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lectrocyclic reaction in his publication instead corey elided the matter 13 rule edit the woodward hoffmann rules can be stated succinctly as a single sentence 16 a ground state pericyclic process involving n electron pairs and a antarafacial components is symmetry allowed if and only if n a is odd a ground state pericyclic process is driven by surplus thermal energy i e heat in the language of aromatic transition state theory the woodward hoffmann rules can be restated as follows a pericyclic transition state involving 4 n 2 electrons with hückel topology or 4 n electrons with möbius topology is aromatic and allowed while a pericyclic transition state involving 4 n electrons with hückel topology or 4 n 2 electrons with möbius topology is antiaromatic and forbidden often the woodward hoffmann rules are extended to analyze photochemical reactions in which the surplus energy is provided by ultraviolet irradiation if such processes occur purely in the excited state then the woodward hoffmann rules predict the exact reverse of the selection rule displayed above that is a pericyclic process involving n electron pairs and a antarafacial components is often favored under photochemical conditions if n a is even this can be rationalized by considering the correlation of the first electronic excited states of the reactants and products however many formally pericyclic reactions taking place under photochemical irradiation exhibit complex mechanisms several modes of electronic excitation are usually possible and electronically excited molecules may undergo intersystem crossing radiationless decay or relax to an unfavorable equilibrium geometry before the excited state pericyclic process can take place thus many apparent pericyclic reactions that take place under irradiation are actually thought to be stepwise processes involving diradical intermediates nevertheless it is frequently observed that the pericyclic selection rules become reversed when switching from thermal to photochemical activation pericyclic reactions involving an odd number of electrons are also known with respect to application of the generalized pericyclic selection rule these systems can generally be treated as though one more electron were involved 17 illustrative examples edit the interconversion of model cyclobutene and butadiene derivatives under thermal heating and photochemical ultraviolet irradiation conditions is illustrative the woodward hoffmann rules apply to either direction of a pericyclic process due to the inherent ring strain of cyclobutene derivatives the thermodynamic equilibrium between the cyclobutene and the 1 3 butadiene strongly favors opening the ring irradiation causes reactions that can absorb photons to occur at a much faster rate and reactions that emit them occur more slowly shifting the equilibrium to a photostationary state only the 1 3 butadiene absorbs significantly at higher wavelengths hence irradiation of the 1 3 butadiene at such a wavelength can result in high conversion to the cyclobutene thermolysis of trans 1 2 3 4 tetramethyl 1 cyclobutene 1 afforded only one geometric isomer e e 3 4 dimethyl 2 4 hexadiene 2 the z z and the e z geometric isomers were not detected in the product mixture similarly thermolysis of cis 1 2 3 4 tetramethyl 1 cyclobutene 3 afforded only e z isomer 4 18 in both ring opening reactions the carbons on the ends of the breaking σ bond rotate in the same direction 19 some thermal and photochemical interconversions of substituted cyclobutenes and butadienes showing conrotatory blue and disrotatory red behavior on the other hand the opposite stereochemical course was followed under photochemical activation when the related compound e e 2 4 hexadiene 5 was exposed to light cis 3 4 dimethyl 1 cyclobutene 6 was formed exclusively as a result of electrocyclic ring closure 20 this requires the ends of the π system to rotate in opposite directions to form the new σ bond thermolysis of 6 follows the same stereochemical course as 3 electrocyclic ring opening leads to the formation of e z 2 4 hexadiene 7 and not 5 21 the woodward hoffmann rules explain these results through orbital overlap in the case of a photochemically driven electrocyclic ring closure of buta 1 3 diene electronic promotion causes ψ 3 displaystyle psi _ 3 to become the homo and the reaction mechanism must be disrotatory conversely in the electrocyclic ring closure of the substituted hexa 1 3 5 triene pictured below the reaction proceeds through a disrotatory mechanism correlation diagrams edit as shown by longuet higgins and e w abrahamson the woodward hoffmann rules can best be derived by examining the correlation diagram of a given reaction 22 17 23 24 in this approach the idea of a conserved symmetry element is introduced a symmetry element is usually a plane or a line about which an object is symmetric or antisymmetric with respect to a rotation or reflection symmetry operation if a symmetry element is present