A three-state effective Hamiltonian for symmetric cationic diarylmethanes

We analyze the low-energy electronic structure of a series of symmetric cationic diarylmethanes, which are bridge-substituted derivatives of Michler's Hydrol Blue. We use a four-electron, three-orbital complete active space self-consistent field and multi-state multi-reference perturbation theory model to calculate a three-state diabatic effective Hamiltonian for each dye in the series. We exploit an isolobal analogy between the active spaces of the self-consistent field solutions for each dye to represent the electronic structure in a set of analogous diabatic states. The diabatic states can be identified with the bonding structures in classical resonance-theoretic models of cyanine dyes. We identify diabatic states with opposing charge and bond-order localization, analogous to the classical resonance structures, and a third state with charge on the bridge. While the left- and right-charged structures are similar for all dyes, the structure of the bridge-charged diabatic state, and the Hamiltonian matrix elements connected to it, change significantly across the series. The change is correlated with an inversion of the sign of the charge carrier on the bridge, which changes from an electron pair to a hole as the series is traversed.     

Largest initial segments pointwise fixed by automorphisms of models of set theory

Given a model \(\mathcal {M}\) of set theory, and a nontrivial automorphism j of \(\mathcal {M}\), let \(\mathcal {I}_{\mathrm {fix}}(j)\) be the submodel of \(\mathcal {M}\) whose universe consists of elements m of \(\mathcal {M}\) such that \(j(x)=x\) for every x in the transitive closure of m (where the transitive closure of m is computed within \(\mathcal {M}\)). Here we study the class \(\mathcal {C}\) of structures of the form \(\mathcal {I}_{\mathrm {fix}}(j)\), where the ambient model \(\mathcal {M}\) satisfies a frugal yet robust fragment of \(\mathrm {ZFC}\) known as \(\mathrm {MOST}\), and \(j(m)=m\) whenever m is a finite ordinal in the sense of \(\mathcal {M}.\) Our main achievement is the calculation of the theory of \(\mathcal {C}\) as precisely \(\mathrm {MOST+\Delta }_{0}^{\mathcal {P}}\)-\(\mathrm {Collection}\). The following theorems encapsulate our principal results: Theorem A. Every structure in \(\mathcal {C}\) satisfies \(\mathrm {MOST+\Delta }_{0}^{\mathcal {P}}\)-\(\mathrm { Collection}\). Theorem B. Each of the following three conditions is sufficient for a countable structure \(\mathcal {N}\) to be in \(\mathcal {C}\):(a) \(\mathcal {N}\) is a transitive model of \(\mathrm {MOST+\Delta }_{0}^{\mathcal {P}}\)-\(\mathrm {Collection}\).(b) \(\mathcal {N}\) is a recursively saturated model of \(\mathrm {MOST+\Delta }_{0}^{\mathcal {P}}\)-\(\mathrm {Collection}\).(c) \(\mathcal {N}\) is a model of \(\mathrm {ZFC}\). Theorem C. Suppose \(\mathcal {M}\) is a countable recursively saturated model of \(\mathrm {ZFC}\) and I is a proper initial segment of \(\mathrm {Ord}^{\mathcal {M}}\) that is closed under exponentiation and contains \(\omega ^\mathcal {M}\) . There is a group embedding \(j\longmapsto \check{j}\) from \(\mathrm {Aut}(\mathbb {Q})\) into \(\mathrm {Aut}(\mathcal {M})\) such that I is the longest initial segment of \(\mathrm {Ord}^{\mathcal {M}}\) that is pointwise fixed by \(\check{j}\) for every nontrivial \(j\in \mathrm {Aut}(\mathbb {Q}).\) In Theorem C, \(\mathrm {Aut}(X)\) is the group of automorphisms of the structure X, and \(\mathbb {Q}\) is the ordered set of rationals.     

Transport properties of arrays of intersecting cylinders

Formalisms are presented which enable the accurate calculation of the polarizability of an isolated square prism, and of the transport properties of square arrays of both circular cylinders and square prisms, over the entire range of volume fractions. For volume fractions close to zero and to unity, the results are shown to agree with dipolar formulae based on the appropriate polarizability. For volume fractions close to touching, the transport property varies rapidly but smoothly through the multipolar region. The results are shown to be in good qualitative agreement with experimental curves.     

