1,3-bis(2,4,6-trinitrophenylaminooxy)propane and its 4-cyano-2,6-dinitrophenyl congener: Synthesis and properties

Starting from N-hydroxyphthalimide (5) and 1,3-dibromopropane (6) we obtained 1,3-bis(phthalimidooxy)propane (7) which led to 1,3-bis(aminooxy)propane dihydrochloride (8). From its reaction with picryl chloride or 4-cyano-2,6-dinitrochlorobenzene, the two title compounds (4b, 4a) were obtained. ¹H-NMR and ¹³C-NMR spectra are presented. For comparison with the analogous N-methoxy-2,6-dinitro-4-R-anilines 1a, 1b (R=CN or R=NO₂), wer report the hydrophobic characteristics (by RPTLC), electronic spectra for the neutral compounds and their anions, pK _a values, and the behavior towards oxidizers (DPPH, PbO₂, Pb(CH₃COO)₄, KMnO₄ and Ag₂O); DPPH converts compounds 1a, 1b and 4a, 4b into betainic structures 2a, 2b respectively.     

13C n.m.r. spectra of some pyrylium salts and related compounds

The ¹³C chemical shifts of several alkyl and phenyl substituted pyrylium perchlorates, together with related pyridine and pyridinium salts, are reported. The shifts in the isoelectronic series benzene, pyridine, pyrylium cation correlate well with charge densities calculated by INDO MO theory. Charge densities also account for the shift changes found at C-3, C-4 and C-5 for protonation of pyridine and 2,4,6-trimethylpyridine. The shift changes observed on protonation for C-2 and C-6, along the series pyridine, 2,4,6-trimethylpyridine and 2,4,6-triphenylpyridine can only be rationalized by consideration of both charge density and π-bond order changes. The effects of alkyl substitution on the shifts of the pyrylium cations are not accounted for by charge density changes. Empirical correlations of these shifts with literature data for the alkylbenzenes and the shifts of the phenyl substituted 6-membered heterocycles are discussed.     

The variational problems for classical N-vector models

We prove existence and regularity properties of solutions of the variational problems introduced in the previous paper [1] for classical lattice N-vector models. These results form a basis of our renormalization group approach to low temperature expansions for the considered models.The work has been partially supported by the NSF Grant DMS-9102639.     

Ultraviolet stability of three-dimensional lattice pure gauge field theories

We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on results of the previous papers on renormalization group method for lattice gauge theories.Work partially supported by the National Science Foundation under Grant PHY 82-03669 and DMS 84-01989On leave of absence, Postal address: Department of Physics, Harvard University, Cambridge, MA 02138, USA     

Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances

Rules for molecular cyclicity based on the global indices resulting from reciprocal distances (Harary number, H) or from resistance distances (Kirchhoff number, Kf) were tested in comparison with those elaborated earlier by means of the Wiener index, W. The Harary number and the Wiener number were found to match molecular cyclicity in an almost identical manner. The Kirchhoff number also generally follows cyclicity trends described previously. H is slightly less degenerate than is W, but Kf has practically no degeneracy in the graphs investigated here. Being much more discriminating than the Wiener number (i.e., practically nondegenerate), Kf allowed the formulation of new rules for systems formed from linearly condensed ribbons of even-membered rings with different sizes as well as for branched ribbons. The topological cyclicity patterns are thus reformulated in an extended basis, proceeding from three different graph metrics. © 1994 John Wiley & Sons, Inc.     

Hierarchic Supramolecular Interactions within Assemblies in Solution and in the Crystal of 2,3,6,7‐Tetrasubstituted 5,5′‐(Anthracene‐9,10‐diyl)bis[pyrimidin‐2‐amines]

The title compounds 6 and 7 were synthesized in good yield (Schemes 1 and 2), and their mode of assembly was studied both in solution, for the tetrakis(decyloxy) derivative 6 , and in the crystal, for the tetramethoxy analogue 7 . The pyrimidin‐2‐amine moieties of 6 and 7 can engage in three different supramolecular interactions: i) metal ligation via one of the pyrimidine N‐atoms, ii) cooperative double H‐bonding via the NH₂ group, and iii) π–π‐stacking interactions. In solution, coordination of the central Zn‐atom within the soluble porphyrinatozinc complex 19 leads to significant changes in the NMR and absorption spectra of 6 . In the absence of metal ligation, the next strongest interaction is H‐bonding which can operate in nonpolar or moderately polar solvents. In these cases, however, no stacking interaction or inclusion compounds could be put into evidence in the case of 6 by absorption, fluorescence, or NMR spectroscopies. The π‐stacking interactions were only observed in the crystal of 7 in conjunction with double H‐bonding. Slightly disordered DMSO molecules are also H‐bonded to the NH₂ groups of 7 , perturbing the expected packing. The present study illustrates some of the challenges inherent to directing hierarchical assembly processes in the solid state.     

Computer generation of acyclic graphs based on local vertex invariants and topological indices. Derived canonical labelling and coding of trees and alkanes

A new procedure (GENLOIS) is presented for generating trees or certain classes of trees such as 4-trees (graphs representing alkanes), identity trees, homeomorphical irreducible trees, rooted trees, trees labelled on a certain vertex (primary, secondary, tertiary, etc.). The present method differs from previous procedures by differentiating among the vertices of a given parent graph by means of local vertex invariants (LOVIs). New graphs are efficiently generated by adding points and/or edges only to non-equivalent vertices of the parent graph. Redundant generation of graphs is minimized and checked by means of highly discriminating, recently devised topological indices based either on LOVIs or on the information content of LOVIs. All trees onN + 1 (N + 1 < 17) points could thus be generated from the complete set of trees onN points. A unique cooperative labelling for trees results as a consequence of the generation scheme. This labelling can be translated into a code for which canonical rules were recently stated by A.T. Balaban. This coding appears to be one of the best procedures for encoding, retrieving or ordering the molecular structure of trees (or alkanes).Dedicated to Professor Alexandru T. Balaban on the occasion of his 60th anniversary.