the 86 electrocyclization 
 cascade of the 
 1,3,5,7-tetraene shown in scheme 1 is an important 
 transformation in biosynthesis and chemical synthesis . a selection 
 of natural products formed by such cascades is shown in scheme 2 . black and colleagues original proposal that the endiandric acids are biosynthesized 
 via nonenzymatic 86 electrocyclizations prompted 
 nicolaou et al . to develop a biomimetic synthetic strategy to access members of 
 this family of natural products . their studies validated black and 
 co - workers biosynthetic proposal . since the initial isolation 
 of the endiandric acids , a number of additional metabolites arising 
 from this pericyclic cascade have emerged ( see scheme 2 ) . subsequent biomimetic syntheses of those molecules by trauner , baldwin , parker , and sherburn have demonstrated the generality of this electrocyclization 
 cascade . with the exception of the elysiapyrones , most of these natural products exist as racemates , suggesting 
 that the cascade reactions can readily occur without catalysis by 
 an enzyme . terminal substitution of the tetraene reactants 
 has been shown 
 to strongly influence the chemistry of these 86 
 electrocyclization cascades . these substituents affect , in particular , 
 the kinetics , thermodynamics , and diastereoselectivity . despite the importance of this electrocyclization 
 cascade in biosynthesis and the attention it has received from the 
 synthetic community , no systematic investigation of the influence 
 of terminal subsititution on the cascade reaction has been reported . we performed a density functional theory ( m06 - 2x ) study to address 
 this problem . the data from this study reveal that terminal substitution 
 reduces the exothermicity of the 8 electrocyclization step 
 of the cascade and that the second ring closure is both kinetically 
 and thermodynamically more favorable . for those substrates that undergo 
 8 ring closure to form chiral 1,3,5-cyclooctatrienes , our work 
 shows that the observed diastereoselectivity of the transannular 6 
 ring closure arises from the steric destabilization of the endo mode of 6 ring closure . we anticipate that these 
 findings will inform the design of synthetic strategies for the stereoselective 
 formation of new bicyclo[4.2.0]octa-2,4-diene scaffolds . the kinetics and thermodynamics of the electrocyclic reactions 
 of 1 , 2 , 5 , 6 , 
 and 7 have been experimentally studied previously . tetraenes 5 and 6 possess substitution patterns similar to those used in the synthesis of the endiandric acids and kinganian natural 
 products , whereas trisubstituted tetraenes 8 and 9 resemble the starting materials used for the preparation 
 of the pyrone - containing natural products ( green box in scheme 1 ) . the electrocyclization cascades of 4 and 10 have not been studied experimentally , and metabolites arising from 
 tetraenes possessing the same substitution patterns as 4 and 10 have not been isolated . the 8 ring closures 
 of 4 , 5 , 6 , and 10 yield achiral 1,3,5-cyclooctatrienes ; thus , the 6 electrocycliczation 
 of these cyclooctatrienes can not be diastereoselective . the energetics and the transition states for the 86 
 electrocyclization cascade of 1 are shown in figure 1 . goldfarb and lindqvist reported that 1,3,5,7-octatetraene 
 undergoes 8 ring closure with an activation enthalpy of about 
 17 kcal mol ; pohnert 
 and boland have expressed concern that this value may be an overestimate , 
 as they have determined that the 8 electrocyclization of tetraene 2 , which shows reactivity similar to that of substrate 1 , has a h298.15  k of 13.6 kcal mol . 14.5 kcal mol ) is in closer agreement 
 with pohnert and boland s experimental data and constitutes 
 a significant improvement in accuracy compared with previously reported 
 hartree  fock or mp2 data . the 
 half - life of the 8 ring closure is 0.5 s ( g = 17 kcal mol ) . gibbs free energy profile and transition structures for the 86 
 ring closure cascade of unsubstituted tetraene 1 . structures 
 and free energies ( kcal mol ) determined using 
 the m06 - 2x/6 - 31+g(d , p ) level of theory . experimentally , the thermal isomerization of 1 does 
 not yield bicyclo[4.2.0]octa-2,4-diene ( 1bcod ) unless performed at 
 elevated temperatures . computations can explain this observation : 
 the 8 and 6 electrocyclization transition states of 1 are nearly isoenergetic ; however , the cyclooctatriene 1cot 
 is significantly more stable than its tetraene precursor . it is for 
 this reason that the rate - determining step for the cascade reaction 
 of compound 1 is the 6 electrocyclization with 
