Woodward–Hoffmann rules

662:

formally disrupts a symmetry plane or axis (e.g., a methyl group) does not generally affect the assessment of whether a reaction is allowed or forbidden. Instead, the symmetry present in an unsubstituted analog is used to simplify the construction of orbital correlation diagrams and avoid the need to perform calculations. Only the phase relationships between orbitals are important when judging whether a reaction is "symmetry"-allowed or forbidden. Moreover, orbital correlations can still be made, even if there are no conserved symmetry elements (e.g., 1,5-sigmatropic shifts and ene reactions). For this reason, the Woodward–Hoffmann, Fukui, and Dewar–Zimmerman analyses are equally broad in their applicability, though a certain approach may be easier or more intuitive to apply than another, depending on the reaction one wishes to analyze.

5866:"I REMEMBER very clearly—and it still surprises me somewhat—that the crucial flash of enlightenment came to me in algebraic, rather than in pictorial or geometric form. Out of the blue, it occurred to me that the coefficients of the terminal terms in the mathematical expression representing the highest occupied molecular orbital of butadiene were of opposite sign, while those of the corresponding expression for hexatriene possessed the same sign. From here it was but a short step to the geometric, and more obviously chemically relevant, view that in the internal cyclisation of a diene, the top face of one terminal atom should attack the bottom face of the other, while in the triene case, the formation of a new bond should involve the top (or pari passu, the bottom) faces of both terminal atoms." 595:, 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. This can be rationalized by considering the correlation of the first electronic excited states of the reactants and products. Although more of a useful heuristic than a rule, a corresponding generalized selection principle for photochemical pericyclic reactions can be stated: 2941:

respectively, as transition states involving two or more antarafacial components are typically disfavored by strain. As exceptions, certain intramolecular reactions may be geometrically constrained in such a way that enforces an antarafacial trajectory for multiple components. In addition, in some cases, e.g., the Cope rearrangement, the same (not necessarily strained) transition state geometry can be considered to contain two supra or two antara π components, depending on how one draws the connections between orbital lobes. (This ambiguity is a consequence of the convention that overlap of either both interior or both exterior lobes of a σ component can be considered to be suprafacial.)

1038: 1049: 20: 841: 813: 5884: 490: 5792: 1568: 5820: 683: 2486: 1381: 1160: 1622: 5784: 1475: 2342: 1354: 1034:. 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. 1389: 2090: 6780:. Hence, an odd number of antarafacial components will force a single phase inversion in order to complete the cycle, while an even number of antarafacial components will allow a cycle to be completed with no phase inversion. Since the number of inversions (modulo 2) is invariant with respect to orbital phasing, these two possibilities (an odd or an even number of antarafacial components) fix whether a Möbius (one inversion) or Hückel (no inversion) system applies, respectively. 1316: 5181: 671: 5029: 723: 1116: 548: 765: 1124: 501: 1366: 1262: 884: 5737: 5222: 649:

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

538: 5841:, Corey makes his claim to priority of the idea: "On May 4, 1964, I suggested to my colleague R. B. Woodward a simple explanation involving the symmetry of the perturbed (HOMO) molecular orbitals for the stereoselective cyclobutene to 1,3-butadiene and 1,3,5-hexatriene to cyclohexadiene conversions that provided the basis for the further development of these ideas into what became known as the Woodward–Hoffmann rules". 4971: 5198:. As its central tenet, aromatic transition state theory holds that 'allowed' pericyclic reactions proceed via transition states with aromatic character, while 'forbidden' pericyclic reactions would encounter transition states that are antiaromatic in nature. In the Dewar-Zimmerman analysis, one is concerned with the topology of the transition state of the pericyclic reaction. If the transition state involves 4 5098: 6776:) of each component. Using these connections, it is possible to continue the shading onto neighboring components such that no inversion is present between components or within a component. This is continued until all interacting orbitals are shaded in and only a final Dewar-Zimmerman connection needs to be made to complete the cycle. No phase inversion has been introduced up to this point. 5768:

WH symmetry-allowed reaction actually takes place in a facile manner. Conversely, it is possible, upon enough energetic input, to achieve an anti-Woodward-Hoffmann product. This is especially prevalent in sterically constrained systems, where the WH-product has an added steric barrier to overcome. For example, in the electrocyclic ring-opening of the dimethylbicycloheptene derivative (

1057:

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.

3357: 170: 1564:

reaction coordinate is traversed. 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.

5078:+ 2 electrocyclic ring opening reaction is also a 2-component pericyclic reaction which is suprafacial with respect to the π-system. Thus, in order for the reaction to be allowed, the number of antarafacial components must be 0, i.e. it must be suprafacial with respect to the breaking σ-bond as well. Thus a disrotatory mechanism is symmetry-allowed. 5804:

predict that the mechanical force, resulting from friction of the polymers, induces bond lengthening along the reaction coordinate of the conrotatory mechanism in the anti-bisubstituted-cyclobutene, and along the reaction coordinate of the disrotatory mechanism in the syn-bisubstituted-cyclobutene. Thus in the syn-bisubstituted-cyclobutene, the

591:). It is important to recognize, however, that the operative mechanism of a formally pericyclic reaction taking place under photochemical irradiation is generally not as simple or clearcut as this dichotomy suggests. Several modes of electronic excitation are usually possible, and electronically excited molecules may undergo 4944:+ 2, then one is in the bottom row of the table. The reaction is thermally allowed if it is suprafacial with respect to both components or antarafacial with respect to both components. That is to say the number of antarafacial components is even (it is 0 or 2). Similarly if the total number of electrons is 4 4522: 3147: 5767:

This pronouncement notwithstanding, it is important to recognize that the Woodward–Hoffmann rules are used to predict relative barrier heights, and thus likely reaction mechanisms, and that they only take into account barriers due to conservation of orbital symmetry. Thus it is not guaranteed that a

2324:

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

648:

element is present throughout the reaction mechanism (reactant, transition state, and 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

5744:

The Woodward–Hoffmann rules are reinterpreted using this formulation by matching favorable interactions between regions of electron density for which the dual descriptor has opposite signs. This is equivalent to maximizing predicted favorable interactions and minimizing repulsive interactions. For

5815:

benzocyclobutene in both syn- and anti- conformations. As predicted, both products gave the same (Z,Z) product as determined by quenching by a stereospecific Diels-Alder reaction with the substituted maleimide. In particular, the syn-substituted product gave the anti-WH product, presumably as the

5732:

This makes intuitive sense as if a region is better at accepting electrons than donating, then the LUMO must dominate and dual descriptor function will be positive. Conversely, if a region is better at donating electrons then the HOMO term will dominate and the descriptor will be negative. Notice

