Regioselective cycloaddition of C-aryl- and C-carbamoylnitrones to methyl 2-benzylidenecyclopropanecarboxylate

C-Aryl- and C-carbamoylnitrones reacted with methyl 2-benzylidenecyclopropanecarboxylate in highly regioselective fashion to give the corresponding 1,3-dipolar cycloaddition products, substituted methyl 5-oxa-6-azaspiro[2.4]heptane-1-carboxylates as mixtures of two diastereoisomers.     

Synthesis of dispiro[2.1.3.1]nonane and trispiro[2.1.1.37.15.13]-dodecane

Russian Journal of Organic Chemistry -     

Reduction and hydrolysis of substituted 5-oxa-6-azaspiro[2.4]heptane-1,2-dicarboxylic acid esters

Substituted 5-oxa-6-azaspiro[2.4]heptane-1,2-dicarboxylic acid esters synthesized by reaction of nitrones with dimethyl 3-methylidenecyclopropane-1,2-dicarboxylate were reduced with lithium tetrahydridoaluminate to the corresponding bis(hydroxymethyl)cyclopropanes. Alkaline hydrolysis of the title compounds gave substituted cyclopropane-1,2-dicarboxylic acids. In both cases, the 5-oxa-6-azaspiro[2.4]heptane fragment remained intact.     

Enthalpies of solvation for dopamine hydrochloride in water-ethanol solutions

The enthalpies of dissolution of dopamine hydrochloride (H₂Dop · HCl) in water-ethanol solvents containing from 0 to 0.8 mole fraction of ethanol are measured by calorimetry at 298.15 K. Standard enthalpies of transfer (??_tr H ^°) for the molecular (H₂Dop) and cationic (H₃Dop⁺) forms of dopamine from water into binary solvents are calculated from the obtained data. The enthalpies of transfer of H₃Dop⁺ cation are determined from the enthalpies of dissolution of H₂Dop · HCl using the familiar method of separating the molar quantities into ionic contributions (Ph₄P⁺ = BPh ₄ ^? ), and by an original alternative procedure. The effect of the composition of the binary solvent on the solvation of dopamine is considered.     

1H NMR, 13C NMR, and computational DFT studies of the structure of 2-acylcyclohexane-1,3-diones and their alkali metal salts in solution

1H and 13C NMR spectra of 2-acyl-substituted cyclohexane-1,3-diones (acyl = formyl, 1; 2-nitrobenzoyl, 2; 2-nitro-4-trifluoromethylbenzoyl, 3) and lithium sodium and potassium salts of 1 have been measured. The compound 3, known as NTBC, is a life-saving medicine applied in tyrosinemia type I. The optimum molecular structures of the investigated objects in solutions have been found using the DFT method with B3LYP functional and 6-31G** and/or 6-311G(2d,p) basis set. The theoretical values of the NMR parameters of the investigated compounds have been calculated using GIAO DFT B3LYP/6-311G(2d,p) method. The theoretical data obtained for compounds 1-3 have been exploited to interpret their experimental NMR spectra in terms of the equilibrium between different tautomers. It has been found that for these triketones an endo-tautomer prevails. The differences in NMR spectra of the salts of 1 can be rationalized taking into account the size of the cation and the degree of salt dissociation. It seems that in DMSO solution the lithium salt exists mainly as an ion pair stabilized by the chelation of a lithium cation with two oxygen atoms. The activation free energy the of formyl group rotation for this salt has been estimated to be 51.5 kJ/mol. The obtained results suggest that in all the investigated objects, including the free enolate ions, all atoms directly bonded to the carbonyl carbons lie near the same plane. Some observations concerning the chemical shift changes could indicate strong solvation of the anion of 1 by water molecules. Implications of the results obtained in this work for the inhibition mechanism of (4-hydroxyphenyl) pyruvate dioxygenase by NTBC are commented upon.     

Large deviations for a symmetric branching random walk on a multidimensional lattice

An important role in the theory of branching random walks is played by the problem of the spectrum of a bounded symmetric operator, the generator of a random walk on a multidimensional integer lattice, with a one-point potential. We consider operators with potentials of a more general form that take nonzero values on a finite set of points of the integer lattice. The resolvent analysis of such operators has allowed us to study branching random walks with large deviations. We prove limit theorems on the asymptotic behavior of the Green function of transition probabilities. Special attention is paid to the case when the spectrum of the evolution operator of the mean numbers of particles contains a single eigenvalue. The results obtained extend the earlier studies in this field in such directions as the concept of a reaction front and the structure of a population inside a front and near its boundary.     

Quenched to annealed transition in the parabolic Anderson problem

We study limit behavior for sums of the form $\frac{1}{|\Lambda_{L|}}\sum_{x\in \Lambda_{L}}u(t,x),$ where the field $\Lambda_L=\left\{x\in {\bf{Z^d}}:|x|\le L\right\}$ is composed of solutions of the parabolic Anderson equation $$u(t,x) = 1 + \kappa \mathop{\int}_{0}^{t} \Delta u(s,x){\rm d}s + \mathop{\int}_{0}^{t}u(s,x)\partial B_{x}(s). $$ The index set is a box in Z ^d , namely $\Lambda_{L} = \left\{x\in {\bf Z}^{\bf d} : |x| \leq L\right\}$ and L = L(t) is a nondecreasing function $L : [0,\infty)\rightarrow {\bf R}^{+}. $ We identify two critical parameters $\eta(1) < \eta(2)$ such that for $\gamma > \eta(1)$ and L(t) = e^{γ t} , the sums $\frac{1}{|\Lambda_L|}\sum_{x\in \Lambda_L}u(t,x)$ satisfy a law of large numbers, or put another way, they exhibit annealed behavior. For $\gamma > \eta(2)$ and L(t) = e^{γ t} , one has $\sum_{x\in \Lambda_L}u(t,x)$ when properly normalized and centered satisfies a central limit theorem. For subexponential scales, that is when $\lim_{t \rightarrow \infty} \frac{1}{t}\ln L(t) = 0,$ quenched asymptotics occur. That means $\lim_{t\rightarrow \infty}\frac{1}{t}\ln\left (\frac{1}{|\Lambda_L|}\sum_{x\in \Lambda_L}u(t,x)\right) = \gamma(\kappa),$ where $\gamma(\kappa)$ is the almost sure Lyapunov exponent, i.e. $\lim_{t\rightarrow \infty}\frac{1}{t}\ln u(t,x)= \gamma(\kappa).$ We also examine the behavior of $\frac{1}{|\Lambda_L|}\sum_{x\in \Lambda_L}u(t,x)$ for L = e ^{γ t} with γ in the transition range $(0,\eta(1))$