Hydrogen Bonding in Fluorinated Amides: FTIR,Two Dimensional Correlation Spectroscopy and DFT Calculations

Fluorinated macromers with amidic functional groups are used as additives in several high tech applications. We show here how aggregation phenomena related to hydrogen bonding are one of the key factor determining their chemical/physical and macroscopic properties. IR spectra are analyzed depending on different external parameters such as the concentration of amide groups and temperature. The experimental findings have been interpreted by means of DFT (Density Functional Theory) calculations on suitable molecular models. Moreover, 2D correlation spectroscopy has been applied to different sets of data, considering concentration and temperature as perturbing variables. The two dimensional correlation approaches confirmed the computational results and give an overall interpretation of the effects due to concentration and temperature.     

On the Effect of Tether Composition on cis/trans Selectivity in Intramolecular Diels–Alder Reactions

Intramolecular Diels–Alder (IMDA) transition structures (TSs) and energies have been computed at the B3LYP/6‐31+G(d) and CBS‐QB3 levels of theory for a series of 1,3,8‐nonatrienes, H₂C?CH? CH?CH? CH₂? X? Z? CH?CH₂ [? X? Z? =? CH₂? CH₂? ( 1 ); ? O? C(?O)? ( 2 ); ? CH₂? C(?O)? ( 3 ); ? O? CH₂? ( 4 ); ? NH? C(?O)? ( 5 ); ? S? C(?O)? ( 6 ); ? O? C(?S)? ( 7 ); ? NH? C(?S)? ( 8 ); ? S? C(?S)? ( 9 )]. For each system studied ( 1 – 9 ), cis‐ and trans‐TS isomers, corresponding, respectively, to endo‐ and exo‐positioning of the ? C? X? Z? tether with respect to the diene, have been located and their relative energies (E_rel^TS) employed to predict the cis/trans IMDA product ratio. Although the E_rel^TS values are modest (typically <3 kJ mol^?1), they follow a clear and systematic trend. Specifically, as the electronegativity of the tether group X is reduced (X?O→NH or S), the IMDA cis stereoselectivity diminishes. The predicted stereochemical reaction preferences are explained in terms of two opposing effects operating in the cis‐TS, namely (1) unfavorable torsional (eclipsing) strain about the C4? C5 bond, that is caused by the ? C? X? C(?Y)? group’s strong tendency to maintain local planarity; and (2) attractive electrostatic and secondary orbital interactions between the endo‐(thio)carbonyl group, C?Y, and the diene. The former interaction predominates when X is weakly electronegative (X?N, S), while the latter is dominant when X is more strongly electronegative (X?O), or a methylene group (X?CH₂) which increases tether flexibility. These predictions hold up to experimental scrutiny, with synthetic IMDA reactions of 1 , 2 , 3 , and 4 (published work) and 5 , 6 , and 8 (this work) delivering ratios close to those calculated. The reactions of thiolacrylate 5 and thioamide 8 represent the first examples of IMDA reactions with tethers of these types. Our results point to strategies for designing tethers, which lead to improved cis/trans‐selectivities in IMDAs that are normally only weakly selective. Experimental verification of the validity of this claim comes in the form of fumaramide 14 , which undergoes a more trans‐selective IMDA reaction than the corresponding ester tethered precursor 13 .     

Chow-Witt groups and Grothendieck-Witt groups of regular schemes

Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective A-module of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d?3, we show that the vanishing of its Euler class in the corresponding Grothendieck-Witt group is a necessary and sufficient condition for P to have a free factor of rank one. If d is odd, we also get some results in that direction. If A is regular, we show that the Chow-Witt groups defined by Morel and Barge appear naturally as some homology groups of a Gersten-type complex in Grothendieck-Witt theory. From this, we deduce that if d=3 then the vanishing of the Euler class of P in the corresponding Chow-Witt group is a necessary and sufficient condition for P to have a free factor of rank one.     

R-matrix Poisson algebras and their deformations

We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.     

Dominant K-theory and integrable highest weight representations of Kac-Moody groups

We give a topological interpretation of the highest weight representations of Kac-Moody groups. Given the unitary form G of a Kac-Moody group (over C), we define a version of equivariant K-theory, KG on the category of proper G-CW complexes. We then study Kac-Moody groups of compact type in detail (see Section 2 for definitions). In particular, we show that the Grothendieck group of integrable highest weight representations of a Kac-Moody group G of compact type, maps isomorphically onto , where EG is the classifying space of proper G-actions. For the affine case, this agrees very well with recent results of Freed-Hopkins-Teleman. We also explicitly compute for Kac-Moody groups of extended compact type, which includes the Kac-Moody group E₁₀.     

Separating invariants and finite reflection groups

A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras.     

On the Normal Subgroup with Exactly Two G-Conjugacy Class Sizes

Let G be a finite group with a non-central Sylow r-subgroup R, Z（G） the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R and the G-conjugacy class size of every element of N is either i or m. Particularly, it is shown that N is Abelian if N ∩ Z（G）=1 and the G-conjugacy class size of every element of N is either 1 or m.     

Finite automata presentable abelian groups

We give new examples of FA presentable torsion-free abelian groups. Namely, for every n2, we construct a rank n indecomposable torsion-free abelian group which has an FA presentation. We also construct an FA presentation of the group in which every nontrivial cyclic subgroup is not FA recognizable.     

Factoring an infinite abelian group by lacunary cyclic subsets

It was proved in Corrádi and Szabó (Math Pannonica 5:275–280, 1994) that if a finite abelian group of odd order is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper extends this result for certain infinite torsion groups.