throughout the reaction path from reactant through transition state to product it is called a conserved symmetry element then throughout the reaction the symmetry of molecular orbitals with respect to this element must be conserved that is molecular orbitals that are symmetric with respect to the symmetry element in the starting material must be correlated to transform into orbitals symmetric with respect to that element in the product conversely the same statement holds for antisymmetry with respect to a conserved symmetry element a molecular orbital correlation diagram correlates molecular orbitals of the starting materials and the product based upon conservation of symmetry from a molecular orbital correlation diagram one can construct an electronic state correlation diagram that correlates electronic states i e ground state and excited states of the reactants with electronic states of the products correlation diagrams can then be used to predict the height of transition state barriers 25 electrocyclic reactions edit the transition state of a conrotatory closure has c 2 symmetry whereas the transition state of a disrotatory opening has mirror symmetry mos of butadiene are shown with the element with which they are symmetric they are antisymmetric with respect to the other considering the electrocyclic ring closure of the substituted 1 3 butadiene the reaction can proceed through either a conrotatory or a disrotatory reaction mechanism as shown to the left in the conrotatory transition state there is a c 2 axis of symmetry and in the disrotatory transition state there is a σ mirror plane of symmetry in order to correlate orbitals of the starting material and product one must determine whether the molecular orbitals are symmetric or antisymmetric with respect to these symmetry elements the π system molecular orbitals of butadiene are shown to the right along with the symmetry element with which they are symmetric they are antisymmetric with respect to the other for example ψ 2 of 1 3 butadiene is symmetric with respect to 180 o rotation about the c 2 axis and antisymmetric with respect to reflection in the mirror plane ψ 1 and ψ 3 are symmetric with respect to the mirror plane as the sign of the p orbital lobes is preserved under the symmetry transformation similarly ψ 1 and ψ 3 are antisymmetric with respect to the c 2 axis as the rotation inverts the sign of the p orbital lobes uniformly conversely ψ 2 and ψ 4 are symmetric with respect to the c 2 axis and antisymmetric with respect to the σ mirror plane the same analysis can be carried out for the molecular orbitals of cyclobutene the result of both symmetry operations on each of the mos is shown to the left as the σ and σ orbitals lie entirely in the plane containing c 2 perpendicular to σ they are uniformly symmetric and antisymmetric respectively to both symmetry elements on the other hand π is symmetric with respect to reflection and antisymmetric with respect to rotation while π is antisymmetric with respect to reflection and symmetric with respect to rotation correlation lines are drawn to connect molecular orbitals in the starting material and the product that have the same symmetry with respect to the conserved symmetry element in the case of the conrotatory 4 electron electrocyclic ring closure of 1 3 butadiene the lowest molecular orbital ψ 1 is asymmetric a with respect to the c 2 axis so this molecular orbital is correlated with the π orbital of cyclobutene the lowest energy orbital that is also a with respect to the c 2 axis similarly ψ 2 which is symmetric s with respect to the c 2 axis is correlated with σ of cyclobutene the final two correlations are between the antisymmetric a molecular orbitals ψ 3 and σ and the symmetric s molecular orbitals ψ 4 and π 17 4 electron electrocyclization reaction correlation diagram with a conrotatory mechanism similarly there exists a correlation diagram for a disrotatory mechanism in this mechanism the symmetry element that persists throughout the entire mechanism is the σ mirror plane of reflection here the lowest energy mo ψ 1 of 1 3 butadiene is symmetric with respect to the reflection plane and as such correlates with the symmetric σ mo of cyclobutene similarly the higher energy pair of symmetric molecular orbitals ψ 3 and π correlate as for the asymmetric molecular orbitals the lower energy pair ψ 2 and π form a correlation pair as do ψ 4 and σ 17 4 electron electrocyclization reaction correlation diagram with a disrotatory mechanism evaluating the two mechanisms the conrotatory mechanism is predicted to have a lower barrier because it transforms the electrons from ground state orbitals of the reactants ψ 1 and ψ 2 into ground state orbitals of the product σ and π conversely the disrotatory mechanism forces the conversion of the ψ 1 orbital into the σ orbital and the ψ 2 orbital into the π orbital thus the two electrons in the ground state ψ 2 orbital are transferred to an excited antibonding orbital creating a doubly excited