2361:

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

1111:

The rationale for the non-observation of thermal cycloadditions begins with the analysis of the four possible stereochemical consequences for the cycloaddition: , , , . The geometrically most plausible mode is forbidden under thermal conditions, while the , approaches are allowed from the point

1056:

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

331:

of such systems. A process in which the HOMO-LUMO interaction is constructive (results in a net bonding interaction) is favorable and considered symmetry-allowed, while a process in which the HOMO-LUMO interaction is non-constructive (results in bonding and antibonding interactions that cancel) is

5053:

electron electrocyclic ring opening reaction can be considered to have 2 components – the π-system and the breaking σ-bond. With respect to the π-system, the reaction is suprafacial. However, with a conrotatory mechanism, as shown in the figure above, the reaction is antarafacial with respect to

924:

is symmetric, the total state is represented by AS. 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

6691:

More precisely, a 'symmetry-forbidden' system with true symmetry has starting material bonding orbitals that correlate with product antibonding orbitals and vice versa. In contrast, when a substituent disrupts the symmetry, these level crossings are 'barely avoided' by energy levels that approach

2583:

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

200:

depending on whether the orbital lobes that interact during the reaction are on the opposite or same side of the nodal plane, respectively. (The older terms conrotatory and disrotatory, which are applicable to electrocyclic ring opening and closing only, are subsumed by the terms antarafacial and

6767:

It is possible to produce a Dewar-Zimmerman analysis with at most one phase inversion and that the outcome depends on the parity of the number of antarafacial components. The process involves shading in the first orbital of any component arbitrarily and completing the shading of the rest of the

5803:

can be used to reshape chemical reaction pathways to lead to products that apparently violate Woodward–Hoffman rules. In this paper, they use ultrasound irradiation to induce a mechanical stress on link-functionalized polymers attached syn or anti on the cyclobutene ring. Computational studies

5745:

the case of a cycloaddition, a simplified schematic of the reactants with the dual descriptor function colored (red=positive, blue=negative) is shown in the optimal supra/supra configuration to the left. This method correctly predicts the WH rules for the major classes of pericyclic reactions.

776:

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

710:

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

6700:

correlation diagrams always have 'barely avoided' crossings, regardless of whether the symmetry is "true" or "approximate". Thus, the presence or absence of a simple substituent that disrupts a formal symmetry element is immaterial, as the state correlation diagram is unchanged in a qualitative

5971:). Moreover, E. Havinga had previously noted that tachysterol underwent electrocyclic ring closing in a conrotatory or disrotatory manner depending on activation mode (photochemical or thermal, respectively) and attributed an orbital symmetry explanation for this phenomenon to L. J. Oosterhoff ( 1563:

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. -rearrangements), there are no symmetry elements that are conserved as the

661:

Although orbital "symmetry" is used as a tool for sketching orbital and state correlation diagrams, the absolute presence or absence of a symmetry element is not critical for the determination of whether a reaction is allowed or forbidden. That is, the introduction of a simple substituent that

5256:

Draw connections between the lobes of basis orbitals that are geometrically well-disposed to interact at the transition state. The connections to be made depend on the transition state topology. (For example, in the figure, different connections are shown in the cases of con- and disrotatory

5229:

In connection with Woodward–Hoffmann terminology, the number of antarafacial components and the number of phase inversions always have the same parity. Consequently, an odd number of antarafacial components gives Möbius topology, while an even number gives Hückel topology. Thus, to restate the

1427:

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

1325:

Correlating the pairs of orbitals in the starting materials and product of the same symmetry and increasing energy gives the correlation diagram to the right. As this transforms the ground state bonding molecular orbitals of the starting materials into the ground state bonding orbitals of the

993:

must transform into the orbitals making up σπ 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

5844:

Corey, then 35, was working into the evening on Monday, May 4, as he and the other driven chemists often did. At about 8:30 p.m., he dropped by Woodward's office, and Woodward posed a question about how to predict the type of ring a chain of atoms would form. After some discussion, Corey

1441:

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

5772:), a conrotatory mechanism is not possible due to resulting angle strain and the reaction proceeds slowly through a disrotatory mechanism at 400 C to give a cycloheptadiene product. Violations may also be observed in cases with very strong thermodynamic driving forces. The decomposition of 5261:

Count the number of connections that occur between lobes of opposite shading: each of these connections constitutes a phase inversion. If the number of phase inversions is even, the transition state is Hückel, while if the number of phase inversions is odd, the transition state is Möbius.

780:

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

4982:

A -cycloaddition is a 4 electron process that brings together two components. Thus, by the above general WH rules, it is only allowed if the reaction is antarafacial with respect to exactly one component. This is the same conclusion reached with correlation diagrams in the section above.

2940:

In this formulation, the electron count refers to the entire reacting system, rather than to individual components, as enumerated in Woodward and Hoffmann's original statement. In practice, an even or odd number of antarafacial components usually means zero or one antarafacial components,

1174:, the starting material molecular orbitals must be considered in tandem. The figure to the right shows the molecular orbital correlation diagram for the cycloaddition. The two π and π molecular orbitals of the starting materials are characterized by their symmetry with respect to first σ 370:

is reached, a composition which depends on both absorbance and quantum yield of the forward and reverse reactions at a particular wavelength. Due to the different degrees of conjugation of 1,3-butadienes and cyclobutenes, only the 1,3-butadiene will have a significant absorbance at higher

125:

Although the symmetry-imposed barrier is often formidable (up to ca. 5 eV or 480 kJ/mol in the case of a forbidden cycloaddition), the prohibition is not absolute, and symmetry-forbidden reactions can still take place if other factors (e.g. strain release) favor the reaction. Likewise, a

157:

describe the relative sense of bond rotation involved in electrocyclic ring-opening and -closing reactions. In a disrotatory process, the breaking or forming bond's two ends rotate in opposing directions (one clockwise, one counterclockwise); in a conrotatory process, they rotate in the

2317:= 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. 5160:

in 1967. In order to allow for inversion of configuration, as the σ bond breaks, the C(H)(D) moiety twists around at the transition state, with the hybridization of the carbon approximating sp, so that the remaining unhybridized p orbital maintains overlap with both carbons 1 and 3.

