Exact relations between the electron density and external potential for systems of interacting and noninteracting electrons

The differential virial theorem (DVT) is an explicit relation between the electron density ρ( r ), the external potential, kinetic energy density tensor, and (for interacting electrons) the pair function. The time‐dependent generalization of this relation also involves the paramagnetic current density. We present a detailed unified derivation of all known variants of the DVT starting from a modified equation of motion for the current density. To emphasize the practical significance of the theorem for noninteracting electrons, we cast it in a form best suited for recovering the Kohn–Sham effective potential v_s( r ) from a given electron density. The resulting expression contains only ρ( r ), v_s( r ), kinetic energy density, and a new orbital‐dependent ingredient containing only occupied Kohn–Sham orbitals. Other possible applications of the theorem are also briefly discussed. © 2012 Wiley Periodicals, Inc.     

A Convenient Approach to 4,7‐Dihydrotetrazolo [5,1‐c][1,2,4]triazine Synthesis

Azo coupling of 1,3‐dicarbonyl compounds with tetrazolyl‐5‐diazonium chloride is used to develop a convenient one‐step procedure for the synthesis of 4,7‐dihydrotetrazolo[5,1‐c][1,2,4]triazines. In contrast to nonfluorinated analogs, 7‐hydroxy‐7‐polyfluoroalkyl‐4,7‐dihydrotetrazolo[5,1‐c][1,2,4]triazines undergo a ring‐chain isomerism resulting from the cleavage at the C7―N7a bond. A distinctive feature of nonfluorinated 4,7‐dihydrotetrazolo[5,1‐c][1,2,4]triazines is the possibility to dehydration, which is accompanied by an azide rearrangement due to the tetrazole ring cleavage with the formation of tetrazolo[1,5‐b][1,2,4]triazines.     

Alkylation of 3‐Phenyl‐1H‐pyrazolo[4,3‐c] quinoline: Theoretical Analysis of Regioselectivity

The interaction of 3‐phenyl‐1H‐pyrazolo[4.3‐c]quinoline with alkylating agents in the presence of NaH leads mainly to N1‐substituted derivatives. The regioselectivity of the reaction has been studied using AM1 semi‐empirical calculations in the isolated molecule approximation.     

Solvent‐Free Iodination of Arenes using Iodine–Silver Nitrate Combination

A simple and environmentally safe general method of iodination of aromatic substrates under sovent‐free conditions using the I₂/AgNO₃ combination in a solid state is reported. Both activated and deactivated aromatic compounds afford the respective aryl iodides in generally high yields (80–90%).     

One-pot synthesis of 2-(dicyanomethylene)-1,2-dihydropyridine derivatives

The synthesis of 2-(dicyanomethylene)-1,2-dihydropyridine derivatives from the reactions of arylmethylidene derivatives of malononitrile dimers with 1,3-dicarbonyl compounds is described.     

Electronic structure,novel synthesis,and O—H...O and C—H...O interactions in two 6‐oxopiperidine‐2‐carboxylic acid derivatives

Molecules of (S)‐6‐oxo‐1‐(thiophen‐2‐ylmethyl)piperidine‐2‐carboxylic acid, C₁₁H₁₃NO₃S, crystallize as single enantiomers in the space group P2₁ and the thiophene ring is disordered over two positions, while (S)‐6‐oxo‐1‐(thiophen‐3‐ylmethyl)piperidine‐2‐carboxylic acid, C₁₁H₁₃NO₃S, crystallizes as a single enantiomer in the space group P2₁2₁2₁. Their absolute configurations were confirmed by anomalous dispersion effects in diffraction measurements on the crystals. The molecules of each compound are linked by a combination of strong O—H...O hydrogen bonds and weak C—H...O interactions, resulting in two‐ and three‐dimensional networks, respectively, in the crystal structures.     

Effect of bulk density on flame resistance of rockwool in combined fire-resistant facings

Journal of Thermal Analysis and Calorimetry - Fire protection of steel structures is playing an increasingly important role nowadays. The fire protection of steel structures can be solved with...     

Multiarm Star-Shaped Polydimethylsiloxanes with a Dendritic Branching Center

New multiarm stars have been synthesized based on polylithium derivatives of high-generation carbosilane dendrimers. In the synthesis of multiarm stars based on the eighth-generation dendrimer, steric hindrances were observed even during the synthesis of a polylithium initiator. Subsequently, this led to chain transfer reactions between growing arms, as well as other side effects. As a result, dense nanogel formations with a higher tendency of ordering than in classical objects of this type were isolated from the reaction mixture. The study of the rheology of multiarm stars based on sixth-generation dendrimers made it possible to determine the activation energies of viscous flow in these objects, which makes it possible to consider them as objects with a macromolecular nature and a reptation flow mechanism.