Finding a subdivision of a prescribed digraph of order 4

The problem of when a given digraph contains a subdivision of a fixed digraph F is considered. Bang‐Jensen et al. [4] laid out foundations for approaching this problem from the algorithmic point of view. In this article, we give further support to several open conjectures and speculations about algorithmic complexity of finding F‐subdivisions. In particular, up to five exceptions, we completely classify for which 4‐vertex digraphs F, the F‐subdivision problem is polynomial‐time solvable and for which it is NP‐complete. While all NP‐hardness proofs are made by reduction from some version of the 2‐linkage problem in digraphs, some of the polynomial‐time solvable cases involve relatively complicated algorithms.     

Microwave-assisted three component synthesis of novel bis-fused quinazolin-8(4H)-ones linked to aliphatic or aromatic spacer via amide linkages

Abstract

A novel series of bis(tetrahydro[1,2,4]triazolo[5,1-b]quinazolin-8-ones) and bis(tetrahydrobenzo[4,5]imidazo[2,1-b]quinazolinones) containing amide linkages were regionselectively prepared via a three-component reaction of bis(aldehydes) with dimedone and 3-amino-1,2,4-triazole (or 2-aminobenzimidazole) under conventional heating as well as under microwave irradiation.     

Efficient synthesis of 1,4-disubstituted triazolyl N-carboxamides via a simple and convenient MCR using basic alumina as solid support

A microwave assisted green protocol for the synthesis of 1,4-disubstituted triazolyl N-carboxamides was explored using basic alumina as solid support. The method allows domino Ullmann-type reaction, Click reaction and formation of ester or amide linkages in a single reaction vessel using Cu(phen)(PPh₃)Br and CMPA as catalyst and basic alumina as solid support in high yield. The protocol did not require addition of any external ligands or base. The method was also found to be equally good for the synthesis of bis triazole adducts.     

Exploring new species on the [H,S, Se,Cl] potential energy surface

This investigation is concerned with the characterization of seleno‐sulfide‐halogen model systems, the isomerization processes, and the dissociation into diatomic fragment channels on the [H, S, Se, Cl] potential energy surface. Structural, energetic, and vibrational data were obtained at the CCSD(T) and MP2 levels of theory with the series of correlation consistent basis sets and extrapolated to the complete basis set (CBS) limit. For the frequencies, additional computations were performed to include the contribution of anharmonic effects, and for the determination of the heats of formation, important corrections incorporating core‐valence correlation effects and relativistic effects (scalar and spin‐orbit) were taken into account. CCSD(T)/CBS relative stability (kcal mol^?1) follows the order: HSSeCl (0.0), HSeSCl (8.80), SSeHCl (23.52), and SeSHCl (25.87). The cis‐rotational barrier for the two lowest isomers is practically identical (10.14 and 10.09 kcal mol^?1), whereas for the trans barrier, we obtained 9.25 (HSSeCl) and 8.45 (HSeSCl) kcal mol^?1. Dissociation of HSSeCl (HSeSCl) into HS (HSe) + SeCl (SCl) requires 59.70 (56.30) kcal mol^?1. For the most stable isomer, we predict a value of the heat of formation at 298.15 K of 2.53 kcal mol^?1. One of the outcomes of this research is that the MP2 results are consistent with those of CCSD(T). The MP2 method turns out to be a reliable alternative for a first exploration of larger catenated species, although it accounts for a lesser fraction of correlation effects. © 2012 Wiley Periodicals, Inc.