Absorption,fluorescence and phosphorescence spectra of the singlet and triplet states of s-tetrazine in the crystal and in mixed crystals at low temperatures

The electronic absorption, fluorescence and phosphorescence spectra of s-tetrazine at low temperatures (4.2-1.5 K) are reported and analyzed in the neat crystal and in several mixed crystals. The ³B_3u-¹A_g (nπ^*) origin is at 18414 ± 5 cm^?1 for neat tetrazine. In the mixed crystal several sites identified. The lowest energy origin is at 17453 cm^?1 for tetrazine in pyrazine; 17 701 cm^?1 in pyrimidine; and 17 676 cm^?1 in pyridazine. The ^eB_3u-¹A_g (nπ^*) origin is at 14 096 ± 2 cm^?1 for the neat crystal. The phosphorescence lifetime of neat tetrazine is measured to be 96.8 ± 2.1 μs at 4.2 and 1.8 K. All the spectra are predominately composed of members of progressions in a single totally symmetric mode (ν_6a) built upon site origins and vibrational fundamentals. The ν_6a interval is: 743 (¹A_g), 715 (³B_3u), and 709 cm^?1 (¹B_3u) in the neat tetrazine crystal; 732 (¹A_g) and 705 cm^?1 (¹B_3u in pyrazine host, 737 (¹A_g) and 701 cm^?1 (¹B_3u) in pyrimidine host, and 732 (¹A_g) and 703 cm^?1 (¹B_3u) in pyridazine host mixed crystals. All emission spectra may be analyzed by Oi → (ν″_6a)^o_n (i), i indicating the observed s     

Uniqueness of barbilian domains

W. Leissner has developed a plane geometry over any Z-ring R, in which a point is an element of R×R and a line is a set of the form {(x+ ra, y + rb):r R} where (x,y) R×R and (a,b) is from a Barbilian domain, i.e., a set of unimodular pairs from R×R satisfying certain axioms. In this note we generalize results of W. Benz guaranteeing the uniqueness of Barbilian domains over several classes of commutative rings. The author wishes to thank Gordon Keller and Douglas Costa for fruitful discussions, the referee for his improvements, and the University of Virginia for its hospitality while this work was done.     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Why are spherical stellar systems relaxed?

Spherical stellar systems, from globular star dusters to compact galaxy clusters, appear to be dynamically relaxed. In galaxies and galaxy clusters, collisional relaxation acts too slowly to produce the observed result; and a new argument suggests that the same may be true of globular star clusters. Violent relaxation requires special initial conditions and seems unable to produce sufficiently extended halos. It is here proposed that dynamical relaxation may result from tidal perturbations by external systems. If this explanation is correct, it has important implications for the early history of galaxies and galaxy clusters.This essay was awarded the fourth prize for 1976 by the Gravity Research Foundation.     

Optimizing two types of discrete functions,subject to linear restrictions

This paper is a collection of four topics; they are: a discussion of two knapsack problems (see, for example, Gilmore and Gomory, 1966), some interesting heuristic remarks on computational experience, some remarks on the underlying algebraic structures directly related to the knapsack functions, and a new proof technique for optimizing the functions mentioned. All functions in sight are discrete and defined on the integers. Also, the proofs of the theorems do not use convexity and monotonicity of the more abstract optimization techniques.     

The cluster expansion for potentials with exponential fall-off

Continuing the work of a previous paper, the Glimm-Jaffe-Spencer cluster expansion from constructive quantum field theory is adapted to treat quantum statistical mechanical systems of particles interacting by potentials that fall off exponentially at large distance. The HamiltonianH ₀+V need be stable in the extended sense thatH ₀+4V+BN0 for someB. In this situation, with a mild technical condition on the potentials, the cluster expansion converges and the infinite volume limit of the correlation functions exists, at low enough density. These infinite volume correlation functions cluster exponentially. A natural system included in the present treatment is that of matter with ther ^–1 potential replaced bye ^–ar/r. The Hamiltonian is stable, but the system would collapse in the absence of the exclusion principle—the potential is unstable. Therefore this system cannot be handled by the classic work of Ginibre, which requires stable potentials.This work was supported in part by NSF Grant MPS 75-10751Michigan Junior Fellow     

Nucleic acid analysis using an expanded genetic alphabet to quench fluorescence

Organic chemistry has made possible the synthesis of molecules that expand on Nature's genetic alphabet. Using the previously described nonstandard DNA base pair constructed from isoguanine and 5-methylisocytosine, we report a highly specific and sensitive method that allows for the fast and specific quantitation of genetic sequences in a closed tube format. During PCR amplification, enzymatic site-specific incorporation of a quencher covalently linked to isoguanine allows for the simultaneous detection and identification of multiple targets. The specificity of method is then established by analysis of thermal denaturation or melting of the amplicons. The appropriate functions of all reactions are further verified by incorporation of an independent target into the reaction mixture. We report that the method is sensitive down to the single copy level, and specificity is demonstrated by multiplexed end-point genotypic analysis of four targets simultaneously using four separate fluorescent reporters. The method is general enough for quantitative and qualitative analysis of both RNA and DNA using previously developed primer sets. Though the method described employs the commonly used PCR, the enzymatic incorporation of reporter groups into DNA site-specifically should find broad utility throughout molecular biology.     

Diphosphine-phosphenium coordination complexes representing monocations with pendant donors and ligand tethered dications

Homoatomic P-P coordinate bonding is exploited to prepare the first examples of triphosphorus monocations and tetraphosphorus dications using dimethylphosphenium or diphenylphosphenium Lewis acceptors with diphosphinomethane, diphosphinoethane, diphosphinohexane, or diphosphinobenzene ligands. Solid-state structures and spectroscopic characterization data for complexes involving bis(diphenylphosphino)methane ligands show coordination of only one donor site of the diphosphine ligand in the monocations, and chelate complexation is not observed. Tetraphosphorus dications are observed with longer diphosphines, in which the ligand tethers two phosphenium acceptors. The structural preferences between monocations with pendant phosphines and tethered dications are dependent on intramolecular steric interactions and the flexibility of the tether.     

Preparation and Characterization of Six Bis(N-methylpyrrolidine)-C(60) Isomers: Magnetic Deshielding in Isomeric Bisadducts of C(60)

A series of isomers of bis(N-methylpyrrolidine)-C(60) 2 (Prato bisadducts) was prepared by the 1,3-dipolar cycloaddition of N-methylazomethine ylide to C(60). Six isomers were separated and characterized by ESI-MS, UV/vis, and (1)H and (13)C NMR spectroscopy. The structures of these bisadducts were assigned based on (1) comparison of their molecular symmetries with their (1)H and (13)C NMR spectra, (2) comparison of their UV/vis spectra with those of corresponding Bingel-Hirsch bisadducts, and (3) the order of deshielding of the methylene and N-methyl (1)H NMR resonances. Prato bisaddition is less chemoselective than Bingel-Hirsch bisaddition to C(60).     

OH-terminated cyanopropyl silicones

Due to their high polarity and unique selectivity, cyanopropyl silicones are basic stationary phases for high resolution capillary gas chromatography. Different OH-terminated cyanopropyl silicones, containing a high cyanopropyl content, were synthesized and chromatographically evaluated. Special attention was paid to the degree of immobilization of the phases in FSOT columns. Depending on the problem at hand, a choice has to be made between immobilization and maximum selectivity.