891:

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

2944:

This alternative formulation makes the equivalence of the Woodward–Hoffmann rules to the Dewar–Zimmerman analysis (see below) clear. An even total number of phase inversions is equivalent to an even number of antarafacial components and corresponds to Hückel topology, requiring

1587:+ 1 electrons: j − 1 from the π-system and 2 from σ-bond. Using FMO analysis, -sigmatropic rearrangements are allowed if the transition state has constructive overlap between the migrating group and the accepting p orbital of the HOMO. In -sigmatropic rearrangements if 5248:

Shade in all basis orbitals that are part of the pericyclic system. The shading can be arbitrary. In particular the shading does not need to reflect the phasing of the polyene MOs; each basis orbital simply need to have two oppositely phased lobes in the case of p or

5727: 1436:

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

957:

is A, the symmetry of this state is given by ASA=A.Now considering the electronic states of the product, cyclobutene, the ground-state is given by σπ, which has symmetry SA=S. The first excited state (ES-1') is again formed from a promotion of an electron from the

3017:

For a pericyclic reaction, if the total number of antarafacial components of a (4n + 2)-electron reaction is even or the total number of antarafacial components of a 4n-electron reaction is odd then it is thermally allowed; otherwise the reaction is thermally

363:

between the cyclobutene and the 1,3-butadiene lies far to the right. Hence, under thermal conditions, the ring opening of the cyclobutene to the 1,3-butadiene is strongly favored by thermodynamics. On the other hand, under irradiation by ultraviolet light, a

335:

Though conceptually distinct, aromatic transition state theory (Zimmerman and Dewar), frontier molecular orbital theory (Fukui), and orbital symmetry conservation (Woodward and Hoffmann) all make identical predictions. The Woodward–Hoffmann rules exemplify

1329:

To make the analysis precise, one can construct the state correlation diagram for the general -cycloaddition. As before, the ground state is the electronic state depicted in the molecular orbital correlation diagram to the right. This can be described as

1182:. Similarly, the σ and σ molecular orbitals of the product are characterized by their symmetry. In the correlation diagram, molecular orbitals transformations over the course of the reaction must conserve the symmetry of the molecular orbitals. Thus π 5435:. This response function is important as the reaction of two components A and B involving a transfer of electrons will depend on the responsiveness of the electron density to electron donation or acceptance, i.e. the derivative of the Fukui function 925:

symmetry transformation (i.e. unaltered) and multiplied by (−1) if they are antisymmetric with respect to a symmetry transformation (i.e. inverted). Thus AS=(−1)(+1)=+1=S. The first excited state (ES-1) is formed from promoting an electron from the

1395:

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

4948:, then one is in the top row of the table. This is thermally allowed if it is suprafacial with respect to one component and antarafacial with respect to the other. Thus the total number of antarafacial components is always odd as it is always 1. 6390:) isomer was not observed is likely due to unfavorable steric interactions between the inwardly rotating methyl groups. (In other cases, the preference for clockwise or counterclockwise bond rotation may be controlled by stereoelectronic factors: 1466:

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

1349:

One can also construct the excited-state correlations as is done above. Here, there is a high energetic barrier to a photo-induced Diels-Alder reaction under a suprafacial-suprafacial bond topology due to the avoided crossing shown below.

126:

symmetry-allowed reaction may be preempted by an insurmountable energetic barrier resulting from factors unrelated to orbital symmetry. All known cases only violate the rules superficially; instead, different parts of the mechanism become

3352:{\displaystyle n_{i}={\begin{cases}0,&N\equiv 0\ (\mathrm {mod} \ 4)\\1,&N\equiv 2\ (\mathrm {mod} \ 4)\end{cases}}\quad \mathrm {and} \quad p_{i}={\begin{cases}0,&i{\text{ is supra}}\\1,&i{\text{ is antara}}\end{cases}}.} 5780:, has been scrutinized computationally. In the absence of fluorescers, the reaction is now believed to proceed in a concerted (though asynchronous) fashion, via a retro--cycloaddition that formally violates the Woodward–Hoffmann rules. 4278: 4642:

To give a concrete example, a hypothetical reaction with the descriptor would be assigned the collection {(1, 0, 1), (0, 1, 2), (1, 1, 3)} in the scheme above. There are two components, (1, 0, 1) and (0, 1, 2), with the property

1373:

The symmetry-imposed barrier heights of group transfer reactions 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.

605:

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.

2337:

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.

185:

was introduced to unify several classes of pericyclic reactions under a single conceptual framework. In short, a set of contiguous atoms and their associated orbitals that react as one unit in a pericyclic reaction is known as a

176:

Eventually, it was recognized that thermally-promoted pericyclic reactions in general obey a single set of generalized selection rules, depending on the electron count and topology of the orbital interactions. The key concept of

1241:

are doubly populated – i.e. the state (SS)(AS). However, this state is neither the ground state (SS)(SA) of cyclobutane, nor the first excited state ES-1'=(SS)(SA)(AS), where an electron is promoted from the HOMO to the LUMO.

1131:

Considering the cycloaddition. This mechanism leads to a retention of stereochemistry in the product, as illustrated to the right. Two symmetry elements are present in the starting materials, transition state, and product:

820:

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

5061:

electron pericyclic reaction of 2 components, there must be one antarafacial component. Thus the reaction must proceed through a conrotatory mechanism. This agrees with the result derived in the correlation diagrams above.

1461:

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

771:

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

657:

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.

489: 2849:

Finally, to complete the argument, and show that this new criterion is truly equivalent to the original criterion, one needs to argue the converse statements as well, namely, that the number of antarafacial components

5384: 5036:

Thus as the total number of antarafacial components is 0, which is even, the reaction is symmetry-allowed. This prediction agrees with experiment as the Diels-Alder reaction is a rather facile pericyclic reaction.

5835:, also a Nobel Prize winner, feels he is responsible for the ideas that laid the foundation for this research, and that Woodward unfairly neglected to credit him in the discovery. In a 2004 memoir published in the 5105:

A -sigmatropic rearrangement is also a two component pericyclic reaction: one component is the π-system, the other component is the migrating group. The simplest case is a -hydride shift across a π-system where

6750:

is analyzed here as a simple unoccupied p orbital), the interaction of these orbitals with those of 1,3-butadiene must be analyzed separately. In general, for a composite process like this cheletropic reaction,

5134:+ 1, then it must be suprafacial. This agrees with experiment that -hydride shifts are generally not observed as the symmetry-allowed antarafacial process is not feasible, but -hydride shifts are quite facile. 2874:

that is given by the Woodward–Hoffmann rules (odd for allowed, even for forbidden). Another round of (somewhat tedious) case analyses will easily show this to be the case. The pericyclic selection rule states:

5277:

Importantly, any scheme of assigning relative phases to the basis orbitals is acceptable, as inverting the phase of any single orbital adds 0 or ±2 phase inversions to the total, an even number, so that the

1018:

attempts to transform into πσσ, which is a different excited state. So ES-1 attempts to correlate with ES-2'=σπσ, which is higher in energy than Es-1'. Similarly ES-1'=σππ attempts to correlate with ES-2=Ψ

3892: 6778:

Crucial observation: The Dewar-Zimmerman connections extending from the two ends of an antarafacial (suprafacial) component to the neighboring components will connect lobes of opposite (the same) shading

5494: 5845:

proposed that the configuration of electrons governed the course of the reaction. Woodward insisted the solution would not work, but Corey left drawings in the office, sure that he was on to something.