 a gibbs free energy of activation of 27 kcal mol , corresponding to a reaction half - life of approximately 130 days 
 at room temperature . the 8 product 1cot and the cascade product 
 1bcod are isoenergetic and are predicted to be observed in almost 
 equal amounts if the cascade reaction is under thermodynamic control . the energy profiles for the cascade reactions of the monosubstituted 
 tetraenes 2 and 3 are qualitatively similar 
 to that for 1 ; the initial 8 electrocyclizations 
 are facile and exothermic , while the subsequent 6 ring closures 
 are significantly more sluggish ( see figure 2 for grxn and g values ) . the monosubstituted z - tetraene 3 is approximately 100-fold more reactive 
 ( at room temperature ) toward 8 ring closure than the e - tetraene 2 . presumably , the z isomer is more reactive toward 8 ring closure due to greater 
 strain relief that occurs upon pyramidalization of the substituted 
 carbon at the transition state . the computed h value of 13.6 kcal mol for 
 the 8 electrocyclization of 2 is in excellent 
 agreement with the experimental h298.15k value of 13.4 kcal mol as 
 determined by pohnert and boland . gibbs free 
 energy profile and transition structures for the 86 
 ring closure cascade of monosubstituted tetraenes 2 and 3 . structures and free energies ( kcal mol ) determined using the m06 - 2x/6 - 31+g(d , p ) level of theory . experimentally , only at high temperatures 
 are 2bcod and 2bcod , the products of the 6 
 ring closure 
 of intermediate 2cot , observed , and then 
 only as minor products in relation to the cyclooctatriene 2cot . our 
 computations indicate that the bicyclic species 2bcod and 
 2bcod are slightly more stable than 2cot . this preference 
 is small , and the deviation between theory and experiment is well 
 within the computational error of our method . because the 1,3,5-cyclooctatriene 
 2cot formed from 2 and 3 is chiral , the 
 ensuing 6 ring closure produces diastereomeric products . according to computations , this ring closure is nonselective , in agreement 
 with experiment . a single terminal methyl substituent alone does not exert a strong 
 influence on the stereochemical course of the second ring closure 
 because it can occupy a sterically uncongested position in both transition 
 states . the reactivity of 4 resembles those of 
 model substrates 13 ; because the 
 8 electrocyclization 
 of 4 results in the formation of an achiral 1,3,5-cyclooctatriene 
 ( 4cot ) ( figure 3 ) , the subsequent 6 
 electrocyclization can not be stereoselective . the 8 ring closure 
 of 4 is predicted to be a facile means of generating 
 a quaternary center in a medium - sized ring . gibbs free energy profile 
 and transition structures for the 86 
 ring closure cascade of gem - disubstituted tetraene 4 . structures and free energies ( kcal mol ) determined using the m06 - 2x/6 - 31+g(d , p ) level of theory . huisgen and co - workers have studied 
 the kinetics of the thermal 
 isomerizations of tetraenes 57 experimentally . the reactions of substrates 5 and 6 correspond to reactions involved in the biosyntheses 
 of the endiandric acid and kinginian families of natural products . the 8 electrocyclization of tetraene 5 proceeds 
 with a h298.15k of 15.1 kcal mol , similar to the computed value of 14.4 kcal mol ( figure 4 ) . in the case of the 8 electrocyclization 
 of 6 , the computed value of h298.15k of 17.6 kcal mol is at variance with the experimental value of 21.8 kcal mol by approximately 4 kcal mol . the thermodynamic product of the 86 
 electrocyclization of 5 and 6 is 5bcod , 
 although computations overestimate the stability of the bicyclic product . gibbs free energy profile and transition structures for 
 the 86 
 ring closure cascade of disubstituted tetraenes 5 and 6 . structures and free energies ( kcal mol ) determined using the m06 - 2x/6 - 31+g(d , p ) level of theory . gibbs free energy profile and transition structures 
 for the 86 
 ring closure cascade of tetraene 7 . structures and free 
 energies ( kcal mol ) determined using the m06 - 2x/6 - 31+g(d , p ) 
 level of theory . both a front view and a side view ( newman projection 
 along the forming bond also shown ) of ts76 and ts76 are provided . note the energies 
 shown are relative to that of the most stable 1,8-dimethyl tetraene , 5 . the 8 ring closures of 
 tetraenes 5 and 6 are approximately 5 kcal 
 mol less exergonic 
 than those of 13 ( grxn = 4 and 9 kcal mol , respectively ) because the product 5cot is destabilized by steric 
 repulsion between vicinal methyl groups at the 7 and 8 positions of 
