Tautomerism of 4-phenyl-2,4-dioxobutanoic acid. Insights from pH ramping NMR study and quantum chemical calculations

Aryldiketo acids (ADKs) exhibit the variety of biological activities, mainly due to large affinity toward divalent metal ions. Metal complexation ability of ADKs, as well as interactions with proteins, depend on tautomeric form present in solution. The main aim of this study was to fully explore the tautomeric preferences of 4-phenyl-2,4-dioxobutanoic acid (4PDA), as ADKs representative, in aqueous media at different pH values. 1D and 2D NMR spectroscopy in combination with quantum chemical calculations was applied in order to better understand the tautomeric preferences of 4PDA. The data in highly acidic media are especially interesting since there are no such findings in the literature due to low solubility of ADKs in molecular form. At low pH values, where 4PDA is unionized, the most abundant tautomeric form is enol with keto group closer to phenyl ring. At higher pH values, mixture of two 4PDA ionic forms coexists in solution. Their ratio calculated according to NMR data fits the values predicted using two experimentally determined pK _a values. Based on the complexity of ¹H NMR spectrum of monoanionic 4PDA form, coexistence of two stable rotamers was assumed. In an alkaline media, 4PDA is mostly present in dianionic form. As π-electrons of dianion are delocalized over an entire keto-enol moiety, spectral distinction between tautomers was not possible. Quantum chemical calculations were used to predict relative stability of tautomers. The predictions were in good accordance with experimental results only in case when explicit water molecule was included in calculations.     

Factorization of staircase class operators in Hilbert space

A class of linear bounded staircase operators (H, G spaces) defined by (1) with two infinite sequences of orthogonal decompositions ofH and chain property (2) is considered. Necessary and sufficient conditions for the factorizationZ=XY are obtained, whereX, Y are block-diagonal, bounded, andY has a bounded inverse. All the pairs (X, Y) are explicitly constructed. These conditions are specialized for finite and infinite dimensions of the blocks ofX, Y and for differentX, Y. A direct application to bitriangular and biquasitriangular operators is indicated.     

A remark on the definition of superselection rules in terms of unbounded operators

The mathematical definition of superselection rules in the case when observables are described by unbounded operators in a fixed Hilbert space (for instance, in the frame of Wightman's axioms) is examined. The additional condition \(P_{H_q } D \subset D\) (whereD is the common domain of definition of the operators,H _q is theqth sector, and \(P_{H_q } \) is the projection onH _q ) is found to be sufficient in order to preserve-as in the case of bounded observables—the one-to-one correspondence between reducing subspacesH _q and projections \(P_{H_q } \) from the commutantA′ of the algebraA of observables. This additional condition is equivalent to the physical requirement that every physical vector state can be uniquely represented as a linear combination of physical states, each belonging to some sector.     

National patterns in physics output by subfields

Conclusions A cluster analysis enabled to determine groups of countries with similar distribution of physics publications by subfield. Though percentage data are used, clusters form around the major producers. Values of ratios between distinct subfields provide a straightforward picture of national preferences in physics research.In some countries (e.g. [23]) the subfield distribution could be confronted with equally structurized manpower figures. For practical decisions, however, it may be necessary to elaborate on better defined narrow specialties (cf. the hitherto tackled in [18, 3]). A full-scale distribution assessment within all of physics is again suitable for bringing fresh arguments to discussions on criteria for priority choice [24] fitted to the needs of individual countries.     

Heavy-metal aromatic rings: cyclopentadienyl anion analogues Sn5(6-) and Pb5(6-) in the Zintl Phases Na8BaPb6, Na8BaSn6, and Na8EuSn6

The title compounds were prepared by direct reactions of the corresponding elements at high temperature. They are isostructural with each other (monoclinic, P2(1)/m, Z = 2; Na(8)BaPb(6), a = 13.116(4), b = 5.351(1), and c = 16.166(5) A, beta = 108.07(2) degrees; Na(8)BaSn(6), a = 12.897(4), b = 5.362(1), and c = 16.826(5) A, beta = 108.19(2) degrees; Na(8)EuSn(6), a = 12.912(2), b = 5.220(1), and c = 15.721(2) A, beta = 108.09(1) degrees ) and contain isolated, flat, and aromatic pentagonal rings of Sn(5)(6)(-) and Pb(5)(6)(-) as well as isolated anions of Sn(4)(-) and Pb(4)(-). According to four-probe conductivity measurements, the tin compounds, Na(8)BaSn(6) and Na(8)EuSn(6), are semiconducting with band gaps of 0.11 and 0.09 eV, respectively, and are therefore electronically balanced. Magnetic measurements show that Na(8)BaSn(6) is diamagnetic while Na(8)EuSn(6) is paramagnetic and undergoes two transitions at low temperatures.     

Nonstationary quantum mechanics. II. On the increase of entropy with time

On the basis of the discussion in our previous work (T1) and the reexamination of the concept of entropy of a pure quantum state it is shown that a natural explanation of the process of entropy increase exists. A new definition of an entropy operator is given and it is shown that there is not any increase of entropy when one confines oneself to the usual formalism of quantum mechanics and uses this definition. Some other attempts of proving theH theorem are briefly discussed.     

Conformal gauges and renormalized equations of motion in massless quantum electrodynamics

A formulation of massless QED is studied with a non-singular Lagrangian and conformal invariant equations of motion. It makes use of non-decomposable representations of the conformal groupG and involves two dimensionless scalar fields (in addition to the conventional charged field and electromagnetic potential) but gauge invariant Green functions are shown to coincide with those of standard (massless) QED. Assuming that the (non-elementary) representation ofG for the 5-potential which leaves the equations of motion invariant and leads to the free photon propagator of Johnson-Baker-Adler (JBA) conformal QED remains unaltered by renormalization, we prove that consistency requirements for conformal invariant 2-, 3-, and 4-point Green functions satisfying (renormalized) equations of motion and standard Ward identities lead to either a trivial solution (withe=0) or to a subcanonical dimensiond=1/2 for the charged field.To the memory of Kurt Symanzik     

Superconformal current algebras and their unitary representations

A natural supersymmetric extension is defined of the current (= affine Kac-Moody Lie) algebra ; it corresponds to a superconformal and chiral invariant 2-dimensional quantum field theory (QFT), and hence appears as an ingredient in superstring models. All unitary irreducible positive energy representations of are constructed. They extend to unitary representations of the semidirect sumS (G) of with the superconformal algebra of Neveu-Schwarz, for , or of Ramond, for =0.On leave of absence from the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences, BG-1184 Sofia, Bulgaria     

Excitation transfer between upper Se+ levels in a positive column He-Se+ laser

The rate coefficients for collision induced transitions from a laser level to neighboring levels of active medium particles are theoretically connected with the intensity of the spontaneous emission originating from these levels and its variation due to 100% modulation of the laser oscillation. The levels pertaining to the configuration 4s ² 4p ²(² P)5p of Se² are explored at conditions of operation of a positive column He-Se⁺ laser. Normalized population transfer rate coefficients are defined. Their values are obtained based on the measured spontaneous emission intensity and its variation. The dominating partners for the mixing collisions with excited selenium ions are suggested as Se⁺, Se and He⁺ in contrast with the free electrons and helium atoms.