[2+2]-cycloadditions of alkenes with the triphenylallenyl cation

The triphenylallenyl cation (8), generated from triphenylpropynol (7) and FSO3H, reacts with alkenes to give the allyl cations 12, which may be deprotonated to yield the methyleneccylobutenes 14. Alternatively, 12 can be converted into the 2-vinyl-indenes 13 two subsequent electrocyclic reactions

Diastereoselective synthesis of β- and γ2-muurolene. A carbocationic pathway from mono- to sesquiterpenes

The Lewis acid catalysed addition of the piperityl chlorides 6 to isoprene yields adduct 7, which undergoes a cis-stereoselective cyclisation to give the diastereoisomeric muurolene monohydrochlorides 8. Treatment with potassium tert-butoxide affords β- and γ2- muurolene 2

Kinetic and Thermodynamic Studies of Carbenium Ion Additions Towards Alkenes

The ionisation (Ar2CHCl + BC13 v=± Ar2CH+BCi;) and dissociation (Ar2CH+BCi; ^=*Ar2CH+ + BCl^) equilibria of diarylmethyl chlorides i n boron trichloride/ dichloromethane solution have been studied by conductimetry, photometry and *H NMR spectroscopy. Small differences i n the UV-vis spectra of diarylcarbenium tetrachloroborates, which have been observed i n solutions of low and high tetrachloroborate concentration, can be attributed to the formation of 1 :1 ion-pairs i n the more concentrated solutions. Low temperature calorimetry was used to determine the heats of addition of diarylcarbenium tetrachloroborates to 2~methyl-1 -pentene (Ar2CH+BCi; + H2C=CRRT ArjCH-CHj-CRR'Cl + BC13), and it is estimated that the standard free enthalpy of t h i s reaction is greater than 0 for systems with pKR+ > -2.6. Kinetic studies have shown that paired and unpaired diarylcarbenium tetrachloroborates exhibit identical reactivity towards alkenes. A rationalisation for the different situation in carbocationic and carbanionic polymerisation i s presented. The rate constants for the initiation of isobutene, styrene and isoprene polymerisation by diarylcarbenium ions have been determined, and it is shown, how propagation rate constants can be estimated from linear free energy relationships

Steric control of regiochemistry in the reactions of methyl substituted pentadienyl cations with isobutene

The dienylic chlorides 1–5 react with isobutene in the presence of zinc chloride/ether in dichloromethane to give the acyclic adducts 6–10 in 64–91% yield. The orientation effects are in contrast to the predictions of perturbational molecular orbital theory and can be explained on the basis of steric effects

Synthesis of 1,1,2,2,3,3-hexamethyl-4,5-bis(methylene)cyclopentane

An efficient synthesis of the title compound 14 is reported, which employs the ZnCl2/Et2O catalyzed addition of acetyl chloride (4) to 2-methyl-2-butene (5) and the [3+ + 2] cycloaddition of the 1,1,2,3-tetramethylallyl cation to 2,3-dimethyl-2-butene as key steps

Conformal Field Theories on K3 and Three-Dimensional Gauge Theories

According to a recent conjecture, the moduli space of the heterotic conformal field theory on a $G\subset$ ADE singularity of an ALE space is equivalent to the moduli space of a pure \cx N=4 supersymmetric three-dimensional gauge theory with gauge group G. We establish this relation using geometric engineering of heterotic strings and generalize it to theories with non-trivial matter content. A similar equivalence is found between the moduli of heterotic CFT on isolated Calabi--Yau 3-fold singularities and two-dimensional Kazama-Suzuki coset theories.Comment: 11pp, harvmac, v2: a relation between heterotic CFT on Calabi-Yau 3-fold singularities and Kazama-Suzuki models has been adde

N=1 Mirror Symmetry and Open/Closed String Duality

We show that the exact N=1 superpotential of a class of 4d string compactifications is computed by the closed topological string compactified to two dimensions. A relation to the open topological string is used to define a special geometry for N=1 mirror symmetry. Flat coordinates, an N=1 mirror map for chiral multiplets and the exact instanton corrected superpotential are obtained from the periods of a system of differential equations. The result points to a new class of open/closed string dualities which map individual string world-sheets with boundary to ones without. It predicts an mathematically unexpected coincidence of the closed string Gromov-Witten invariants of one Calabi-Yau geometry with the open string invariants of the dual Calabi-Yau.Comment: harvmac, 29 pages (b), 3 figures; v2: references adde

Summing up Open String Instantons and N=1 String Amplitudes

We compute the instanton expansions of the holomorphic couplings in the effective action of certain \cx N=1 supersymmetric four-dimensional open string vacua. These include the superpotential $W(\phi)$, the gauge kinetic function $f(\phi)$ and a series of other holomorphic couplings which are known to be related to amplitudes of topological open strings at higher world-sheet topologies. The results are in full agreement with the interpretation of the holomorphic couplings as counting functions of BPS domain walls. Similar techniques are used to compute genus one partition function for the closed topological string on Calabi--Yau 4-fold which gives rise to a theory with the same number of supercharges in two dimensions.Comment: 29 pages harvmac(b); v2: references adde