 the cyclooctatriene ( shown in figure 4 , h the g of 6 electrocyclization of 5cot is 23 kcal mol , and 5bcod is 3 kcal mol more stable than its 
 cyclooctatriene precursor . the increased reactivity of 5cot relative 
 to 1cot ( g6 = 4 kcal mol ) and the increased stability of 
 the bicyclo[4.2.0]octadiene resulting from the ring closure of 5cot 
 is due to relief of the steric clash found in 5cot . what prevents the c7 and c8 methyl substituents from clashing 
 with one another in ts56 and 5bcod ? formation of 
 a strained four - membered ring leads to compression of the c5c6c7 
 and c1c7c6 angles from approximately 110 to 
 90. compression of these internal angles of the cyclobutane 
 is accompanied by a widening of the external angles of the ring , which 
 results in the positioning of the vicinal methyl groups far enough 
 away from one another that they no longer clash . the activation 
 free energy ( ca . 21 kcal mol ) for the first step 
 of the cascade process for the electrocyclization 
 of 7 is similar to those of tetraenes 5 and 6 , differing by only 4 and 2 kcal mol , 
 respectively . the computed h298.15k for the conversion of 7 into 7cot 
 is 1.4 kcal mol lower than the experimental value 
 of 17.8 kcal mol . the 8 electrocylic reaction 
 of 7 is 1 kcal mol less exergonic 
 than those of 5 and 6 . like intermediate 
 5cot , in fact , the steric clash between the syn - methyl groups of 7cot is more severe than the clash present in 5cot . as found for the 6 electrocyclization of 5cot , relief of steric 
 strain explains the favorable kinetics and thermodynamics for the 
 second ring closure . according to computations , the second step 
 of the cascade , the 
 6 electrocyclization , occurs with exclusive selectivity for 
 the exo diastereomer , 7bcod . the transition 
 states for the 6 ring closure of 7cot are shown in figure 5 . a destabilizing steric clash in the endo transition state ( ts76 ) is responsible for this preference . natural products 
 featuring a cis arrangement of the c7 and c8 substituents 
 ( as in 7bcod ) have not been reported . the 86 
 electrocyclic reactions of trisubstituted 
 tetraenes 8 and 9 , which resemble reactions 
 used by nature to synthesize the -pyrone - containing metabolites , 
 are both facile and selective . both electrocyclic reactions have similar 
 g values , and the rate - determining 
 step of the cascades is now the 8 electrocyclization . figure 6 shows the 8 
 and 6 electrocyclization transition states of substrates 8 and 9 . steric repulsion 
 is more severe in 8cot than in 6cot or 7cot due to the presence of 
 a third methyl substituent in 8cot , which introduces a second steric 
 clash . relief of both clashes by the geometric changes occurring during 
 formation of the cyclobutane ring of 8bcod explains the high reactivity 
 of 8cot . the ring closure of intermediate 8cot is also highly diastereoselective 
 ( g = 4.7 kcal mol ) , exclusively forming 8bcod . in fact , 
 our computations overestimate the diastereoselectivity of this ring 
 closure on the basis of the biomimetic tandem electrocyclizations 
 used to synthesize the elysiapyrones and snf4435 c and d. structural differences between the substrates studied 
 computationally and those used by nature to construct these natural 
 products , including the presence of additional substituents , may be 
 responsible for this lack of quantitative agreement . qualitatively , 
 the diastereoselectivity of this ring closure can be rationalized 
 using the same argument made to explain the selectivity of the 6 
 electrocyclization of the disubstituted cyclooctatriene 7cot . this 
 effect is responsible for increased closed - shell repulsion and geometric 
 distortion of ts86. gibbs free energy profile 
 and transition structures for the 86 
 ring closure cascade of trisubstituted tetraenes 8 and 9 . structures and free energies ( kcal mol ) determined using the m06 - 2x/6 - 31+g(d , p ) level of theory . both a 
 front view and a side view ( newman projection ) of ts86 and ts86 are provided . the reaction of the tetrasubstituted 
 tetraene 10 has 
 a g = 24.2 kcal mol ( see figure 7 ) . tetrasubstitution 
 destabilizes the cyclooctatriene intermediate such that the initial 
 8 electrocyclization is endergonic . although 
 tetrasubstituted tetraenes like 10 are not known in nature , 
 these results suggest that the formation of two vicinal quaternary 
 centers via an 86 electrocyclization cascade 
 is possible . gibbs free energy profile and transition structures for 
 the 86 
 ring closure cascade of tetrasubstituted tetraene 10 . structures and free energies ( kcal mol ) determined 
