Internal rotation: single diagonalization approach versus standard approaches, application to the methyl peroxy radical Ã←X̃ transition

A new approach avoiding double (two-step) diagonalization is proposed to deal with internal rotation. The development of this method was stimulated by the jet-cooled high resolution spectrum of the vibrationless A?←X? transition of the deuterated species of the methyl peroxy radical. This spectrum, originally analyzed with a rigid rotor Hamiltonian including spin-rotation but neglecting internal rotation, has been revisited in the previous paper (P. Dupre?, J. Chem. Phys. 134, 244308 (2011)) and a determinable yaw of the molecular principal axes of inertia about the c-axis (axis-switching) during the electronic transition was established. The spectral resolution of the jet-cooled data of the vibrationless transition (～7355 - 7390?cm(-1)) does not allow the observation of splitting due to internal rotation of the methyl top, but when these data are combined with the low resolution room temperature data (～7200 - 8000?cm(-1)) accurate fits or simulations of the two sets of data are possible. A recent study of the room temperature data has been reported in this journal (G. M. P. Just et al., J. Chem. Phys. 127, 044310 (2007)) showing evidence of the internal rotation coupling by analyzing the intensity of the torsional mode energy progression. That investigation combined ab initio quantum chemistry calculations and the rho-axis-method (RAM) to model the internal rotation. Here, a comparison of full spectral intensity analyses based on both the usual RAM and on the new approach requiring a single-diagonalization principal-axis-method is presented. The comparison favors the single-diagonalization approach. Axis-switching and spin-rotation coupling are incorporated in the analysis, in which the use of the principal axes of inertia is maintained. Symmetries, energy levels, and advantages are carefully discussed for all methods.     

Lanthanide polyoxocationic complexes: experimental and theoretical stability studies and Lewis acid catalysis

The [ε-PMo(V)(8)Mo(VI)(4)O(36)(OH)(4){Ln(III)(H(2)O)}(4)](5+) (Ln=La, Ce, Nd, Sm) polyoxocations, called εLn(4), have been synthesized at room temperature as chloride salts soluble in water, MeOH, EtOH, and DMF. Rare-earth metals can be exchanged, and (31)P NMR spectroscopic studies have allowed a comparison of the affinity of the reduced {ε-PMo(12)} core, thus showing that the La(III) ions have the highest affinity and that rare earths heavier than Eu(III) do not react with the ε-Keggin polyoxometalate. DFT calculations provide a deeper insight into the geometries of the systems studied, thereby giving more accurate information on those compounds that suffer from disorder in crystalline form. It has also been confirmed by the hypothetical La→Gd substitution reaction energy that Ln ions beyond Eu cannot compete with La in coordinating the surface of the ε-Keggin molybdate. Two of these clusters (Ln=La, Ce) have been tested to evidence that such systems are representative of a new efficient Lewis acid catalyst family. This is the first time that the catalytic activity of polyoxocations has been evaluated.     

Research activities of the “environmental geochemistry” European associated laboratory

The results of research activities of the Laboratoire Europénne Associé en Géochimie Environnementale (LEAGE) (“Environmental Geochemistry” European Associated Laboratory) devoted to study of fluids at low and high temperatures during the first year activity were presented.     

Light scattering study of the isotropic-to-blue phase transition in cholesteryl oleyl carbonate (COC) and its mixtures with a nematogen

Abstract

Light scattering experiments have been performed on cholesteryl oleyl carbonate (COC) and its mixtures with a nematogen in order to investigate pretransition phenomena accompanying the transition from the isotropic to the blue phase. Estimates of the critical temperature for the flat-spiral (m = 2) mode have been obtained in each case. The critical temperatures approach the transition temperature, T _c, in the mixtures, probably due to an impurity-induced blurring of the phase transition. Measurements of the optical rotatory power have also been carried out on pure COC as well as its mixtures with the nematogen and possible origins for the pretransition phenomena observed are discussed.     

A Banach Algebra Version of the Sato Grassmannian and Commutative Rings of Differential Operators

We show that commutative rings of formal pseudodifferential operators can be conjugated as subrings in noncommutative Banach algebras of operators in the presence of certain eigenfunctions. Techniques involve those of the Sato Grassmannian as used in the study of the KP hierarchy as well as the geometry of an infinite dimensional Stiefel bundle with structure modeled on such Banach algebras. Generalizations of this procedure are also considered.     

Electrochemical study of intercalated vanadyl phosphate

A detailed electrochemical study of Li intercalation/deintercalation in VOPO₄ compounds with various inserted molecules (H₂O, HCOOH and CH₃COOH) is presented. For VOPO₄·2H₂O, water oxidation is responsible for capacity fading. In order to improve the cyclability, the electrochemical behavior of other intercalated VOPO₄ compounds, such as VOPO₄·H₂O, VOPO₄·HCOOH and VOPO₄·0.78CH₃COOH, has been studied. For all these materials, the intercalation (deintercalation) takes place in several steps. The electrochemical study of the monohydrate indicates that the vanadium-coordinated water molecule is more stable than the second water molecule towards cycling. The highest initial specific capacity values (approximately 100 mAh/g) are obtained for the compounds with the largest interlayer space. Upon cycling, the pillaring molecules are destroyed by a high-potential oxidation process, yielding a collapse of the 2D structure and thus a loss of crystallinity. As a result, the observed specific capacity is the same for all the materials after a long cycling. This capacity is higher than the anhydrous one.     

The Stiefel bundle of a Banach algebra

We introduce the Stiefel bundle associated to a given Banachable algebra and study the properties of this analytic principal fiber bundle over the Grassmannian of equivalence classes of idempotents in the algebra. Our main application concerns the bounded linear operators of a Banach space. In particular, the problem of smooth parametrization of subspaces can then be reduced to one involving the smooth extension of sections.