Twin Paradox and the Logical Foundation of Relativity Theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND.     

Development of resin-to-resin transfer reactions (RRTR) using Sonogashira chemistry

Sonogashira chemistry can be used according to the ‘resin-to-resin transfer reaction’ (RRTR) concept. Two fragments, one containing the halide moiety and the second one incorporating the alkyne functionality, are anchored on different solid supports using allyl and/or Wang-type linkages. Treatment with Pd(0) cleaves the allyl-linked fragment(s) which subsequently undergo Sonogashira coupling under the same conditions.     

Non-Watson-Crick base pairing in RNA. quantum chemical analysis of the cis Watson-Crick/sugar edge base pair family

Large RNA molecules exhibit an astonishing variability of base-pairing patterns, while many of the RNA base-pairing families have no counterparts in DNA. The cis Watson-Crick/sugar edge (cis WC/SE) RNA base pairing is investigated by ab initio quantum chemical calculations. A detailed structural and energetic characterization of all 13 crystallographically detected members of this family is provided by means of B3LYP/6-31G and RIMP2/aug-cc-pVDZ calculations. Further, a prediction is made for the remaining 3 cis WC/SE base pairs which are yet to be seen in the experiments. The interaction energy calculations point at the key role of the 2'-OH group in stabilizing the sugar-base contact and predict all 16 cis WC/SE base-pairing patterns to be nearly isoenergetic. The perfect correlation of the main geometrical parameters in the gas-phase optimized and X-ray structures shows that the principle of isosteric substitutions in RNA is rooted from the intrinsic structural similarity of the isolated base pairs. The present quantum chemical calculations for the first time analyze base pairs involving the ribose 2'-OH group and unambiguously correlate the structural information known from experiments with the energetics of interactions. The calculations further show that the relative importance and absolute value of the dispersion energy in the cis WC/SE base pairs are enhanced compared to the standard base pairs. This may by an important factor contributing to the strength of such interactions when RNA folds in its polar environment. The calculations further demonstrate that the Cornell et al. force field commonly used in molecular modeling and simulations provides satisfactory performance for this type of RNA interactions.     

On-resin native chemical ligation for cyclic peptide synthesis

A novel cysteine derivative, N(alpha)-trityl-S-(9H-xanthen-9-yl)-l-cysteine [Trt-Cys(Xan)-OH] has been introduced for peptide synthesis, specifically for application to a new strategy for the preparation of cyclic peptides. The following steps were carried out to synthesize the cyclic model peptide cyclo(Cys-Thr-Abu-Gly-Gly-Ala-Arg-Pro-Asp-Phe): (i). side-chain anchoring of Fmoc-Asp-OAl via its free beta-carboxyl as a p-alkoxybenzyl ester to a solid support; (ii). stepwise chain elongation of the peptide by standard Fmoc/tBu solid-phase chemistry; (iii). removal of the N-terminal Fmoc group; (iv). coupling of Trt-Cys(Xan)-OH; (v). selective Pd(0)-promoted cleavage of the C-terminal allyl ester; (vi). coupling of the C-terminal residue, i.e., H-Phe-SBzl, preactivated as a thioester; (vii). selective removal of the N(alpha)-Trt and S-Xan protecting groups under very mild acid conditions; (viii). on-resin cyclization by native chemical ligation in an aqueous milieu; and (ix). final acidolytic cleavage of the cyclic peptide from the resin. The strategy was evaluated for three supports: poly[N,N-dimethacrylamide-co-poly(ethylene glycol)] (PEGA), cross-linked ethoxylate acrylate resin (CLEAR), and poly(ethylene glycol)-polystyrene (PEG-PS) graft resin supports. For PEGA and CLEAR, the desired cyclic product was obtained in 76-86% overall yield with initial purities of approximately 70%, whereas for PEG-PS (which does not swell nearly as well in water), results were inferior. Solid-phase native chemical ligation/cyclization methodology appears to have advantages of convenience and specificity, which make it promising for further generalization.     