2584:

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.

4004: 3009:

For a pericyclic reaction, if the sum of the number of suprafacial 4q + 2 components and antarafacial 4r components is odd then it is thermally allowed; otherwise the reaction is thermally forbidden.

2503:, 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: 224:, but could not predict which stereoisomer a reaction might select. In 1965, Woodward–Hoffmann realized that a simple set of rules explained the observed stereospecificity at the ends of open-chain 825:

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

6362:

Although the figure below shows both ends rotating clockwise, it is important to recognize that orbital symmetry only distinguishes between rotation in the same direction or opposing directions (

5580: 6061:

Zimmerman, H. E. (1966). "On Molecular Orbital Correlation Diagrams, the Occurrence of Möbius Systems in Cyclization Reactions, and Factors Controlling Ground- and Excited-State Reactions. I".

1544:

A general sigmatropic rearrangement can be classified as order , meaning that a σ bond originally between atoms denoted 1 and 1', adjacent to one or more π systems, is shifted to between atoms

5110:

is odd. In this case, as the hydrogen has only a spherically symmetric s orbital, the reaction must be suprafacial with respect to the hydrogen. The total number of electrons involved is (

1478:

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.

1280:

One symmetry element is conserved in this transformation – the mirror plane through the center of the reactants as shown to the left. The molecular orbitals of the reactants are the set {Ψ

2390:

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:

6928:

Geerlings, Paul; Ayers, Paul W.; Toro-Labbé, Alejandro; Chattaraj, Pratim K.; De Proft, Frank (2012). "The Woodward–Hoffmann Rules Reinterpreted by Conceptual Density Functional Theory".

6279:

Geerlings, Paul; Ayers, Paul W.; Toro-Labbé, Alejandro; Chattaraj, Pratim K.; De Proft, Frank (2012). "The Woodward–Hoffmann Rules Reinterpreted by Conceptual Density Functional Theory".

1450:

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

8280: 2949:+ 2 electrons for aromaticity, while an odd total number of phase inversions is equivalent to an odd number of antarafacial components and corresponds to Möbius topology, requiring 4 5851:

he wrote. But the next day, Woodward flew into Corey's office as he and a colleague were leaving for lunch and presented Corey's idea as his own – and then left. Corey was stunned.

1618:

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.

4230: 3634: 3429: 1037: 5574:, the region is nucleophilic. Using the frontier molecular orbital assumption and a finite difference approximation of the Fukui function, one may write the dual descriptor as 1048: 4576: 4094: 840: 812: 266:, terminal bonding interaction within ground-state molecules requires overlap of orbital envelopes on the same face of the system, attainable only by disrotatory displacements. 5496:. In fact, from a simplistic viewpoint, the dual descriptor function gives a readout on the electrophilicity or nucleophilicity of the various regions of the molecule. For 4998:-1,5-Cyclooctadiene is also believed to undergo dimerization via this mode. Ketenes are a large class of reactants favoring cycloaddition with olefins. The MO analysis of 4681: 4616: 4270: 4134: 3472: 3139: 3073: 209:

Woodward and Hoffmann developed the pericyclic selection rules after performing extensive orbital-overlap calculations. At the time, Woodward wanted to know whether certain

4772: 4728: 4180: 5572: 5533: 7112:

Hickenboth, Charles R.; Moore, Jeffrey S.; White, Scott R.; Sottos, Nancy R.; Baudry, Jerome; Wilson, Scott R. (2007). "Biasing reaction pathways with mechanical force".

4044: 3932: 3796: 3759: 3710: 3672: 3564: 3522: 285:

to state a generalized pericyclic selection rule equivalent to that now attached to their name: a pericyclic reaction is allowed if the sum of the number of suprafacial 4

10638:

Ayers, Paul W.; Morell, Christophe; De Proft, Frank; Geerlings, Paul (5 October 2007). "Understanding the Woodward–Hoffmann Rules by Using Changes in Electron Density".

6973:

Ayers, Paul W.; Morell, Christophe; De Proft, Frank; Geerlings, Paul (5 October 2007). "Understanding the Woodward–Hoffmann Rules by Using Changes in Electron Density".

1471:+ 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. 10495: 532: 371:

wavelengths, assuming the absence of other chromophores. Hence, irradiation of the 1,3-butadiene at such a wavelength can result in high conversion to the cyclobutene.

5816:

mechanical stretching along the coordinate of the disrotatory pathway lowered the barrier of the reaction under the disrotatory pathway enough to bias that mechanism.

5413: 5002:

is rendered complicated and ambiguous by the simultaneous but independent interaction of the orthogonal orbitals of the ketene but may involve a interaction as well.

251:

is such that a bonding interaction between the ends must involve overlap between orbital envelopes on opposite faces of the system and this can only be achieved in a

4517:{\displaystyle \sum _{i}n_{i}+p_{i}\equiv \sum _{n_{i}\neq p_{i}}n_{i}+p_{i}=\sum _{n_{i}\neq p_{i}}1=\#\{(n_{i},p_{i},i)\ |\ n_{i}\neq p_{i}\}\ (\mathrm {mod} \ 2)} 5733:

that although the concept of phase and orbitals are replaced simply by the notion of electron density, this function still takes both positive and negative values.

2880:

A pericyclic process involving 4n+2 or 4n electrons is thermally allowed if and only if the number of antarafacial components involved is even or odd, respectively.

5883: 1614:

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

1322:

The molecular orbitals of the product are the symmetric and antisymmetric combinations of the two newly formed σ and σ bonds and the π and π bonds as shown below.

6701:

sense. The rise in energy of the ground state as the 'barely avoided' crossing is approached results in a symmetry-imposed energy barrier at the transition state.

7061:

Farahani, Pooria; Baader, Wilhelm J. (2017-02-16). "Unimolecular Decomposition Mechanism of 1,2-Dioxetanedione: Concerted or Biradical? That is the Question!".

6016:, 75), has been recognized as an alternative approach that is completely equivalent to, but predates, Woodward and Hoffmann's statement of the generalized rule. 5433: 1571:

In -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.

