Methyl radicals substituted by one ester or nitrile group are on the borderline between nucleophilic and electrophilic behavior. In addition reactions of these borderline radicals to styrenes, polar effects of both, electron-withdrawing and electron-donating substituents at the alkeae, increase the rates. But these polar effects are smaller compared to those of nucleophilic or electrophilic radicals. In consequence, the stability of the radicals formed during the addition of the borderline radicals to styrenes are of major importance for the rate of the reaction.Rates and selectivities of radical reactions are often ruled by polar effects'.*'. This is explained by the frontier molecular orbital (FMO) theory as an interplay between the SOMO of the radical and the LUMO or the HOMO of the In nucleophilic radical reactions SOMO-LUMO interactions dominate, whereas electrophilic radical reactions are controlled by SOMO-HOMO interactions.We have now studied the question how radicals behave, which are on the borderline between nucleophilic and electrophilic reac-

Enthalpies of stabilization of polyenyl radicals, recently determined by thermal cis-trans isomerization about double bonds, are incorporated into a model for thermal cyclodimerization (and its reverse, cycloreversion) of polyene based on the ethylene-cyclobutane paradigm. This model accommodates the butadiene-divinylcyclobutane equilibrium satisfactorily. When the model is applied to polyenes of higher order, enthalpies of activation in both directions are predicted to be strikingly lowered as the order of the polyene increases. Photochemical dimerization at -75 O C of optically pure triene (R)-3 of the title, produces a single dimer (of three allowed), to which a cyclobutane structure in the anti and, tentatively, endo,endo configuration, (R,R)-4a,n,n, is assigned. The remarkable stereospecificity is ascribed to an intermediate excimer, in which maximum overlap and minimal steric repulsion are hypothetically achieved in either of the two incipiently anti arrangements. Irradiation of racemic (R,S)-3 at -75 O C produces two of six possible isomers, now racemic 4 , , , and racemic 4,,,. Each of the photochemically favored cyclobutanes begins to equilibrate above -20 O C (very rapidly at 20 "C and above) with the other two stereoisomers in its set. From rates measured between -22.7 and 0.0 O C , Eyring parameters, AH* = 21.2 kcal/mol and AS* = 2.7 eu, are obtained. In the temperature range of 0.0 to 22.0 O C , the mixture of dimers, continuously maintained at equilibrium, undergoes thermal, [2 + 21 cycloreversion to the triene (R)-3 with Eyring parameters, AH* = 24.2 kcal/mol and AS* = 5.8 eu.Although syn-anti rearrangement competes with cycloreversion in divinylcyclobutanes, the gap in enthalpy of activation between the two paths is significantly larger in these dibutadienylcyclobutanes. (7) Energies in Schemes I and I1 are in units of kcalfmol. AfHo 2(+12.56) = +25.1 exp AfH* +68.6 AH* +61.8 H k AfHo +6.8 I i 2(-3.74) t -% AfHo 2(+26.11) = +52.2 exp AH* +23.0

4324J. Am. Chem. Soc. Mo-bound methyl group. (ii)The coupling constant between the methyl protons and the 31P nuclei increases from 1.8 Hz at -20 O C (at lower temperatures the corresponding signal is unresolved) to 3.0 Hz at 20 "C. For comparison, in the structurally characterized met hyl-tungsten c o m p l e x e~~~+~ W (CH3)( L-L) (CO),-(PMe3)2 (L-L = acac, S2CNR2, S2COR) this coupling ranges from 3.5 to 8 Hz. (iii) The solution IR spectrum of 4 (20 "C) is more complex than those of 1-3 and shows, in addition to bands due to the carbonyl functionalities in the agostic and q2-acyl isomers, two absorptions at ca. 191 2 and 1836 cm-I which can be tentatively assigned to the terminal carbonyl ligands in the methyl dicarbonyl species Mo( CHJ (S2CO-i-Pr) (C02) ( PMe3)2.In conclusion, our results indicate that in the system under investigation there are small energy differences among the isomeric structures A, B, and C , so that both types of acyl coordination, B and C, are kinetically and thermodynamically accessible from their isomeric alkyl-xrbonyl structure A. Since most of the acyl complexes of molybdenum known to date have q2 structures while the only known agostic acyls are those discussed in this paper, it seems that the C-He-Mo interaction becomes structurally and thermodynamically competitive only in the presence of strongly electron releasing ligands such as the dithiocarbamates and xanthates. Note however that the analogous tungsten complexes have alkyl-carbonyl structure^.^ Therefore it is clear that very subtle electronic effects must be responsible for the observation in the present system of the three isomeric structures A, B, and . On the Transition States of Electrophilic Radical Additions to Alkenes Revised Manuscript Received March 30, 1991Carbon-centered radicals are nucleophilic or electrophilic species, depending upon the substituent at the radical center. Electron-donating substituents like alkyl or alkoxy groups increase the nucleophilicity' of radicals whereas electron-withdrawing substituents like ester or nitrile groups augment their electrophilic9 behavior. Calculations for a variety of cases have shown that nucleophilic radicals approach the olefinic carbon atoms at angles between 1 0 4 O and 108" at the UHF/3-21G level.3 Figure 1 shows the geometry for the addition of the methyl radical to ethylene at the UHF/6-31G* leveLJbAuthor to whom correspondence should be addressad.' University of Basel. Transition state 1 is also in accord with substituent effects on rates. Thus, in addition of the nucleophilic cyclohexyl radical 2 to substituted acrylates 3 (Scheme I), alkyl groups R2 reduce the rate of addition only slightly, but alkyl groups R' at the attacked olefinic carbon atom exert huge ratedecreasing effects.Ib Absolute rate measurements for reactions of tert-butyl radicals with various alkenes exhibit comparable results.'These unequal substituent effects point to unsymmetrical transition states 1 in which only the attacked olefinic carbon atom deviates considerably from its ground-sta...

flections may have suffered a phase change so that the information in the appropriate frequency range is transferred with reversed contrast. The second stage in image analysis involves image reconstruction, where the electron micrograph now serves as object. Filtering of Fourier frequencies in reciprocal space (secondary diffraction pattern) is performed generally with the aid of a computer. The various stages of frequency filtering are very complex and must be treated with careful consideration of the physics involved. Otherwise, artifacts can easily be introduced. The safest way to guard against this is to compare the original image (which must be of very high quality) with the computer-treated image, and to ensure that defects have not been introduced which were not in the original. Details regarding these procedures will be published elsewhere [16].

Der zweite Schritt hesteht in einer Bildrekonstruktion, bei der die elektronenmikroskopische Ahbildung selbst nun als Ohjekt dient. Die Filterung von Fourier-Frequenzen im reziproken Raum (sekundares Beugungsbild) wird dahei ublicherweise mit einem leistungsstarken Personal-Computer durchgefiihrt. Die Frequenzfilterung umfant sehr komplizierte Schritte, bei denen die physikalischen Grundlagen genauestens beriicksichtigt werden mussen, um keine Artefakte zu produzieren. Der sicherste Weg ist der direkte Vergleich des Originalhildes (welches von sehr hoher Qualitat sein mul3) rnit dem computerverarbeiteten Bild, um sicherzustellen, daB keine Defekte eingefuhrt wurden (genaue Beschreibung der Methode siehe [16]).