Kinetics and mechanisms in carbocationic polymerization: The quest for true rate constants

This article is a critical analysis of kinetic dataavailable on carbocationic polymerizations. A survey of published propagation rate constant (k_p) data revealed several orders of magnitude differences. In this article, an explanation of this apparent discrepancy is offered with a case study involving the carbocationic polymerization of 2,4,6‐trimethylstyrene (TMS). With the polymerization mechanism originally proposed for this system, k_p = 1.35 × 10⁴ L mol^?1 s^?1 was extracted from experimental data with the Predici polyreaction package. The alternative mechanism yielded k_p = 1.01 × 10⁷ L mol^?1 s^?1, close to that predicted by Mayr's Linear Free Energy Relationship (LFER). We propose that true rate constants can only be obtained from direct competition experiments or from kinetic interpretation based on independently proven mechanisms. The second part of this review discusses critical analysis of the temperature and concentration dependence of various living IB systems. Comparison of the temperature dependence in systems initiated with 2‐ chloro‐2,4, 4‐ trimethylpentane (TMPCl)/TiCl₄ from various laboratories yielded of ΔH ～?25 and ?34.5 kJ/mol for high and low TMPCl/TiCl₄ ratios, respectively. Aromatic (cumyl‐type) initiators show ΔH ～ ?40 kJ/mol, whereas H₂O/TiCl₄ in the presence of the strong electron‐ pair donor dimethylacetamide gave ΔH = ?12 kJ/mol. The significant differences indicate different underlying mechanisms with complex elementary reactions. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5394–5413, 2005     

Lanthanide complexes of [alpha-2-P2W17O61]10-: solid state and solution studies

We have isolated the 1:1 Ln:[alpha-2-P2W17O61]10- complexes for a series of lanthanides. The single-crystal X-ray structure of the Eu3+ analogue reveals two identical [Eu(H2O)3(alpha-2-P2W17O61)]7- moieties connected through two Eu-O-W bonds, one from each polyoxometalate unit. An inversion center relates the two polyoxometalate units. The Eu(III) ion is substituted for a [WO]4+ unit in the "cap" region of the tungsten-oxygen framework of the parent Wells-Dawson ion. The point group of the dimeric molecule is Ci. The extended structure is composed of the [Eu(H2O)3(alpha-2-P2W17O61)]214- anions linked together by surface-bound potassium cations. The space group is P, a = 12.7214(5) A, b = 14.7402(7) A, c = 22.6724(9) A, alpha = 71.550(3), beta = 84.019(3)degrees, gamma = 74.383(3), V = 3883.2(3) A3, Z = 1. The solution studies, including 183W NMR spectroscopy and luminescence lifetime measurements, show that the molecules dissociate in solution to form monomeric [Ln(H2O)4(alpha-2-P2W17O61)]7- species.     

Nitrogen bridgehead compounds. Part 76 Synthesis and stereochemistry of ethyl 9-benzylidene-6,7,8,9-tetrahydro-2-oxo-2H- and 4-oxo-4H-pyrido[1,2-a]pyrimidine-3-carboxylates and their homologues

Ethyl 4-oxo-6,7,8,9-tetrahydro-4H-pyrido[1,2-a]pyrimidine-3-carboxylates 1–4 , their piperidine ring homologues 5–6 and their 2-oxo isomers 7–9 were reacted with benzaldehyde. At low temperature, kinetically stable addition products were formed. Thermodynamically stable condensation products were obtained at higher temperature, which were also formed when the addition products were refluxed in benzene. The 9-benzyl derivatives were prepared by the hydrogenation of the condensation products over Pd/C. The stereochemical features of the new compounds were determined via ¹H and ¹³C nmr chemical shift and coupling constant analysis and NOE measurements.     

Kinetic simulation of living carbocationic polymerizations. II. Simulation of living isobutylene polymerization using a mechanistic model

This paper discusses the kinetic simulation of TiCl₄--coinitiated living carbocationic isobutylene (IB) polymerizations governed by dormant-active equilibria, using a mechanistic model. Two kinetic models were constructed from the same underlying mechanism: one using a commercial simulation software package (Predici^®), and the other using the method of moments. Parameter estimation from experimental batch reactor data with Predici yielded a rate constant of propagation k_p = 4.64 × 10⁸ ± 2.75 × 10⁸ L/mol s, with no constraints imposed. This agrees with k_p data measured with diffusion clock and competition methods, but disagrees with kinetically obtained k_p values. Estimation of rate constants with Predici^® and the GREG parameter estimation software packages revealed that it was difficult to estimate the complete set of kinetic parameters, due to correlated effects of the parameters on model predictions. Estimability analysis confirmed that some of the strongly correlating parameters could not be estimated simultaneously using the available experimental data. Using k_p = 6 × 10⁸ ± 2.75  × 10⁸ L/mol s measured by Mayr, and using starting estimates of other rate constants defined by experimentally observed correlations, yielded the set of rate constants required for the simulations. Both kinetic models yielded good agreement with experimental data, with the exception of M_w values that slightly diverged from the theoretically predicted ‘M_w−M_n = constant’ relationship. This may indicate the occurrence of a minor side reaction. However, the k_p/k₋₁ = 17.5 L/mol average run length calculated from measured and simulated MWD data agrees well with earlier literature values.