340:'s power, and indeed helped demonstrate that useful chemical results could arise from orbital analysis. The discovery would earn Hoffmann and Fukui the 1981 6768:

component so that no phase inversion takes place within it. One draws in the Dewar-Zimmerman connections between components based on the bond topology (

2378:, respectively. These descriptors can be used to characterize the topology of the bond forming and breaking that takes place in any pericyclic process. 912:. 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 544:

Conversely in the electrocyclic ring-closure of the substituted hexa-1,3,5-triene pictured below, the reaction proceeds through a disrotatory mechanism.

609:

In the language of aromatic transition state theory, the Woodward–Hoffmann rules can be restated as follows: A pericyclic transition state involving (4

6860:

Zimmerman, H. E. (1966). "On Molecular Orbital Correlation Diagrams, Möbius Systems, and Factors Controlling Ground and Excited State Reactions. II".

5137:

For a -alkyl shift, where the reaction can be antarafacial (i.e. invert stereochemistry) with respect to the carbon center, the same rules apply. If

9611: 9556: 6755:

of the separate orbital interactions have to allowed for the reaction to be allowed. The FMO approach probably gives the most intuitive picture here.

1233:

are both doubly populated – i.e. the state (SS)(AS). As such, this state attempts to correlate with the electronic state in the product where both σ

493:

Some thermal and photochemical interconversions of substituted cyclobutenes and butadienes showing conrotatory (blue) and disrotatory (red) behavior.

10324: 6825:

Berson, Jerome A.; Nelson, George L. (1967-10-01). "Inversion of configuration in the migrating group of a thermal 1,3-sigmatropic rearrangement".

5145:− 1 then the reaction is symmetry-allowed if it is either antarafacial with respect to the π-system, or inverts stereochemistry at the carbon. If 789:

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

9666: 5874:

of the compound dihydrocostunolide. Although they describe an electrocyclic reaction, Corey has nothing to offer with respect to explaining the

1326:

product in a symmetry conservative manner this is predicted to not have the great energetic barrier present in the ground state reaction above.

5301: 580:). In contrast, an excited-state pericyclic process takes place if a reactant is promoted to an electronically excited state by activation with 231:

when heated or irradiated. In their original publication, they summarized the experimental evidence and molecular orbital analysis as follows:

9816: 8450: 6601: 737:

are symmetric with respect to the mirror plane as the sign of the p-orbital lobes is preserved under the symmetry transformation. Similarly, Ψ

600:

A pericyclic process involving N electron pairs and A antarafacial components is often favored under photochemical conditions if N + A is even.

359:

The Woodward–Hoffmann rules apply to either direction of a pericyclic process. Due to the inherent ring strain of cyclobutene derivatives, the

5153:+ 1 then the reaction is symmetry-allowed if it is suprafacial with respect to the π-system and retains stereochemistry at the carbon center. 4787:

This formulation for a 2 component reaction is equivalent to the selection rules for a -cycloaddition reactions shown in the following table:

10545: 10319: 8145: 2984:

A ground-state pericyclic process involving N electron pairs and A antarafacial components is symmetry-allowed if and only if N + A is odd.

569:

A ground-state pericyclic process involving N electron pairs and A antarafacial components is symmetry-allowed if and only if N + A is odd.

1454:π-electrons, then it is conrotatory under thermal conditions and disrotatory under photochemical conditions. Conversely in a polyene of 4 9421: 7342: 4951:

The following are some common ground state (i.e. thermal) reaction classes analyzed in light of the generalized Woodward–Hoffmann rules.

435:

direction. On the other hand, the opposite stereochemical course was followed under photochemical activation: When the related compound (

1225:

This is made precise in the state correlation diagram below. The ground state in the starting materials is the electronic state where π

9991: 9191: 7935: 2592:

Using this notation, Woodward and Hoffmann state in their 1969 review the general formulation for all pericyclic reactions as follows:

2432:

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.

1458:+ 2 π-electrons, an electrocyclic ring closure is disrotatory under thermal conditions and conrotatory under photochemical conditions. 1312:

is antisymmetric with respect to the mirror plane. Similarly π is symmetric and π is antisymmetric with respect to the mirror plane.

10156: 10086: 10066: 9561: 8728: 8190: 5298:(DFT). The key to the analysis is the dual descriptor function, proposed by Christophe Morell, André Grand and Alejandro Toro-Labbé 5238:+ 2)-electron reaction is thermally allowed if and only if it has an even number of antarafacial components (i.e., Hückel topology). 1486:

electrocyclic reaction will resemble the diagram for the 4 electron cyclization of 1,3-butadiene, while the correlation diagram any 4

5234:-electron reaction is thermally allowed if and only if it has an odd number of antarafacial components (i.e., Möbius topology); a (4 4986:

A rare but stereochemically unambiguous example of a -cycloaddition is shown on the right. The strain and steric properties of the

3801: 8609: 8165: 6088:

Zimmerman, Howard E. (1971-08-01). "Moebius-Hueckel concept in organic chemistry. Application of organic molecules and reactions".

1377:

The only conserved symmetry element in this reaction is the mirror plane through the center of the molecules as shown to the left.

644:

is a point of reference (usually a plane or a line) about which an object is symmetric with respect to a symmetry operation. If a

6638: 5438: 7378: 2093:

Generalized synchronous double group transfer reaction between a component with p π electrons and a component with q π electrons.

9911: 5811:

This computational prediction was backed up by experiment on the system below. Link-functionalized polymers were conjugated to

10389: 10339: 8743: 9846: 5849:"I felt that this was going to be a really interesting development and was looking forward to some sort of joint undertaking," 5025:

reaction is a -cycloaddition (i.e. suprafacial with respect to both components), as exemplified by the reaction to the right.

3937: 1490:+ 2 electron electrocyclic reaction will resemble the correlation diagram for the 6 electron cyclization of 1,3,5-hexatriene. 10485: 10294: 9951: 9931: 9891: 8698: 7641: 5722:{\displaystyle f^{(2)}(r)={\frac {\partial f(r)}{\partial N}}\cong |\phi _{\text{LUMO}}(r)|^{2}-|\phi _{\text{HOMO}}(r)|^{2}} 801:

axis, is correlated with σ of cyclobutene. The final two correlations are between the antisymmetric (A) molecular orbitals Ψ

6123:

Dewar, M.J.S. (1966-01-01). "A molecular orbital theory of organic chemistry—VIII: romaticity and electrocyclic reactions".

