Large field renormalization. I. The basic step of the ℝ operation

We construct the renormalization operation of the expressions connected with the large field regions. This operation, denoted by , removes the main obstacle to prove the ultraviolet stability of four-dimensional gauge field theories. The proof will be completed in the second part of this paper.Research supported in part by the National Science Foundation under Grant DMS-86 02207     

Crystal Structure of the E-2,4-Dinitrophenylhydrazone of 2-Acetyl-3-phenyl-5-methylfuran

The molecular structure of the title E-(syn)-2,4-dinitrophenylhydrazone (DNPH) has been determined and compared with that of the known parent ketone. Semiempirical (AM1, PM3) and molecular mechanics (MM+, Sybyl) calculations gave inconclusive results regarding the possible configurations (syn versus anti) and conformations (s-cis versus s-trans). In the crystal the title molecule is almost planar in an s-trans conformation with the phenyl ring twisted by 30.0° out of the furan plane. Thus, the present DNPH, in the syn configuration, mimics very well the conformation of the parent crystalline ketone. The previous assignment based on solution data of this DNPH as anti is incorrect. It is thus shown that due to the strong intramolecular hydrogen bond NHO₂N (ortho) within the DNPH part, the syn-anti DNPH formation is not affected by the putative hydrogen bond to the furanic oxygen atom.C. D. Nenitzescu     

Energies for cyclic and acyclic aggregations of adamantane and diamantane units sharing vertices,edges, or six‐membered rings

Diamondoids are hydrocarbons having a carbon scaffold comprised from polymer‐like composites of adamantane cages. This article describes computed total energies and “SWB‐tension” energies (often referred to as “strain” energies) for species having n adamantane or diamantane units sharing pairwise: one carbon atom (spiro‐[n]adamantane or spiro‐[n]diamantane); one C? C bond (one‐bond‐sharing‐[n]adamantane or one‐bond‐sharing‐[n]diamantane); or one chair‐shaped hexagon of carbon atoms (1234‐helical‐cata‐[n]diamantanes). Each of the five investigated polymer‐like types is considered either as an acyclic or a cyclic chain of adamantane‐ or diamantane‐unit cages. With increasing n values, SWB‐tension energies for acyclic aggregates are found to increase linearly, while the net SWB‐tension energies of cyclic aggregates often go thru a minimum at a suitable value of . In all five cases, a limiting common energy per unit ( ) is found to be approached by both cyclic and acyclic chains as , as revealed from plots of versus 1/n for acyclic chains and of versus 1/n² for cyclic chains. © 2015 Wiley Periodicals, Inc.     

Protochirons and protohelices

A simple “protochiron” is used to systematically develop and describe molecular helices, especially on the cubic and diamond lattices.     

Application of variable anti-connectivity index to active sites. Modelling pK a values of aliphatic monocarboxylic acids

A partial distance-weighted variable anti-connectivity topological index was introduced for modelling pK _a values of 31 aliphatic carboxylic acids and haloalkyl-carboxylic acids. The partial distance-weighted variable anti-connectivity index showed superior modelling capabilities compared with the index calculated from the complete graph, because it is capable of accounting correctly for the intramolecular interactions of unconnected vertices to specific bond strengths (active site), thereby improving the RMS_CV error by about 30% (0.221 pK _a units).     

Local aromaticity in benzo- and benzocyclobutadieno-annelated anthracenes

Abstract  

Considerations based on the energetics of cyclic conjugation in individual rings indicate that benzocyclobutadieno-annelation has the opposite effect on local aromaticity in benzenoid hydrocarbons to benzo-annelation. This finding is now tested and corroborated by density functional theory (DFT) calculations of the geometry of all benzo- and benzocyclobutadieno-annelated congeners of anthracene. The harmonic oscillator model of aromaticity (HOMA) and some similar (geometry-based) indices of local aromaticity are found to have the same dependence on the modes of annelation as the molecular-graph-based energy effects.     

On structural interpretation of several distance related topological indices.

We consider the role that individual bonds play in bond-additivities in order to better understand the structural basis of various topological indices. In particular we consider indices closely related to the Wiener index (W) and the distance matrix and search for optimal weights of terminal and interior CC bonds in alkanes for a selection of physicochemical properties. It is interesting to note that different properties are associated with different relative roles of the exterior and the interior CC bonds.     

An Investigation of the N-Arylsulfonylation of 2-Azetidinones

N-Arylsulfonylation of 2-azetidinones can lead to the diastereoselective formation of oligomerization products. However, a simple increase of arylsulfonyl chloride concentration minimized oligomerization and allowed preparation of 1-arylsulfonyl-2-azetidinones in good yield.