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tions can also be analyzed using correlation diagrams a model reaction is the transfer of a pair of hydrogen atoms from ethane to perdeuterioethylene shown to the right the only conserved symmetry element in this reaction is the mirror plane through the center of the molecules as shown to the left conserved mirror plane in transfer reaction the molecular orbitals of the system are constructed as symmetric and antisymmetric combinations of σ and σ c h bonds in ethane and π and π bonds in the deutero substituted ethene thus the lowest energy mo is the symmetric sum of the two c h σ bond σ s followed by the antisymmetric sum σ a the two highest energy mos are formed from linear combinations of the σ ch antibonds highest is the antisymmetric σ a preceded by the symmetric σ a at a slightly lower energy in the middle of the energetic scale are the two remaining mos that are the π cc and π cc of ethene the full molecular orbital correlation diagram is constructed in by matching pairs of symmetric and asymmetric mos of increasing total energy as explained above as can be seen in the adjacent diagram as the bonding orbitals of the reactants exactly correlate with the bonding orbitals of the products this reaction is not predicted to have a high electronic symmetry imposed barrier 17 25 selection rules edit using correlation diagrams one can derive selection rules for the following generalized classes of pericyclic reactions each of these particular classes is further generalized in the generalized woodward hoffmann rules the more inclusive bond topology descriptors antarafacial and suprafacial subsume the terms conrotatory and disrotatory respectively antarafacial refers to bond making or breaking through the opposite face of a π system p orbital or σ bond while suprafacial refers to the process occurring through the same face a suprafacial transformation at a chiral center preserves stereochemistry whereas an antarafacial transformation reverses stereochemistry electrocyclic reactions edit the selection rule of electrocyclization reactions is given in the original statement of the woodward hoffmann rules if a generalized electrocyclic ring closure occurs in a polyene of 4 n π electrons then it is conrotatory under thermal conditions and disrotatory under photochemical conditions conversely in a polyene of 4 n 2 π electrons an electrocyclic ring closure is disrotatory under thermal conditions and conrotatory under photochemical conditions this result can either be derived via an fmo analysis based upon the sign of p orbital lobes of the homo of the polyene or with correlation diagrams taking first the first possibility in the ground state if a polyene has 4 n electrons the outer p orbitals of the homo that form the σ bond in the electrocyclized product are of opposite signs thus a constructive overlap is only produced under a conrotatory or antarafacial process conversely for a polyene with 4 n 2 electrons the outer p orbitals of the ground state homo are of the same sign thus constructive orbital overlap occurs with a disrotatory or suprafacical process 2 a 4n electron electrocyclic reaction achieves constructive homo orbital overlap if it is conrotatory while a 4n 2 electrocyclic reaction achieves constructive overlap if it is disrotatory additionally the correlation diagram for any 4 n electrocyclic reaction will resemble the diagram for the 4 electron cyclization of 1 3 butadiene while the correlation diagram any 4 n 2 electron electrocyclic reaction will resemble the correlation diagram for the 6 electron cyclization of 1 3 5 hexatriene 17 this is summarized in the following table thermally allowed photochemically allowed 4 n conrotatory disrotatory 4 n 2 disrotatory conrotatory sigmatropic rearrangement reactions edit a general sigmatropic rearrangement can be classified as order i j meaning that a σ bond originally between atoms denoted 1 and 1 adjacent to one or more π systems is shifted to between atoms i and j thus it migrates i 1 j 1 atoms away from its original position a formal symmetry analysis via correlation diagrams is of no use in the study of sigmatropic rearrangements as there are in general only symmetry elements present in the transition state except in special cases e g 3 3 rearrangements there are no symmetry elements that are conserved as the reaction coordinate is traversed 17 25 nevertheless orbital correlations between starting materials and products can still be analyzed and correlations of starting material orbitals with high energy product orbitals will as usual result in symmetry forbidden processes however an fmo based approach or the dewar zimmerman analysis is more straightforward to apply in 1 j sigmatropic rearrangements if 1 j 4n then supra antara is thermally allowed and if 1 j 4n 2 then supra supra or antara antara is thermally allowed one of the most prevalent classes of sigmatropic shifts is classified as 1 j where j is odd that means one terminus of the σ bond migrates j 1 bonds away across a π system while the other terminus does not migrate it is a reaction involving j 1 electrons j 1 from the π system and 2 from σ bond using fmo analysis 1 j sigmatropic rearrangements are allowed if the transition state has constructive overlap between the migrating group and the accepting p orbital of the homo in 1 j sigmatropic rearrangements if j 1 4 n then supra antara is thermally allowed and if j 1 4 n 2 then supra supra or antara antara is thermally allowed 25 the other prevalent class of sigmatropic rearrangements are 3 3 notably the cope and claisen rearrangements here the constructive interactions must be between the homos of the two allyl radical fragments in the transition state the ground state homo ψ 2 of the allyl fragment is shown below as the terminal p orbitals are of opposite sign this reaction can either take place in a supra supra topology or an antara antara topology 25 the 3 3 sigmatropic ground state reaction is allowed via either a supra supra or antara antara topology the selection rules for an i j sigmatropic rearrangement are as follows for supra supra or antara antara i j sigmatropic shifts if i j 4 n 2 they are thermally allowed and if i j 4 n they are photochemically allowed for supra antara i j sigmatropic shifts if i j 4 n they are thermally allowed and if i j 4 n 2 they are photochemically allowed this is summarized in the following table i j thermally allowed photochemically allowed 4 n i s j a or i a j s i s j s or i a j a 4 n 2 i s j s or i a j a i s j a or i a j s cycloaddition reactions edit a general p q cycloaddition is a concerted addition reaction between two components one with p π electrons and one with q π electrons this reaction is symmetry allowed under the following conditions 17 for a supra supra or antara antara cycloaddition it is thermally allowed if p q 4 n 2 and photochemically allowed if p q 4 n for a supra antara cycloaddition it is thermally allowed if p q 4 n and photochemically allowed if p q 4 n 2 this is summarized in the following table p q thermally allowed photochemically allowed 4 n p s q a or p a q s p s q s or p a q a 4 n 2 p s q s or p a q a p s q a or p a q s group transfer reactions edit a general double group transfer reaction which is synchronous can be represented as an interaction between a component with p π electrons and a component with q π electrons as shown generalized synchronous double group transfer reaction between a component with p π electrons and a component with q π electrons then the selection rules are the same as for the generalized cycloaddition reactions 17 that is for supra supra or antara antara double group transfers if p q 4 n 2 it is thermally allowed and if p q 4 n it is photochemically allowed for supra antara double group transfers if p q 4 n it is thermally allowed and if p q 4 n 2 it is photochemically allowed this is summarized in the following table p q thermally allowed photochemically allowed 4 n p s q a or p a q s p s q s or p a q a 4 n 2 p s q s or p a q a p s q a or p a q s the case of q 0 corresponds to the thermal elimination of the transferred r groups there is evidence that the pyrolytic eliminations of dihydrogen and ethane from 1 4 cyclohexadiene and 3 3 6 6 tetramethyl 1 4 cyclohexadiene respectively represent examples of this type of pericyclic process the ene reaction is often classified as a type of group transfer process even though it does not involve the transfer of two σ bonded groups rather only one σ bond is transferred while a second σ bond is formed from a broken π bond as an all suprafacial process involving 6 electrons it is symmetry allowed under thermal conditions the woodward hoffmann symbol for the ene reaction is π 2 s π 2 s σ 2 s see below general formulation edit though the woodward hoffmann rules were first stated in terms of electrocyclic processes they were eventually generalized to all pericyclic reactions as the similarity and patterns in the above selection rules should indicate conrotatory motion is antarafacial while disrotatory motion is suprafacial in the generalized woodward hoffmann rules everything is characterized in terms of antarafacial and suprafacial bond topologies the terms conrotatory and disrotatory are sufficient for describing the relative sense of bond rotation in electrocyclic ring closing or opening reactions as illustrated on the right however they are unsuitable for describing the topologies of bond forming and breaking taking place in a general pericyclic reaction as described in detail below in the general formulation of the woodward hoffmann rules the bond rotation terms conrotatory and disrotatory are subsumed by the bond topology or faciality terms antarafacial and suprafacial respectively these descriptors can be used to characterize the topology of the bond forming and breaking that takes place in any pericyclic process woodward hoffmann notation edit a component is any part of a molecule or molecules that function as a unit in a pericyclic