Pyrazolyc 3-hydroxychromones: Regulation of ESIPT reaction by the “flavonol-like” intramolecular hydrogen bonding to carbonyl group oxygen,which dominates over the “alternative” H-bond to heterocyclic nitrogen

Two isomeric pyrazole derivatives of 3-hydroxychromone (3HC) with and without the possibility of the multiple intramolecular hydrogen bonds formation were compared theoretically and experimentally with the aim to find out whether the excited state intramolecular proton transfer (ESIPT) reaction follows the traditional to the most of 3HCs “flavonol-like” direction towards the CO group oxygen or an “alternative” direction towards the heterocyclic nitrogen atom.Quantum-chemical modeling and comparative study of the experimental spectral parameters of the title compounds indicated the preferential realization of “flavonol-like” ESIPT to oxygen channel.The 3HC systems with the “alternative” intramolecular hydrogen bond to nitrogen were characterized as low fluorescent and practically unable to ESIPT with participation of the nitrogen containing heterocyclic unit.     

A new form of symplectically invariant multimode uncertainty relations

We derive symplectically invariant uncertainty relations for a set of canonically conjugated variables. The uncertainty relations obtained are multimode analogs of the Robertson–Schrödinger inequalities. Our uncertainty relations are equivalent to the necessary and sufficient conditions for a matrix to be a correlation matrix of some quantum state, obtained by R. Simon and coauthors. The advantage of our inequalities, compared to that suggested by Simon, consists in its simplicity and more obvious symplectic invariance. We derive our inequalities for the case of a two-mode system in explicit form. Particular cases of small and large degrees of correlation between the first and second modes are analyzed in detail.     

Simultaneous establishing of stationary growth rate and composition of supercritical droplets at isothermal binary condensation in the diffusion-controlled regime

General integral relations expressing the droplet radius and time of the droplet nonstationary growth as nonlinear functions of solution concentration in the droplet have been derived. These relations are valid for a supercritical droplet (i.e., sufficiently large droplet, for which the Laplace pressure effect on the concentration at saturation of vapors is negligible) isothermally growing via stationary diffusion in the mixture of two condensing vapors and an incondensable carrier gas. The initial composition in the droplet may be arbitrary and partial molecular volumes of components are not fixed. Explicit analytical relations have been found for droplet composition and the droplet size as functions of time at small deviations from the stationary concentration in the growing droplet. These relations show that the assumption of the steady droplet growth rate is not valid for non-small deviations from the stationary concentration. Some illustrations of the general nonlinear theory have been done in situation when solution in the droplet can be considered ideal.     

Minimum degree of the difference of two polynomials over {\mathbb Q}, and weighted plane trees

A weighted bicolored plane tree (or just tree for short) is a bicolored plane tree whose edges are endowed with positive integral weights. The degree of a vertex is defined as the sum of the weights of the edges incident to this vertex. Using the theory of dessins d’enfants, which studies the action of the absolute Galois group on graphs embedded into Riemann surfaces, we show that a weighted plane tree is a graphical representation of a pair of coprime polynomials \(P,Q\in {\mathbb C}\,[x]\) such that: (a)  \(\deg P = \deg Q\) , and \(P\) and \(Q\) have the same leading coefficient; (b) the multiplicities of the roots of  \(P\) (respectively, of  \(Q\) ) are equal to the degrees of the black (respectively, white) vertices of the corresponding tree; (c) the degree of the difference \(P-Q\) attains the minimum which is possible for the given multiplicities of the roots of \(P\)  and  \(Q\) . Moreover, if a tree in question is uniquely determined by the set of its black and white vertex degrees (we call such trees unitrees), then the corresponding polynomials are defined over \({\mathbb Q}\) . The pairs of polynomials \(P,Q\) such that the degree of the difference \(P-Q\) attains the minimum, and especially those defined over \({\mathbb Q}\) , are related to some important questions of number theory. Dozens of papers, from 1965 (Birch et al. in Norske Vid Selsk Forh 38:65–69, 1965) to 2010 (Beukers and Stewart in J Number Theory 130:660–679, 2010), were dedicated to their study. The main result of this paper is a complete classification of the unitrees, which provides us with the most massive class of such pairs defined over  \({\mathbb Q}\) . We also study combinatorial invariants of the Galois action on trees, as well as on the corresponding polynomial pairs, which permit us to find yet more examples defined over  \({\mathbb Q}\) . In a subsequent paper, we compute the polynomials \(P,Q\) corresponding to all the unitrees.     

