Supernovae and the Arrow of Time

Supernovae are explosions of stars and are a central problem in astrophysics. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities develop during the star’s explosion and lead to intense interfacial RT/RM mixing of the star materials. We handle the mathematical challenges of the RT/RM problem based on the group theory approach. We directly link the conservation laws governing RT/RM dynamics to the symmetry-based momentum model, derive the model parameters, and find the analytical solutions and characteristics of RT/RM dynamics with variable accelerations in the linear, nonlinear and mixing regimes. The theory outcomes explain the astrophysical observations and yield the design of laboratory experiments. They suggest that supernova evolution is a non-equilibrium process directed by the arrow of time.     

Correlated MO study of the low-barrier intramolecular motions in donor-acceptor ethenes

Correlated MP2 and MCSCF MO calculations of several model push-pull ethenes in most cases indicate no great participation of excited singlet and triplet electronic configurations in either the minima or the transition structures for the suggested facilitated intramolecular rotation about the polarized C=C bond. This situation changes significantly only in molecules with sulfur atoms in the molecule as either donors or acceptors. The outstanding contribution of sulfur atoms as either donors or acceptors is a significant increase of push-pull ethene molecular polarizabilities. Thus, within the studied small series of mostly planar push-pull ethenes, polarizability appears a better indicator of rapid intramolecular motions about the C=C bond than straight polarity. Substituents with larger steric demands around the C=C bond are shown to likely preclude its complete turnaround, thus prompting a ramification of the interpretations of dynamic NMR phenomena in sterically constrained push-pull ethenes as large-amplitude librations resulting from strong rovibrational and relatively weak electronic coupling. These librations, as shown by complete vibrational mode analysis of corresponding rotational transition structures, cover in fact certain sectors of the intuitively suggested full rotations similar to those about C-C single bonds.     

A computational study of the Diels-Alder reaction of ethyl-S-lactyl acrylate and cyclopentadiene. Origins of stereoselectivity

The eight diastereoisomeric transition structures of the Diels-Alder addition of ethyl-S-lactyl acrylate and cyclopentadiene have been investigated in the gas phase and in solution by HF, MP2, and density functional theory (B3LYP and B3PW91) methods with the 6-31G(d,p) basis set. At all levels of theory used, the s-cis transition structures are more stable than the s-trans ones. The contribution of the s-trans transition structures increases in solution and, although still small, has to be taken in consideration for correct prediction of stereoselectivity. Diastereofacial selectivity is interpreted in terms of electrostatic (weak hydrogen bonding) C=O...H(C) interactions between the carbonyl group(s) of the dienophile and cyclopentadiene in the energetically favored transition structures. Endo/exo reaction selectivity is attributed to positive orbital interactions between the diene and the acrylate carbonyl oxygen in the endo s-cis transition structures. Ab initio methods reproduce well the experimentally observed trends in both endo/exo and diastereofacial selectivity. Density functional calculations in the gas phase correctly reproduce the observed trends in diastereofacial selectivity but single-point MP2 calculations are necessary to reproduce the experimental trend in endo/exo selectivity.     

Complexes of esters of ethylenediphosphonic acid with lanthanide nitrates—synthesis and structure

The lanthanide complexes L₂Ln(NO₃)₃ ( 3 ) and L′ ₃[Ln(NO₃)₃]₂ ( 5 ) (Stewart and Siddall III. J Inorg Nucl Chem 1971, 33, 2965–2970) were obtained, where L is the tetraethyl ester of ethylenediphosphonic acid ( 2 ), L′ is the tetraisopropyl ester of ethylenediphosphonic acid ( 4 ), and Ln is La, Ce, Sm, Eu, and Er. In extension of a former study, they were characterized additionally with NMR spectroscopy. In contrast to the compounds of type 3 , the erbium complex of the ligand L is consistent with the formula L₃[Er(NO₃)₃]₂. The crystal structure of the complex 3a (Ln = La) is determined by single crystal X‐ray diffraction. The complex is found to crystallize in the monoclinic space group C2/c with a = 15.1415(4) Å, b = 14.9749(4) Å, c = 18.3887(5) Å, β = 114.129(1)ˆ, T = 153 K, V = 3805.2(2) ų, Z = 4, ρ_calc = 1.622 g/cm³, R₁ = 0.023, R2w = 0.058, S = 1.08 for all 6823 reflections. The complex 3a consists of polymer chains with bridged bidentate phosphonate ligands. The lanthanum atom is coordinated by ten oxygen atoms, six of them from the three bidentate nitrate ions, and four from the two phosphonate ligands. © 2006 Wiley Periodicals, Inc. Heteroatom Chem 17:36–46, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20188     