reaction a component consists of one or more atoms and any of the following types of associated orbitals an isolated p or sp x orbital unfilled or filled symbol ω a conjugated π system symbol π a σ bond symbol σ the electron count of a component is the number of electrons in the orbital s of the component the electron count of an unfilled ω orbital i e an empty p orbital is 0 while that of a filled ω orbital i e a lone pair is 2 the electron count of a conjugated π system with n double bonds is 2 n or 2 n 2 if a formal lone pair from a heteroatom or carbanion is conjugated thereto the electron count of a σ bond is 2 the bond topology of a component can be suprafacial and antarafacial the relationship is suprafacial symbol s when the interactions with the π system or p orbital occur on the same side of the nodal plane think syn for a σ bond it corresponds to interactions occurring on the two interior lobes or two exterior lobes of the bond the relationship is antarafacial symbol a when the interactions with the π system or p orbital occur on opposite sides of the nodal plane think anti for a σ bond it corresponds to interactions occurring on one interior lobe and one exterior lobe of the bond illustration of the assignment of orbital overlap as suprafacial or antarafacial for common pericyclic components using this notation all pericyclic reactions can be assigned a descriptor consisting of a series of symbols σ π ω n s a connected by signs and enclosed in brackets describing in order the type of orbital s number of electrons and bond topology involved for each component some illustrative examples follow the diels alder reaction a 4 2 cycloaddition is π 4 s π 2 s the 1 3 dipolar cycloaddition of ozone and an olefin in the first step of ozonolysis a 3 2 cycloaddition is π 4 s π 2 s the cheletropic addition of sulfur dioxide to 1 3 butadiene a 4 1 cheletropic addition is ω 0 a π 4 s ω 2 s π 4 s 27 the cope rearrangement a 3 3 sigmatropic shift is π 2 s σ 2 s π 2 s or π 2 a σ 2 s π 2 a the 1 3 alkyl migration with inversion at carbon discovered by berson a 1 3 sigmatropic shift is σ 2 a π 2 s the conrotatory electrocyclic ring closing of 1 3 butadiene a 4π electrocyclization is π 4 s the conrotatory electrocyclic ring opening of cyclobutene a reverse 4π electrocyclization is σ 2 a π 2 s or σ 2 s π 2 a the disrotatory electrocyclic ring closing of 1 3 cyclooctadien 5 ide anion a 6π electrocyclization is π 6 s a wagner meerwein shift of a carbocation a 1 2 sigmatropic shift is ω 0 s σ 2 s antarafacial and suprafacial are associated with conrotation or inversion and disrotation or retention respectively a single descriptor may correspond to two pericyclic processes that are chemically distinct that a reaction and its microscopic reverse are often described with two different descriptors and that a single process may have more than a one correct descriptor one can verify using the pericyclic selection rule given below that all of these reactions are allowed processes original statement edit using this notation woodward and hoffmann state in their 1969 review the general formulation for all pericyclic reactions as follows a ground state pericyclic change is symmetry allowed when the total number of 4q 2 s and 4r a components is odd 17 here 4 q 2 s and 4 r a refer to suprafacial 4 q 2 electron and antarafacial 4 r electron components respectively moreover this criterion should be interpreted as both sufficient stated above as well as necessary not explicitly stated above see if and only if derivation of an alternative statement edit alternatively the general statement can be formulated in terms of the total number of electrons using simple rules of divisibility by a straightforward analysis of two cases first consider the case where the total number of electrons is 4 n 2 4 n 2 a 4 q 2 s b 4 p 2 a c 4 t s d 4 r a where a b c and d are coefficients indicating the number of each type of component this equation implies that one of but not both a or b is odd for if a and b are both even or both odd then the sum of the four terms is 0 mod 4 the generalized statement of the woodward hoffmann rules states that a d is odd if the reaction is allowed now if a is even then this implies that d is odd since b is odd in this case the number of antarafacial components b d is even likewise if a is odd then d is even since b even in this case the number of antarafacial components b d is again even thus regardless of the initial assumption of parity for a and b the number of antarafacial components is even when the electron count is 4 n 2 contrariwise b d is odd in the case where the total number of electrons is 4 n similar arguments omitted here lead to the conclusion that the number of antarafacial components b d must be odd in the allowed case and even in the forbidden case finally to complete the argument and show that this new criterion is truly equivalent to the original criterion one needs to argue the conv...
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