5202:

electrons, the Möbius topology is aromatic and the Hückel topology is antiaromatic, while if the transition state involves 4

2078:

A general double group transfer reaction which is synchronous can be represented as an interaction between a component with

864:) into ground-state orbitals of the product (σ and π). Conversely, the disrotatory mechanism forces the conversion of the Ψ 686:

MOs of butadiene are shown with the element with which they are symmetric. They are antisymmetric with respect to the other.

10480: 10410: 10309: 9966: 9821: 9451: 9296: 8906: 8533: 8310: 1087:

See below "General formulation" for a detailed description of the generalization of WH notation to all pericyclic processes

977:

of 1,3-butadiene correlates with the ground state σπ of cyclobutene as demonstrated in the MO correlation diagram above. Ψ

5941:, who proposed orbital symmetry conservation as an explanation for the stereochemical outcome of electrocyclic reactions ( 5225:

Examples of Dewar-Zimmerman analysis applied to common pericyclic reactions. (The red curves represent phase inversions.)

2470:). For a σ bond, it corresponds to interactions occurring on the two "interior" lobes or two "exterior" lobes of the bond. 576:

A ground-state pericyclic process is brought about by addition of thermal energy (i.e., heating the system, symbolized by

10683: 10560: 10344: 9656: 9146: 8821: 7198: 7008:

Morell, Christophe; Grand, André; Toro-Labbé, Alejandro (1 January 2005). "New Dual Descriptor for Chemical Reactivity".

9366: 455:) was formed exclusively as a result of electrocyclic ring closure. This requires the ends of the π-system to rotate in 10555: 10269: 10131: 9921: 9886: 6611: 690:

Considering the electrocyclic ring closure of the substituted 1,3-butadiene, the reaction can proceed through either a

6444:

Winter, Rudolph Ernst K. (1965-01-01). "The preparation and isomerization of cis- and trans-3,4-dimethylcyclobutene".

2994:

The equivalence of the two formulations can also be seen by a simple parity argument without appeal to case analysis.

10678: 10445: 10384: 9916: 9831: 9801: 9781: 9646: 9641: 9016: 8941: 8584: 8538: 8405: 7666: 6635: 5206:+ 2 electrons, the Hückel topology is aromatic and the Möbius topology is antiaromatic. The parity of the number of 2572: 2481:). For a σ bond, it corresponds to interactions occurring on one "interior" lobe and one "exterior" lobe of the bond. 1346:π which is also SSA=S. As such this ground state reaction is not predicted to have a high symmetry-imposed barrier. 2744:

are coefficients indicating the number of each type of component. This equation implies that one of, but not both,

10550: 10510: 10460: 10136: 9936: 9686: 9616: 8105: 7676: 5740:

Dual-descriptor coloring (red>0, blue<0) of electron density in the Diels-Alder supra/supra transition state.

5101:

Berson's classic (1967) example of a -sigmatropic alkyl shift proceeding with stereochemical inversion (WH symbol )

2477:(symbol: a) when the interactions with the π system or p orbital occur on opposite sides of the nodal plane (think 309: 9751: 8644: 8365: 2489:

Illustration of the assignment of orbital overlap as suprafacial or antarafacial for common pericyclic components.

2466:(symbol: s) when the interactions with the π system or p orbital occur on the same side of the nodal plane (think 507:

In the case of a photochemically driven electrocyclic ring-closure of buta-1,3-diene, electronic promotion causes

10304: 10146: 10016: 10011: 9826: 9301: 9211: 8801: 8733: 8624: 8200: 7955: 7880: 7335: 6790:

Yamabe, Shinichi; Kuwata, Kayoko; Minato, Tsutomu (1999). "Frontier-orbital analyses of ketene cycloadditions".

5795:

Computationally predicted products of 4e electrocyclic ring opening under thermal, photo, and mechanical control.

5188:

The generalized Woodward–Hoffmann rules, first given in 1969, are equivalent to an earlier general approach, the

1045:

The same analysis can be applied to the disrotatory mechanism to create the following state correlation diagram.

10061: 6606:(3rd printing, 1st ed.). Weinheim, BRD: Verlag Chemie GmbH (BRD) and Academic Press (USA). pp. 1–178. 10590: 10475: 10374: 10314: 9961: 9756: 9716: 9691: 9601: 9061: 8095: 8025: 7661: 7591: 6679: 5983: 5175: 633: 9181: 2493:

Using this notation, all pericyclic reactions can be assigned a descriptor, consisting of a series of symbols

352:

The interconversion of model cyclobutene and butadiene derivatives under thermal (heating) and photochemical (

10580: 10166: 10056: 9676: 9401: 9186: 9131: 8976: 8936: 8768: 8523: 8240: 8090: 107: 10540: 10101: 9546: 5210:(described in detail below) in the transition state determines its topology. A Möbius topology involves an 5054:

the σ-bond. Conversely with a disrotatory mechanism it is suprafacial with respect to the breaking σ-bond.

10575: 10490: 10465: 10440: 10425: 10349: 10264: 10161: 10121: 9986: 9941: 9706: 9251: 9236: 9101: 8891: 8559: 8315: 7995: 7970: 7940: 7531: 5837: 2350: 1438: 585: 192: 143: 4185: 10525: 10470: 10415: 10126: 10046: 9946: 9661: 9626: 9471: 9361: 9076: 9071: 8896: 8856: 8753: 8564: 8528: 8380: 8370: 8225: 8085: 7945: 7895: 7890: 7865: 7825: 7536: 7526: 7501: 6573:

Longuet-Higgins, H. C.; Abrahamson, E. W. (1965). "The Electronic Mechanism of Electrocyclic Reactions".

6409:

Srinivasan, R. (1968-07-01). "Mechanism of the photochemical valence tautomerization of 1,3-butadienes".

3581: 3376: 1583:− 1) bonds away across a π-system while the other terminus does not migrate. It is a reaction involving 1416:

at a slightly lower energy. In the middle of the energetic scale are the two remaining MOs that are the π

711:

element with which they are symmetric. They are antisymmetric with respect to the other. For example, Ψ

312:. In the Dewar-Zimmerman approach the orbital overlap topology (Hückel or Möbius) and electron count (4 214: 6193:

Fukui, Kenichi (1965-01-01). "Stereoselectivity associated with noncycloaddition to unsaturated bonds".

