Bonds convexity

The convexity measure increases with the square of maturity it decreases as both coupon and yield rise. It is a function of modified duration, so index-linked bonds, which have greater duration than conventional bonds of similar maturities, also have greater convexity. For a conventional vanilla bond, convexity is almost always positive. Negative convexity occurs most frequently with callable bonds. 

Our journey begins with the photo-induced union of 3,4-dimethylfuran (19) and / -(benzyloxy)-propanal (18) (see Scheme 5). Irradiation of a solution of these two simple, achiral compounds in benzene with a 450 W Hanovia lamp equipped with a vycor filter results in the exclusive formation of head-to-head, exo photoadduct 17 in 63% yield. As a cw-fused dioxabicyclo[3.2.0]heptene system, intermediate 17 possesses a folded molecular framework to which access is obstructed on the concave face. In the presence of mCPBA, the less hindered convex face of the enol ether double bond is oxidized in a completely diastereoselective fashion, affording intermediate 16 in 80% yield after regioselective opening of... 

The wide variety of methods available for the synthesis of orga-noselenides,36 and the observation that the carbon-selenium bond can be easily cleaved homolytically to give a carbon-centered radical creates interesting possibilities in organic synthesis. For example, Burke and coworkers have shown that phenylselenolactone 86 (see Scheme 16), produced by phenylselenolactonization of y,S-unsaturated acid 85, can be converted to free radical intermediate 87 with triphenyltin hydride. In the presence of excess methyl acrylate, 87 is trapped stereoselectively, affording compound 88 in 70% yield 37 it is noteworthy that the intramolecular carbon-carbon bond forming event takes place on the less hindered convex face of bicyclic radical 87. 

Completely closed, convex, single-shell clusters are called closo clusters their atoms form a polyhedron. If the polyhedron has only triangular faces, it is also called a delta-hedron. Depending on the number of available electrons, we can distinguish four general bonding types for closo clusters ... 

Pyramidalization is also a well-established indicator of increased reactivity of alkenes where the 7r-type HOMO makes the major contribution to the reaction.12 This increased reactivity is specific to the more open (convex) face, and contributes to the well-known exo-selectivity of attack on bicyclo[2,2,l]hept-2-enes [60]. The electron density distribution of a derivative of [60] showed a measurable displacement of the electron-density maximum of the double bond in the exo direction (Irngartinger et al.,... 

The 1,2-carbonyl transposition takes place through the enJo-epoxide 18 easily prepared through the tosylhydrazone 16, followed by regioselective cleavage to the less substituted double bond (17) with 2 equivalents of methyllithium [4] and epoxidation with MCPBA in chloroform from the more accesible convex face of the decalin system. 

The pairwise nature of the bond-boost makes this task easier since such traps would show up as a non-convexity of some of the biased effective pair potentials, which in the canonical ensemble can be taken to be the pairwise potential of mean force (PMF, denoted as V). Thus, assuming that V is approximately quadratic for lei safety condition can be enforced by setting Sa[Pg.92]

Due to the pyramidalization of the C atoms and the rigid cage structure of Cjq the outer convex surface is very reactive towards addition reactions but at the same time the inner concave surface is inert (chemical Faraday cage). This allows the encapsulation, observation and tuning of the wavefimction of extremely reactive species that otherwise would immediately form covalent bonds with the outer surface. 

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