The stereodynamics of 3,5-bis(trifluoromethylsulfonyl)-1,3,5-oxadiazinane and 1,3,5-tris(trifluoromethylsulfonyl)-1,3,5-triazinane—an experimental and theoretical study

Multinuclear dynamic NMR spectroscopy of 3,5-bis(trifluoromethylsulfonyl)-1,3,5-oxadiazinane (3) revealed the existence of two conformers with differently oriented CF₃ groups with respect to the ring, and two dynamic processes: ring inversion and restricted rotation about the N-S bond. Two transition states connecting the two conformers and corresponding to clockwise and counterclockwise rotations about the N-S bond were found; the calculated activation barriers of about 12 kcal/mol are in excellent agreement with those measured experimentally for the related molecule 1,3,5-tris(trifluoromethylsulfonyl)-1,3,5-triazinane (1). X-ray analysis proved the existence of the symmetric isomer of 3, which is the minor isomer in solutions but the only one in the crystal due to packing effects. The normal Perlin effect (JCH_ax<JCH_eq) was observed for 2(6)-CH₂ in 3, whereas the reversed Perlin effect was found for the 4-CH₂ group in 3 as well as for all CH₂ groups in 1 both experimentally and theoretically. The latter effect in compounds 1, 3, and 1-(methylsulfonyl)-3,5-bis(trifluoromethylsulfonyl)-1,3,5-triazinane (2) can be considered as a genuine reverse Perlin effect since larger values of ¹J_CH are observed for longer C-H bonds.     

Cyclobutadiene dianion derivatives – Planar 4c,6e or three-dimensional 6c,6e aromaticity?

The spatial magnetic properties (Through Space NMR Shieldings – TSNMRS) of two cyclobutadiene derivatives (2 and 5) and of a number of cyclobutadiene dianion derivatives (3, 4 and 6–8) have been calculated by the GIAO perturbation method employing the Nucleus-Independent Chemical Shift (NICS) concept of P. v. Ragué Schleyer, and visualized as Iso-Chemical-Shielding Surfaces (ICSS) of various size and direction. TSNMRS values can be successfully employed to quantify and visualize the (anti)aromaticity of the compounds studied and to discuss the influence of Li⁺ complexation to cyclobutadiene dianion (4a, 7 and 8) on planar 4c,6e or three-dimensional 6c,6e aromaticity.     

Synthetische und NMR-spektroskopische Untersuchungen der Benzylaminaddition an N-Maleyl-aminosäurederivate

Summary During the addition of amines to maleylamino acids in general -amino derivatives are formed. In order to change the reactivity within the vinylogous maleyl system we introduced the -benzylester group into the starting compound N-(cis--carboxyacryloyl)-phenylalanine methylester1. The obtained benzylester2 is adding benzylamine in -position yielding N-benzyl--aspartyl(-benzyl)-phenylalanine methylester4. The addition reaction was investigated by¹H-NMR-spectroscopy. The structures of the compounds have been confirmed by elemental analysis, IR,¹H-NMR and¹³C-NMR spectroscopy.

     

An almost sure invariance principle for stationary ergodic sequences of Banach space valued random variables

Summary In this paper we establish an almost sure invariance principle with an error termo((t log logt)^1/2) (ast) for partial sums of stationary ergodic martingale difference sequences taking values in a real separable Banach space. As partial sums of weakly dependent random variables can often be well approximated by martingales, this result also leads to almost sure invariance principles for a wide class of stationary ergodic sequences such as ø-mixing and -mixing sequences and functionals of such sequences. Compared with previous related work for vector valued random variables (starting with an article by Kuelbs and Philipp [27]), the present approach leads to a unification of the theory (at least for stationary sequences), moment conditions required by earlier authors are relaxed (only second order weak moments are needed), and our proofs are easier in that we do not employ estimates of the rate of convergence in the central limit theorem but merely the central limit theorem itself.