Development of perfluorocarbon (PFC) primary standards for monitoring of emissions from aluminum production

An EPA Voluntary Aluminum Industrial Partnership (VAIP) program has been formed to help US primary producers focus on reducing the emissions of two perfluorocarbons (PFCs), tetrafluoromethane (CF4) and hexafluoroethane (C2F6), during the production of aluminum. To ensure comparability of measurements over space and time, traceability to national sources was desirable. Hence, the EPA approached the NIST to develop a suite of primary standards to cover a mole fraction (concentration) range of 0.1 to 1400 micromol mol(-1) for CF4 and 0.01 to 150 micromol mol(-1) of C2F6. A total of eight gravimetric PFC gas standards were prepared with relative expanded uncertainties of < or = 0.52% (approximately 95% confidence level). These primary standards were ultimately used to assign values to a series of secondary gas standards at three mole-fraction levels with relative expanded uncertainties ranging from +/- 0.7% to 5.3% (approximately 95% confidence level). This series of secondary standards was used within the aluminum industry to calibrate instruments used to make emission measurements. Assignment of values to the secondary standards was performed by use of gas chromatography with flame-ionization detection (GC-FID) and Fourier transform infrared spectrometry (FTIR). Real time pot-line and stack samples from a local aluminum plant were also obtained and sub-samples sent to each participating facility for analysis. The data generated from each facility were sent to NIST for analysis. The maximum difference between the NIST and individual facilities' values for the same sub-sample was +/- 26%.     

A procedure for sampling and analysis of air for energetics and related compounds

A procedure for the sampling and analysis of energetics and related compounds in the atmosphere is described. The basic procedure consists of the collection of air samples using sampling cartridges containing XAD-2 resin, extraction of the resin with isoamyl acetate, and an analysis of the extract using gas chromatography with electron capture detection. Modifications and additions to this procedure are discussed, such as the use of a prefilter before the resin sampler to collect particulates and the use of a mass selective detector to analyze for some propellant compounds of interest or for quantitative confirmation purposes. Two differing sizes of samplers are evaluated according to the air volumes required for collection. The procedure is tested through the analysis of spiked resin samples, which had air pulled through them for periods of time corresponding with the required sampling volumes. This procedure has application toward the measurement of energetic residues in atmospheres resulting from weapons testing and operations during training exercises involving munitions.     

Nilpotent and solvable radicals in locally finite congruence modular varieties

The Loewy rank of a modular latticeL of finite height is defined as the leastn for which there exista ₀=0t, < ... r=1 inL such that each interval I[a_i, a_i+1] is a complemented lattice. In this paper, a generalized notion of Loewy rank is applied to obtain new results in the commutator theory of locally finite congruence modular varieties. LetV be a finitely generated congruence modular variety. We prove that every algebra inV has a largest nilpotent congruence and a largest solvable congruence. Moreover, there exist first order formulas which define these special congruences in every algebra ofV.     

A new product of algebras and a type reduction theorem

A construction is defined which associates, to every algebra of a fixed but arbitrary finite similarity type, a groupoidF . The identities ofF are finitely based if and only if those of are, andF is finite if and only if is finite. Up to isomorphism,F has the same endomorphism monoid and subalgebra lattice as , but the congruence lattice ofF is the result of adjoining a new 1 to the congruence lattice of .F is functorial, preserves the satisfaction (and the non-satisfaction) of most Mal'cev conditions, and produces, by composition with the operation of forming the generated variety, an isomorphism of the lattice of varieties of fixed type to an interval in the lattice of varieties of groupoids.The construction makes use of a new product operation, applicable to two algebras of differing similarity types, which is introduced and studied in this paper.Research supported by National Science Foundation grant MCS-8103455.Presented by K. A. Baker.     

Azo group-assisted nucleophilic aromatic substitutions in haloarene derivatives: preparation of substituted 1-iodo-2,6-bispropylthiobenzenes

Aryldiazo substituents were used in nucleophilic aromatic substitution reactions of halogens. The Ph-N=N- group activates ortho fluorine atoms toward alkylthiolation under mild conditions. In contrast, the Me(2)N-C(6)H(4)-N=N- group has virtually no activation effect in nucleophilic aromatic substitution, and serves as a "neutral" mask for the amino group. The Ph-N=N- group was efficiently introduced by diazo coupling of aryllithium with dry PhN(2)(+)BF(4)(-) salt.