 using the m06 - 2x/6 - 31+g(d , p ) level of theory . table 1 summarizes the 
 results of our computational 
 investigation of tetraenes 110 . while 14 only undergo 8 electrocyclization , 510 readily undergo both steps of the 
 86 electrocyclization cascade . destabilization 
 of the 1,3,5-cyclooctatriene intermediates by steric repulsion of 
 vicinal groups at the 7 and 8 positions of cyclooctatrienes 5bcod , 
 7bcod , 8bcod , and 10bcod reduces the barriers of the 6 ring 
 closures of these intermediates , explaining why the cascade reactions 
 of 510 are so efficient . tetraenes 79 yield chiral 1,3,5-cyclooctatrienes 
 that are predicted to undergo highly diastereoselective 6 ring 
 closures , favoring the formation of the exo mode 
 of disrotatory ring closure . the diastereoselectivities in these cases 
 are attributed to a destabilizing steric clash in the endo transition state . lastly , by modeling the cascade electrocyclizations 
 of tetraene 10 , we demonstrate a potential means of generating 
 vicinal quaternary centers in a single chemical step . g8 and g6 are the free energies of activation for 8 
 and 6 ring closure of the indicated tetraene , respectively . the reaction energies for the 
 8 
 and 6 electrocyclizations are , respectively , g8 and g6. the exo and endo designations indicate which of the two 
 stereoproducts 
 is more stable ( where relevant ) . all gibbs free energies 
 are reported 
 in kilocalories per mole and were calculated using the tetraene precursor 
 as the point of reference . geometry optimizations and frequency calculations 
 were carried out using the m06 - 2x metahybrid 
 functional with the 6 - 31+g(d , p ) basis set . the m06 - 2x functional was 
 chosen for its accuracy in modeling main group chemistry . the b3lyp/6 - 31g(d ) model chemistry was also 
 tested ; however , it was inferior in terms of accuracy to the m06 - 2x/6 - 31+g(d , p ) 
 level of theory . the details of the b3lyp/6 - 31g(d ) computations are 
 presented in the supporting information . the structures described herein are the lowest energy m06 - 2x/6 - 31+g(d , p)-optimized 
 conformers . for the m06 - 2x/6 - 31+g(d , p ) computations , a numerical integration 
 grid consisting of 99 radial shells and 590 angular points per shell 
 was employed . all stationary points were characterized as minima or 
 transition states on the basis of normal vibrational mode analysis . thermal corrections were computed from unscaled frequencies , assuming 
 a standard state of 298.15 k and 1 atm . the vibrational partition 
 functions used to calculate the entropic contributions of the gibbs 
 free energies were evaluated using truhlar s quasiharmonic 
 approximation , in which all vibrational modes with frequencies below 
 100 cm were raised to 100 cm to reduce errors arising from the treatment of low modes as harmonic 
 oscillations .
m06 - 2x/6 - 31+g(d , p ) 
 computations are reported for the 86 
 electrocyclization cascades of 1,3,5,7-tetraenes . 
 the rate - determining 
 step for these cascades is typically the second ( 6 ) ring closure . 
 according to experiment and theory , un- and 
 monosubstituted tetraenes 
 readily undergo 8 electrocyclic ring closure to form 1,3,5-cyclooctatrienes ; 
 however , the 6 electrocyclizations of these cyclooctatriene 
 intermediates are slow and reversible , and mixtures of monocyclic 
 and bicyclic products are formed . 
 computations indicate that di- and 
 trisubstituted tetraenes undergo facile but less exergonic 8 
 electrocyclization due to a steric clash that destabilizes the 1,3,5-cyclooctatriene 
 intermediates . 
 relief of this steric clash ensures the subsequent 
 6 ring closures of these intermediates are both kinetically 
 facile and thermodynamically favorable , and only the bicyclic products 
 are observed for the cascade reactions of naturally occurring tri- 
 and tetrasubstituted tetraenes ( in agreement with computations ) . 
 the 
 6 electrocyclization step of these cascade electrocyclizations 
 is also potentially diastereoselective , and di- and trisubstituted 
 tetraenes often undergo cascade reactions with high diastereoselectivities . 
 the exo mode of ring closure is favored for these 
 6 electrocyclizations due to a steric interaction that destabilizes 
 the endo transition state . 
 thus , theory explains 
 both the recalcitrance of the unsubstituted 1,3,5,7-octatetraene and 
 1-substituted tetraenes toward formation of the bicyclo[4.2.0]octa-2,4-diene 
 products , as well as the ease and the stereoselectivity with which 
 terminal di- and trisubstituted tetraenes are known to react biosynthetically .