they are absent in bishomoaromatic structure 10d , where cyano groups replace the phenyl groups at C‐2 and C‐6 in 10g . © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1565–1573, 2001     

The role of hydrogen bonding in pseudo-macrocyclic ring formation in 2,6-dimethyl-1,3,5,7-cyclooctatetraene 1,3,5,7-tetracarboxylic acid monohydrate

2,6-Dimethyl-1,3,5,7-cyclooctatetraene-1,3,5,7-tetracarboxylic acid 3, C₁₄H₁₄O₉, was prepared by thermolysis of the corresponding semibullvalene and characterized by spectroscopic and single-crystal X-ray diffraction studies. The monohydrate of 3 crystallizes in the tetrahedral space group P-4n2, a = 11.0924(3) Å, c = 12.6799(5) Å, V = 1560.15(9) ų, Z = 4. The cyclooctatetraene ring adopts a tub-shaped conformation with a crystallograpically imposed twofold rotational symmetry, and is composed of localized C=C double bonds in the 1,3,5, and 7 positions with an average interatomic distance of 1.327 (5) Å and C–C single bonds with an average interatomic distance of 1.489(5) Å. The average C=C–C angle in the ring is 122.6(3)°. Each symmetry generated eight-membered ring contains four carboxyl groups, two of which are coplanar with the methyl groups across the C=C ring atoms. However, across the C–C bonds the carboxyl groups and the methyl groups show a torsion angle of 64.3(4)°. The presence of a water molecule in the crystal lattice generates a three-dimensional network of close hydrogen bondings between water and the carboxyl groups of multiple rings. This creates a network of orthogonal 10-membered rings between the 8-membered rings. Two given cyclooctatetraene rings are intermolecularly hydrogen bonded not only directly through their carboxyl groups but also via a bridging water molecule. This effect is rare in polycarboxylic acids and their monohydrates which bond only with water or among themselves.     

Zero-dimensional spaces from linear structures

It is well known that spaces defined from a separated uniform structure with a linearly ordered base of uncountable cofinality (ω_μ-metrizable spaces) are ultraparacompact and have an ortho-base, hence are non-Archimedean spaces in the sense of A. Monna. Our results concern whether certain wider classes of spaces defined from linear structures retain these properties. We construct for every regular cardinal ω_μ, examples of ω_μ-additive, ω_μ-stratifiable spaces (i.e., ω_μ-Nagata spaces) that do not have an ortho-base. We give a number of examples of linearly stratifiable spaces, one of which is related to an example of Eric K. van Douwen concerning countable box products of stratifiable spaces.     

Analyzing the performance of simultaneous generalized hill climbing algorithms

Simultaneous generalized hill climbing (SGHC) algorithms provide a framework for using heuristics to simultaneously address sets of intractable discrete optimization problems where information is shared between the problems during the algorithm execution. Many well-known heuristics can be embedded within the SGHC algorithm framework. This paper shows that the solutions generated by an SGHC algorithm are a stochastic process that satisfies the Markov property. This allows problem probability mass functions to be formulated for particular sets of problems based on the long-term behavior of the algorithm. Such results can be used to determine the proportion of iterations that an SGHC algorithm will spend optimizing over each discrete optimization problem. Sufficient conditions that guarantee that the algorithm spends an equal number of iterations in each discrete optimization problem are provided. SGHC algorithms can also be formulated such that the overall performance of the algorithm is independent of the initial discrete optimization problem chosen. Sufficient conditions are obtained guaranteeing that an SGHC algorithm will visit the globally optimal solution for each discrete optimization problem. Lastly, rates of convergence for SGHC algorithms are reported that show that given a rate of convergence for the embedded GHC algorithm, the SGHC algorithm can be designed to preserve this rate.     

Diophantine approximation on planar curves: the convergence theory

The convergence theory for the set of simultaneously ψ-approximable points lying on a planar curve is established. Our results complement the divergence theory developed in [1] and thereby completes the general metric theory for planar curves. Dedicated to Walter Hayman and Klaus Roth on their eightieth birthdays Mathematics Subject Classification (2000) 11J83; 11J13, 11K60     

The importance of reaction conditions in the use of the (η5-cyclohexadienyl)tricarbonyliron cation in organic synthesis

The reactions of (η⁵-C₆H₇)Fe(CO)₃⁺BF₄^? with oxy anions in acetonitrile lead to variable yields of C₅-substituted (η⁴-cyclohexadiene)tricarbonyliron complexes, as well as dimeric complexes, depending upon the anion and the reaction conditions.     

Ion trajectories through the input ion optics of an inductively coupled plasma-mass spectrometer

A commercial program (MacSimion) has been used to model the einzel lens and bessel box input lens system of an inductively coupled plasma-mass spectrometer (ICP-MS). A number of plots are presented illustrating the effect of various lens voltages on ion trajectories. The trajectories are dependent on ion kinetic energy and since ion kinetic energy is mass dependent in ICP-MS, these plots clarify the mass dependence of ion lens voltage settings. Plots are also presented illustrating the interdependence of some lens voltage settings and how, in fact, different lens voltage settings can result in similar ion throughput. The model can be used to predict relative signal intensities for a range of ion masses as a function of lens potentials and these are shown to agree with experimentally measured data.