10500: 10201: 10006: 9441: 9326: 9006: 8981: 8921: 8778: 8513: 8220: 8000: 7965: 7870: 7561: 7496: 7328: 5190: 617:

electrons with Möbius topology is aromatic and allowed, while a pericyclic transition state involving 4

305: 9791: 8055: 4531: 4049: 10600: 10505: 10359: 10239: 10211: 10181: 10096: 10026: 9981: 9956: 9876: 9776: 9736: 9431: 9051: 9041: 8966: 8490: 8350: 8345: 8325: 8010: 7807: 7786: 7746: 7671: 6336:

Criegee, Rudolf; Noll, Klaus (1959). "Umsetzungen in der Reihe des 1.2.3.4-Tetramethyl-cyclobutans".

5295: 4646: 4581: 4235: 4099: 3437: 3092: 3034: 2838:, similar arguments (omitted here) lead to the conclusion that the number of antarafacial components 2515: 1625:

The -sigmatropic ground state reaction is allowed via either a supra/supra or antara/antara topology.

880:

of the cyclobutene. This would lead to a significantly higher transition state barrier to reaction.

7491: 6323: 3300: 3169: 10565: 10455: 10435: 10299: 10141: 10051: 10021: 10001: 9896: 9851: 9681: 9591: 9521: 9406: 9396: 9226: 8783: 8723: 8688: 8495: 8475: 8435: 8210: 8080: 8045: 8005: 7756: 7596: 7586: 7516: 5274:

and the transition state is Möbius; otherwise, conclude that the pericyclic reaction is forbidden.

4139: 2661:

number of electrons using simple rules of divisibility by a straightforward analysis of two cases.

2508: 1069:

reactions through correlation diagrams. A cycloaddition brings together two components, one with

877: 341: 337: 10031: 6716:

Hoffmann, Roald; Woodward, R. B. (1965). "Selection Rules for Concerted Cycloaddition Reactions".

5538: 5499: 4734: 4690: 1030:. These correlations can not actually take place due to the quantum-mechanical rule known as the 636:

and E. W. Abrahamson showed that the Woodward–Hoffmann rules can best be derived by examining the

10688: 10535: 10394: 10244: 10186: 10111: 10091: 9811: 9761: 9621: 9586: 9526: 9456: 9011: 8758: 8738: 8470: 8390: 8285: 8245: 8215: 8150: 8035: 8020: 7930: 7920: 7581: 7506: 7461: 5762:

There are none! Nor can violations be expected of so fundamental a principle of maximum bonding.

4636: 4009: 3897: 2362:

detail below, in the general formulation of the Woodward–Hoffmann rules, the bond rotation terms

7796: 5870:

In addition, Hoffmann points out that in two publications from 1963 and 1965, Corey described a

5156:

On the right is one of the first examples of a -sigmatropic shift to be discovered, reported by

3764: 3727: 3678: 3640: 3532: 3490: 431:. In both ring opening reactions, the carbons on the ends of the breaking σ-bond rotate in the 19: 10274: 9996: 9746: 9726: 9701: 9651: 9566: 9541: 9496: 9466: 9446: 9416: 9381: 9336: 9311: 9286: 9171: 9096: 8876: 8569: 8505: 8305: 8030: 7950: 7636: 7611: 7388: 7383: 2565: 2558: 2551: 2097:

Then the selection rules are the same as for the generalized cycloaddition reactions. That is

510: 270: 210: 5389: 10610: 10196: 10151: 9866: 9836: 9806: 9741: 9721: 9636: 9631: 9596: 9551: 9536: 9531: 9511: 9501: 9436: 9426: 9356: 9306: 8826: 8629: 8205: 8160: 7990: 7980: 7726: 7651: 7446: 7408: 5934: 2634:)-electron components, respectively. Moreover, this criterion should be interpreted as both 1611: 1428:

products, this reaction is not predicted to have a high electronic symmetry-imposed barrier.

366: 138:

A pericyclic reaction is an organic reaction that proceeds via a single concerted and cyclic

96: 68: 7656: 1442:

preserves stereochemistry, whereas an antarafacial transformation reverses stereochemistry.

1156:. These are both local-symmetry elements in the case that the components are not identical. 10379: 10329: 10279: 10259: 10249: 10106: 10081: 9796: 9786: 9671: 9486: 9481: 9411: 9196: 8996: 8956: 8886: 8851: 8806: 8773: 8639: 8614: 8594: 8415: 8375: 8335: 8300: 8230: 7985: 7855: 7830: 7368: 7213:"A Claim on the Development of the Frontier Orbital Explanation of Electrocyclic Reactions" 7121: 7070: 7017: 6746:

has orthogonal lone pair and antibonding orbitals (the allyl-like antibonding orbital of SO

6237: 5279: 4999: 2530: 1850:

A general -cycloaddition is a concerted addition reaction between two components, one with

592: 360: 5952:, 395) and articulated a fully generalized pericyclic selection rule several years later ( 2886:

Summary of the results of the equivalent Dewar–Zimmerman aromatic transition state theory

1265:

The mirror plane is the only conserved symmetry element of the Diels-Alder -cycloaddition.

698:

reaction mechanism. As shown to the left, in the conrotatory transition state there is a

8: 10585: 10570: 10216: 10191: 10176: 10171: 9901: 9856: 9841: 9731: 9711: 9606: 9491: 9476: 9321: 9266: 9256: 9221: 8986: 8861: 8836: 8748: 8604: 8589: 8574: 8395: 8340: 8110: 7960: 7905: 7776: 7691: 7551: 7476: 6002: 5903: 5230:

results of aromatic transition state theory in the language of Woodward and Hoffmann, a 4

301: 84: 10595: 9246: 8430: 7621: 7125: 7074: 7021: 6241: 5791: 1296:} of molecular orbitals of 1,3-butadiene shown above, along with π and π of ethylene. Ψ 844:

4 electron electrocyclization reaction correlation diagram with a disrotatory mechanism.

816:

4 electron electrocyclization reaction correlation diagram with a conrotatory mechanism.

411:) geometric isomers were not detected in the product mixture. Similarly, thermolysis of 10334: 10284: 10254: 10116: 9906: 9696: 9581: 9516: 9506: 9271: 9201: 9166: 9161: 9141: 9136: 9081: 8991: 8841: 8703: 8693: 8599: 8385: 8330: 8260: 8180: 8075: 7975: 7910: 7835: 7681: 7546: 7481: 7466: 7279:

Corey, E. J.; Hortmann, Alfred G. (1965). "The total synthesis of dihydrocostunolide".

7145: 6910: 6807: 6253: 6031:

Woodward, R. B.; Hoffmann, Roald (1965). "Stereochemistry of Electrocyclic Reactions".

