X-ray structural analyses and DFT study of 7-thianorbornenes: 4-aza-4-phenyl-10-thiatricyclo[5.2.1.0.<Superscript>2,6</Superscript>]deca-8-ene-3,5-dione and 4-aza-l,4,7-trimethyl-10-thiatricyclo[5.2.1.0.<Superscript>2,6</Superscript>]deca-8-ene-3,5-dione

X-ray structures of Diels–Alder adducts of thiophene with N-methylmaleimide and 2,5-dimethylthiophene with N-phenylmaleimide were determined and compared to literature data. In addition, quantum chemical calculations at various levels of theory were used to study their molecular and electronic structure. A comparison with experimental results showed that MP2/6-31G^*, HF/6-311+G^** and PBE1PBE/6-31G^* methods give the most accurate structures.

Dipolar Cycloaddition Reactions of Azomethine Ylides Generated by endocyclic‐exocyclic 1,3‐dipole Rearrangement

Dipolar cycloaddition of polycyclic azomethine ylides, in which the central nitrogen atom is part of a pyrrolidine ring and bears a methoxycarbonyl group with norbornenes has been shown to produce two main types of products featuring pyrrolizidine rings. In conjuction with results of quantum chemical calculations (B3LYP), mechanistic rationale was postulated. The key reaction step is unprecedented endocyclic to exocyclic azomethine ylide rearrangement by an intermolecular prototropic migration (formal [1,3] H‐shift).     

Tetrakis‐(N‐pyrrolyl)methane: Structurally Important Member of the C(NR2)4 Family

The structural motif C(NR₂)₄ is rare in chemistry. The formation, NMR spectroscopic characteristics, and X‐ray structure are reported for a structurally interesting member of this family, namely tetrakis‐(N‐pyrrolyl)methane.     

Ion-specific and charge effects in counterion binding to poly(styrenesulfonate) anions

In order to obtain a deeper insight into effects occurring when an electrolyte solution is added to a solution of a strong polyelectrolyte, the microcalorimetric and potentiometric titrations of poly(sodium 4-styrenesulfonate) (Na(+)PSS(-)) solution with different alkali, earth-alkali and tetraalkylammonium nitrate, perchlorate and chloride solutions were performed. From the calorimetric titrations the differences in sign and magnitude of enthalpy change upon addition of various electrolytes were observed depending on the salt used. Potentiometric titrations using a sodium ion selective electrode have revealed that addition of an electrolyte is accompanied by the increase in sodium activity until a certain critical value is reached, which seems to be the consequence of counterion substitution on the polyelectrolyte chain. In the case of addition of lithium and sodium salts the experimental results for ΔH of mixing can be qualitatively correctly explained by the Poisson-Boltzmann and Monte Carlo calculations based on the continuum solvent models. This is not the case for the mixtures with KNO(3), RbNO(3) and CsNO(3) salts. The results suggest that the ion-specific effects, associated with the changes in the water structure, have to be taken into account when thermodynamic properties of polyelectrolytes in solution are concerned. The calorimetric results imply that the enthalpically observed cation specificity for binding to a poly(styrenesulfonate) group could be correlated with corresponding cation hydration enthalpies. The counterion substitution of sodium with divalent cations was found to be endothermic, which is in qualitative agreement with the electrostatic theory.     

Thermal reaction of [3,4]-benzo-8-substituted-3Z,5Z,7E-octatetraenes and quantum-chemical study of the (8π,6π)-electrocyclisation

The first example of thermal (8π,6π)-electrocyclisation of 1,3,5,7-octatetraene with one double bond embedded in an aromatic moiety is described. By this process, [3,4]-benzo-8-substituted octatetraene derivatives, the cis,trans-1-(o-vinylphenyl)-4-(R = Me, Ph, 2-furyl)buta-1,3-dienes were transformed to a new endo-7-(R = Me, Ph, 2-furyl) and exo-7-(R = Me)-2,3-benzobicyclo[4.2.0]octa-2,4-dienes. Mechanism of reaction was also studied by DFT quantum-chemical calculations. The M06/6-311+G(d,p)//M06/6-31+G(d,p) calculations indicate that formation of the single endo-isomer in the case of phenyl and 2-furyl substituents is determined by higher activation barriers for exo-6π-electrocyclisation than for 8π-cycloreversion.     

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.     

Structure of Diels-Alder adduct of phenylated germole and 1,4-epoxy-1,4-dihydronaphthalene revisited

High pressure synthesis of Diels-Alder adduct of 1,1-dimetyl-2,3,4,5-tetraphenylgermole and 6,7-dibromo-1,4-epoxy-1,4-dihydronaphthalene is described. The X-ray crystallography analysis of the so obtained adduct indicated that the adduct has exo,endo-structure in agreement with our earlier proposal for the stereochemistry of the structurally related germa analogue, 11,11-dimethyl-9,10-epoxy-1,4-germa-1,2,3,4-tetraphenyl-1,4,4a,9,9a,10-hexahydroanthracene based on NMR analysis.