electronic state of the cyclobutene this would lead to a significantly higher transition state barrier to reaction 17 first excited state es 1 of butadiene however as reactions do not take place between disjointed molecular orbitals but electronic states the final analysis involves state correlation diagrams a state correlation diagram correlates the overall symmetry of electronic states in the starting material and product the ground state of 1 3 butadiene as shown above has 2 electrons in ψ 1 and 2 electrons in ψ 2 so it is represented as ψ 1 2 ψ 2 2 the overall symmetry of the state is the product of the symmetries of each filled orbital with multiplicity for doubly populated orbitals thus as ψ 1 is asymmetric with respect to the c 2 axis and ψ 2 is symmetric the total state is represented by a 2 s 2 to see why this particular product is mathematically overall s that s can be represented as 1 and a as 1 this derives from the fact that signs of the lobes of the p orbitals are multiplied by 1 if they are symmetric with respect to a symmetry transformation i e unaltered and multiplied by 1 if they are antisymmetric with respect to a symmetry transformation i e inverted thus a 2 s 2 1 2 1 2 1 s the first excited state es 1 is formed from promoting an electron from the homo to the lumo and thus is represented as ψ 1 2 ψ 2 ψ 3 as ψ 1 is a ψ 2 is s and ψ 3 is a the symmetry of this state is given by a 2 sa a now considering the electronic states of the product cyclobutene the ground state is given by σ 2 π 2 which has symmetry s 2 a 2 s the first excited state es 1 is again formed from a promotion of an electron from the homo to the lumo so in this case it is represented as σ 2 ππ the symmetry of this state is s 2 as a the ground state ψ 1 2 ψ 2 2 of 1 3 butadiene correlates with the ground state σ 2 π 2 of cyclobutene as demonstrated in the mo correlation diagram above ψ 1 correlates with π and ψ 2 correlates with σ thus the orbitals making up ψ 1 2 ψ 2 2 must transform into the orbitals making up σ 2 π 2 under a conrotatory mechanism however the state es 1 does not correlate with the state es 1 as the molecular orbitals do not transform into each other under the symmetry requirement seen in the molecular orbital correlation diagram instead as ψ 1 correlates with π ψ 2 correlates with σ and ψ 3 correlates with σ the state ψ 1 2 ψ 2 ψ 3 attempts to transform into π 2 σσ which is a different excited state so es 1 attempts to correlate with es 2 σπ 2 σ which is higher in energy than es 1 similarly es 1 σ 2 ππ attempts to correlate with es 2 ψ 1 ψ 2 2 ψ 4 these correlations can not actually take place due to the quantum mechanical rule known as the avoided crossing rule this says that energetic configurations of the same symmetry can not cross on an energy level correlation diagram in short this is caused by mixing of states of the same symmetry when brought close enough in energy so instead a high energetic barrier is formed between a forced transformation of es 1 into es 1 in the diagram below the symmetry preferred correlations are shown in dashed lines and the bold curved lines indicate the actual correlation with the high energetic barrier 17 25 4 electron electrocyclization state correlation diagram with a conrotatory mechanism the same analysis can be applied to the disrotatory mechanism to create the following state correlation diagram 17 25 4 electron electrocyclization state correlation diagram under disrotatory mechanism thus if the molecule is in the ground state it will proceed through the conrotatory mechanism i e under thermal control to avoid an electronic barrier however if the molecule is in the first excited state i e under photochemical control the electronic barrier is present in the conrotatory mechanism and the reaction will proceed through the disrotatory mechanism these are not completely distinct as both the conrotatory and disrotatory mechanisms lie on the same potential surface thus a more correct statement is that as a ground state molecule explores the potential energy surface it is more likely to achieve the activation barrier to undergo a conrotatory mechanism 25 cycloaddition reactions edit the woodward hoffmann rules can also explain bimolecular cycloaddition reactions through correlation diagrams 26 a π p π q cycloaddition brings together two components one with p π electrons and the other with q π electrons cycloaddition reactions are further characterized as suprafacial s or antarafacial a with respect to each of the π components see below general formulation for a detailed description of the generalization of wh notation to all pericyclic processes 2 2 cycloadditions edit for ordinary alkenes 2 2 cycloadditions are only observed under photochemical activation the rationale for the non observation of thermal 2 2 cycloadditions begins with the analysis of the four possible stereochemical consequences for the 2 2 cycloaddition π 2 s π 2 s π 2 a π 2 s π 2 s π 2 a π ...
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