The conversion of phenylpropanedinitrile (phenylmalononitrile) into the carbanion, followed by IR spectra, ab initio and DFT force field calculations

The spectral and structural changes, caused by the conversion of phenylpropanedinitrile (phenylmalononitrile) into the carbanion, have been followed by IR spectra, ab initio HF, MP2 and DFT BLYP force field calculations. In agreement between theory and experiment, the conversion is accompanied with strong frequency decreases (with 114 cm(-1), mean value) of the cyano stretching bands nu(C triple bond N), dramatic increases in the corresponding integrated intensities (136-fold, total value), strong enhancement of the nu(C triple bond N) vibrational coupling and other essential spectral changes. According to the calculations, the strongest structural changes take place at the carbanionic center: (i) shortenings of the Cz-Ph and Cz-CN bonds with 0.064-0.092 A, and increases in the corresponding bond orders with 0.14-0.21 U; (ii) simultaneous enlargements of the bond angles at the same carbon atom with 7.6 degrees -9.7 degrees, as from tetrahedral its configuration becomes trigonal. The carbanionic charge is distributed between the two cyano groups (0.44-0.52 e(-)), phenyl ring (0.31-0.34 e(-)) and carbanionic center (0.14-0.25 e(-)). The formation of moderately strong (CH(3))(2)S=O...H-C(CN)(2)C(6)H(5) hydrogen bonds has been found experimentally.     

Synthesis and Structure of Complexes of the Diethyl Ester of 2-Dimethylamino-2-oxoethylphosphonic Acid with Lanthanide Nitrates

The lanthanide complexes LnL 2 (NO 3 ) 3 ( 3a-g ) are obtained where Ln is La, Sm, Yb, Er, Ce, Eu, Gd, and L is the diethyl ester of 2-dimethylamino-2-oxoethylphosphonic acid [(C 2 H 5 O) 2 P(O)CH 2 CON(CH 3 ) 2 ] 1 . They are characterized by elemental analysis, i.r. and NMR spectroscopy. The crystal structure of 3a is determined by single crystal X-ray diffraction. The complex is found to crystallize in the triclinic space group P 1 with a = 8.4220(17) Å, b = 11.123(2) Å, c = 17.560(4) Å, f = 87.20(3);, g = 82.27(3);, n = 76.89(3);, V = 1587.3(5) Å 3 , Z = 2, calcd = 1.614 mg/m 3 , R = 0.047, R w = 0.107, S = 1.034 for 5762 reflections with I > 2 (I). The structure contains monomeric units of the complex with the lanthanum atom coordinated by 10 oxygen atoms, six of them from the three bidentate nitrate ions and four from the two phosphonate ligands. The coordination is realized by both phosphoryl and amide-carbonyl oxygen atoms. The stereochemistry of the starting ligand 1 is investigated by NMR spectroscopy.     

Synthesis and Characterization of an Exopolysaccharide by Antarctic Yeast Strain <Emphasis Type="Italic">Cryptococcus laurentii</Emphasis> AL<Subscript>100</Subscript>

An exopolysaccharide-producing Antarctic yeast strain was selected and identified as Cryptococcus laurentii AL₁₀₀. The physiological properties of the strain and its ability to utilize and biotransform different carbon sources (pentoses, hexoses, and oligosaccharides) into exopolysaccharide and biomass were investigated. Sucrose was chosen as a suitable and accessible carbon source. The biosynthetic capacity of the strain was studied in its dynamics at different sucrose concentrations (20, 30, 40, and 50 g/L) and temperatures (22 and 24 °C). The maximum biopolymer quantity of 6.4 g/L was obtained at 40 g/L of sucrose, 22 °C temperature and 96-h fermentation duration. The newly synthesized microbial carbohydrate was a heteropolysaccharide having the following monosaccharide composition: arabinose, 61.1%; mannose, 15.0%; glucose, 12.0%; galactose, 5.9%; and rhamnose, 2.8%. It was characterized by polydispersity of the polymer molecule, 60% of it having molecular mass of 4200 Da. The exopolysaccharide demonstrated good emulsifying and stabilizing properties with regard to oil/water emulsions and a pronounced synergistic effect with other hydrocolloids such as xanthan gum, guar gum, and alginate.     

Strict stability in terms of two measures for impulsive differential equations with ‘supremum’

Strict stability for a nonlinear system of impulsive differential equations with ‘supremum’ is defined and studied. Razhumikhin method with piecewise continuous scalar Lyapunov functions and comparison results for scalar impulsive differential equations are the bases of the main proofs. To unify a variety of stability concepts and to offer a general framework for the investigation of the stability theory, the notion of stability in terms of two measures has been applied. An example illustrating the usefulness of the obtained sufficient conditions is also included.