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.     

Beiträge zur Massenspektrometrie der Gelsemium-Alkaloide

Zusammenfassung Von den Nebenalkaloiden vonGelsemium sempervirens (L.) Ait. konnte eine Verbindung, zunächst als Gelsemium-Alkaloid A bezeichnet, in reiner Form dargestellt und ihre Konstitution als N-1-Methoxygelsemin aufgeklärt werden. Für die Strukturermittlung erwies sich die Massenspektrometrie als besonders wertvoll. Die Massenspektren einiger Gelsemiumalkaloide sind wiedergegeben, die Fragmentierung dieser Verbindungen wird diskutiert.Au\erdem wurde eine größere Anzahl neuer Basen in kleiner Menge nachgewiesen.

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Contributions to mass-spectrometry of gelsemium-alkaloids (The structure of gelsemium-alkaloid A)

From the minor alkaloids ofGelsemium sempervirens (L.) Ait., one compound, preliminary designated as Gelsemiumalkaloid A, could be isolated and was identified as N-1-Methoxy-gelsemine. For the structure-elucidation mass-spectrometry has been proven to be of great value. Mass spectra of some Gelsemium-alkaloids are reported and the fragmentation of these compounds is discussed.There were further detected a quantity of new alkaloids in small amounts.

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Anmerkung bei der Korrektur (23.10.1972): Während der Drucklegung dieser Arbeit erschien eine Publikation vonE. Wenkert u. Mitarb. [Exper.28, 377 (1972)], in der die Struktur des Gelsevirins als N-1-Methoxy-gelsemin angegeben wird; somit ist Gelsemium-Alkaloid A offensichtlich mit Gelsevirin identisch. Eine solche Identifizierung was uns nicht möglich, da einerseits kein authentisches Präparat von Dr.Marion verfügbar was (Brief von Dr.Edwards, Ottawa, vom 21.6.1971) und andrerseits die wenigen, bisher veröffentlichten Daten über Gelsevirin hierfür nicht ausreichen.     

Toward true DNA base-stacking energies: MP2, CCSD(T), and complete basis set calculations

Stacking energies in low-energy geometries of pyrimidine, uracil, cytosine, and guanine homodimers were determined by the MP2 and CCSD(T) calculations utilizing a wide range of split-valence, correlation-consistent, and bond-functions basis sets. Complete basis set MP2 (CBS MP2) stacking energies extrapolated using aug-cc-pVXZ (X = D, T, and for pyrimidine dimer Q) basis sets equal to -5.3, -12.3, and -11.2 kcal/mol for the first three dimers, respectively. Higher-order correlation corrections estimated as the difference between MP2 and CCSD(T) stacking energies amount to 2.0, 0.7, and 0.9 kcal/mol and lead to final estimates of the genuine stacking energies for the three dimers of -3.4, -11.6, and -10.4 kcal/mol. The CBS MP2 stacking-energy estimate for guanine dimer (-14.8 kcal/mol) was based on the 6-31G(0.25) and aug-cc-pVDZ calculations. This simplified extrapolation can be routinely used with a meaningful accuracy around 1 kcal/mol for large aromatic stacking clusters. The final estimate of the guanine stacking energy after the CCSD(T) correction amounts to -12.9 kcal/mol. The MP2/6-31G(0.25) method previously used as the standard level to calculate aromatic stacking in hundreds of geometries of nucleobase dimers systematically underestimates the base stacking by ca. 1.0-2.5 kcal/mol per stacked dimer, covering 75-90% of the intermolecular correlation stabilization. We suggest that this correction is to be considered in calibration of force fields and other cheaper computational methods. The quality of the MP2/6-31G(0.25) predictions is nevertheless considerably better than suggested on the basis of monomer polarizability calculations. Fast and very accurate estimates of the MP2 aromatic stacking energies can be achieved using the RI-MP2 method. The CBS MP2 calculations and the CCSD(T) correction, when taken together, bring only marginal changes to the relative stability of H-bonded and stacked base pairs, with a slight shift of ca. 1 kcal/mol in favor of H-bonding. We suggest that the present values are very close to ultimate predictions of the strength of aromatic base stacking of DNA and RNA bases.     

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.