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.     

Application of main component fraction collection method for purification of compound libraries

In order to support high-throughput library purification, a novel UV triggered fraction collection method was developed in which a maximum-seeking-algorithm-driven, six-port valve collects the largest chromatographic peak. This straightforward strategy achieves the one sample-one fraction approach, thus resulting in a simpler and less error prone workup procedure. The effectiveness of this main component fraction collection method will be illustrated here by the results of the purification of compound libraries (altogether 6086 compounds, having an averaged success rate of 79.4%). Advanced applications, where the desired component differs from the main component, will also be discussed.     

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.     

Treating singularities present in the Sutcliffe-Tennyson vibrational Hamiltonian in orthogonal internal coordinates

Two methods are developed, when solving the related time-independent Schrodinger equation (TISE), to cope with the singular terms of the vibrational kinetic energy operator of a triatomic molecule given in orthogonal internal coordinates. The first method provides a mathematically correct treatment of all singular terms. The vibrational eigenfunctions are approximated by linear combinations of functions of a three-dimensional nondirect-product basis, where basis functions are formed by coupling Bessel-DVR functions, where DVR stands for discrete variable representation, depending on distance-type coordinates and Legendre polynomials depending on angle bending. In the second method one of the singular terms related to a distance-type coordinate, deemed to be unimportant for spectroscopic applications, is given no special treatment. Here the basis set is obtained by taking the direct product of a one-dimensional DVR basis with a two-dimensional nondirect-product basis, the latter formed by coupling Bessel-DVR functions and Legendre polynomials. With the basis functions defined, matrix representations of the TISE are set up and solved numerically to obtain the vibrational energy levels of H3+. The numerical calculations show that the first method treating all singularities is computationally inefficient, while the second method treating properly only the singularities having physical importance is quite efficient.     

A study of structural and bonding variations in the homologous series [Mo(2)(CN)(6)(dppm)(2)](n-) (n = 2, 1, 0)

Reaction of Mo(2)Cl(4)(dppm)(2) (dppm = bis(diphenylphosphino)methane) with 6 equiv of [n-Bu(4)N][CN] or [Et(4)N][CN] in dichloromethane yields [n-Bu(4)N](2)[Mo(2)(CN)(6)(dppm)(2)] (1) and [Et(4)N](2)[Mo(2)(CN)(6)(dppm)(2)] (2), respectively. The corresponding one- and two-electron oxidation products [n-Bu(4)N][Mo(2)(CN)(6)(dppm)(2)] (3) and Mo(2)(CN)(6)(dppm)(2) (4)were prepared by reactions of 1 with the oxidant NOBF(4). Single-crystal X-ray structures of 2.2CH(3)CN, 3.2CH(3)CN.2H(2)O, and 4.2CH(3)NO(2) were performed, and the results confirmed that all three complexes contain identical ligand sets with trans dppm ligands bisecting the Mo(2)(mu-CN)(2)(CN)(4) equatorial plane. The binding of the bridging cyanide ligands is affected by the oxidation state of the dimolybdenum core as evidenced by an increase in side-on pi-bonding overlap of the mu-CN in going from 1 to 4. The greater extent of pi-donation into Mo orbitals is accompanied by a lengthening of the Mo-Mo distance (2.736(1) A in Mo(2)(II,II) (2), 2.830(1) A in Mo(2)(II,III) (3), and 2.936(1) A in Mo(2)(III,III) (4)). A computational study of the closed-shell members of this homologous series, [Mo(2)(CN)(6)(dppm)(2)](n)() (n = 2-, 0), indicates that the more pronounced side-on pi-donation evident in the X-ray structure of 4 leads to significant destabilization of the delta orbital and marginal stabilization of the delta() orbitals with respect to nearly degenerate delta and delta orbitals in the parent compound, 2. The loss of delta contributions combined with the reduced orbital overlap due to higher charges on molybdenum centers in oxidized complexes 3 and 4 is responsible for the observed increase in the length of the Mo-Mo bond.     

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