Estimation of Jc(B) dependence from self-field alternating current (AC) losses measured on Bi-2223/Ag tapes

Transport AC losses measured in self-field conditions on multifilamentary Bi-2223 tapes are often found to be lower than those calculated within the framework of the critical state model for a bulk wire with elliptical cross section, though generally higher than predicted for a strip. This effect is sometimes ascribed to the non-ideal geometry of the tapes, which does not exactly reproduce either shape. Here we propose an alternative explanation assuming that the critical current density of superconducting material depends on magnetic field. In practice, we analyzed the AC loss curve and deduced different I_c values for the individual data points, using the standard Norris equation for elliptical conductor. This gives the relation between ‘calculated' I_c and the self-field associated to AC transport current, which can be regarded as an alternative way to qualify the dependence of J_c on magnetic field. Important is that this procedure covers the range of fields below the self-field at I_c where the measurement in background DC field can not be used to determine J_c(B).     

On invariant subspaces and eigenfunctions of regular Hecke operators on spaces of multiple theta constants

Invariant subspaces and eigenfunctions of regular Hecke operators acting on spaces spanned by products of even number of Igusa theta constants with rational characteristics are constructed. For some of the eigenfunctions of genuses g=1 and g=2, corresponding zeta functions of Hecke and Andrianov are explicitly calculated.     

The Trifluoromethyl Anion

First evidence for the existence of free trifluoromethyl anion CF₃^? has been obtained. The 3D‐caged potassium cation in [K(crypt‐222)]⁺ is inaccessible to CF₃^?, thus rendering it uncoordinated (“naked”). Ionic [K(crypt‐222)]⁺ CF₃^? has been characterized by single‐crystal X‐ray diffraction, solution NMR spectroscopy, DFT calculations, and reactivity toward electrophiles.     

Homogeneous nucleophilic radiofluorination and fluorination with phosphazene hydrofluorides

A series of phosphazenium hydrofluorides, P(1)(tBu)·[(18/19)F]HF, P(1)(tOct)·[(18/19)F]HF, P(2)(Et)·[(18/19)F]HF, and P(4)(tBu)·[(18/19)F]HF, was synthesized. The radioactive phosphazenium [(18)F]hydrofluorides were obtained by the one-step formation and trapping of gaseous [(18)F]HF with the respective phosphazene bases. The [(19)F] isotopomers were prepared from the corresponding phosphazene bases and Et(3)N·3HF. Under the design of experiment (DoE)-optimized conditions, P(2)(Et)·HF and P(4)(tBu)·HF fluorinated alkyl chlorides, bromides, and pseudohalides in 76-98% yield, but gave lower yields with iodides and electron-deficient arenes. DoE models showed that fluorination can be performed in glass vessels, and that the reactivity of P(2)(Et)·HF and P(4)(tBu)·HF is dominated by solvent polarity but is insensitive to water to at least 2 equiv. In contrast, P(1)(tBu)·HF and P(1)(tOct)·HF were unstable towards autofluorolysis. DFT calculations were performed to rationalize this finding in terms of diminished steric bulk, higher Parr's electrophilicity, and chemical hardness of P(1)(R)H(+). The corresponding radiofluorination reaction gave no valid DoE model but displayed similar substrate scope. High specific activity and excellent radiochemical yields with various pseudohalides (81-91%) suggest that the proposed radiofluorination methodology can complement the current [(18)F]KF/Kryptofix methods, particularly in the areas for which nonpolar reaction conditions are required.     

Peculiarities of the complexation of copper and silver adducts of a 3,5-bis(trifluoromethyl)pyrazolate ligand with organoiron compounds

Interaction of the copper, {[3,5-(CF(3))(2)Pz]Cu}(3), and silver, {[3,5-(CF(3))(2)Pz]Ag}(3), macrocycles [3,5-(CF(3))(2)Pz = 3,5-bis(trifluoromethyl)pyrazolate] with cyclooctatetraeneiron tricarbonyl, (cot)Fe(CO)(3), was investigated by IR and NMR spectroscopy for the first time. The formation of 1:1 complexes was observed at low temperatures in hexane. The composition of the complexes (1:1) and their thermodynamic characteristics in hexane and dichloromethane were determined. The π-electron system of (cot)Fe(CO)(3) was proven to be the sole site of coordination in solution and in the solid state. However, according to the single-crystal X-ray data, the complex has a different (2:1) composition featuring the sandwich structure. The complexes of ferrocene with copper and silver macrocycles have a columnar structure (X-ray data).