5773: 5418: 5283: 2537: 1607: 1338:, of total symmetry SS A=S. This correlates with the ground state of the cyclohexene σ 707: 699: 645: 103: 99: 6457: 6206: 6136: 848:

Evaluating the two mechanisms, the conrotatory mechanism is predicted to have a lower

10655: 10637: 10071: 9391: 9276: 9241: 9206: 9151: 9106: 9021: 9001: 8951: 8946: 8916: 8901: 8811: 8718: 8654: 8619: 8445: 8320: 8195: 8120: 8100: 8015: 7850: 7845: 7791: 7701: 7606: 7566: 7521: 7403: 7398: 7363: 7296: 7234: 7180: 7137: 7094: 7086: 7043: 6990: 6972: 6955: 6842: 6811: 6675: 6631: 6607: 6461: 6426: 6395: 6306: 6261: 6210: 6175: 6140: 6105: 5964: 5909: 5875: 5856: 5832: 5800: 2410: 1567: 1041:

4 electron electrocyclization state correlation diagram with a conrotatory mechanism.

749:

axis as the rotation inverts the sign of the p-orbital lobes uniformly. Conversely Ψ

581: 225: 221: 142:, the geometry of which allows for the continuous overlap of a cycle of (π and/or σ) 92: 88: 80: 9066: 6914: 6480:

A ground-state pericyclic change is symmetry-allowed when the total number of (4q+2)

6382:(both ends rotating counterclockwise) is therefore also symmetry allowed. That the ( 5819: 2597:

A ground-state pericyclic change is symmetry-allowed when the total number of (4q+2)

2349:

In the generalized Woodward–Hoffmann rules, everything is characterized in terms of

1273:

reaction. The simplest case is the reaction of 1,3-butadiene with ethylene to form

1112:

of view of symmetry but are rare due to an unfavorable strain and steric profile.

1108:

For ordinary alkenes, cycloadditions only observed under photochemical activation.

1052:

4 electron electrocyclization state correlation diagram under disrotatory mechanism.

682: 678:

symmetry, whereas the transition state of a disrotatory opening has mirror symmetry.

10647: 10605: 10450: 10420: 10364: 10289: 10221: 9976: 9926: 9771: 9576: 9351: 9346: 9291: 9281: 9056: 8866: 8846: 8816: 8713: 8649: 8634: 8465: 8420: 8410: 8400: 8295: 8275: 8270: 8255: 8250: 8130: 8125: 8065: 8050: 8040: 7885: 7875: 7741: 7731: 7631: 7626: 7601: 7541: 7393: 7352: 7288: 7261: 7252:

Corey, E. J.; Hortmann, Alfred G. (1963). "Total Synthesis of Dihydrocostunolide".

7224: 7172: 7149: 7129: 7078: 7033: 7025: 6982: 6945: 6937: 6900: 6869: 6834: 6799: 6725: 6582: 6555: 6453: 6418: 6345: 6296: 6288: 6245: 6202: 6167: 6132: 6097: 6070: 6040: 5987: 5157: 2544: 2447:+ 2, if a (formal) lone pair from a heteroatom or carbanion is conjugated thereto). 1380: 1031: 849: 829:

and π correlate. As for the asymmetric molecular orbitals, the lower energy pair Ψ

641: 328: 297: 244: 139: 7721: 6490:

However, the statement given here is mathematically equivalent. For a proof, see:

6478:

The original statement given by Woodward and Hoffmann is somewhat more elaborate:

1621: 1159: 966:, so in this case it is represented as σππ. The symmetry of this state is SAS=A. 10515: 10206: 10041: 10036: 9331: 9316: 9261: 9216: 9176: 9126: 9091: 9086: 9031: 9026: 8961: 8911: 8831: 8659: 8543: 8518: 8480: 8455: 8440: 8425: 8360: 8235: 8185: 8175: 8155: 8115: 7925: 7915: 7900: 7696: 7616: 7486: 7456: 7441: 7436: 6546:

Woodward, R. B.; Hoffmann, Roald (1969). "The Conservation of Orbital Symmetry".

6249: 5871: 5783: 1575:

One of the most prevalent classes of sigmatropic shifts is classified as , where

1474: 236: 76: 2979:

As a mnemonic, the above formulation can be further restated as the following:

1858:π-electrons. This reaction is symmetry allowed under the following conditions: 10520: 10430: 10369: 9461: 9371: 9341: 9116: 8971: 8708: 8485: 8355: 8170: 8140: 7840: 7736: 7511: 7373: 7317:

Understanding the Woodward–Hoffmann Rules by Using Changes in Electron Density

6692:(near the transition state) but then diverge. In contrast to the difference in 5938: 5861: 5776:

to two molecules of carbon dioxide, famous for its role in the luminescence of

5294:

Recently, the Woodward–Hoffmann rules have been reinterpreted using conceptual

2646: 2485: 2399: 2341: 577: 277:

leading to a reversal of terminal symmetry relationships and stereospecificity.

111: 72: 7320: 2428:

of a component is the number of electrons in the orbital(s) of the component:

1353: 10672: 10530: 10231: 10076: 9971: 9766: 9156: 9121: 9111: 9046: 9036: 8926: 8763: 8579: 8290: 8265: 8135: 7781: 7766: 7751: 7646: 7576: 7556: 7471: 7090: 7082: 6846: 6465: 6430: 6349: 6214: 6179: 6144: 6109: 5891: 5289: 1862:

For a supra/supra or antara/antara cycloaddition, it is thermally allowed if

1066: 876:

orbital are transferred to an excited antibonding orbital, creating a doubly

324: 274: 127: 6905: 6888: 2819:, the number of antarafacial components is even when the electron count is 4 2345:

Conrotatory motion is antarafacial, while disrotatory motion is suprafacial.

2325:

thermal conditions. The Woodward-Hoffmann symbol for the ene reaction is (

2089: 1388: 10659: 10651: 9571: 8931: 8683: 8460: 8060: 7860: 7711: 7706: 7571: 7426: 7238: 7229: 7212: 7184: 7141: 7098: 7047: 6994: 6986: 6959: 6559: 6310: 6265: 6171: 6158:

Dewar, Michael J. S. (1971-11-01). "Aromaticity and Pericyclic Reactions".

5894:

reaction involving 6 = 4×1 + 2 electrons is now recognized as conrotatory.

5266:

Conclude that the pericyclic reaction is allowed if the electron count is 4

5180: 3433:

is thermally allowed if and only if the number of symbols with the property

2953:

electrons for aromaticity. To summarize aromatic transition state theory:

2811:, is again even. Thus, regardless of the initial assumption of parity for 2321: 1315: 1082: 893: 853: 670: 201:

suprafacial, respectively, under this more general classification system.)

7300: 6803: 6228:

Fukui, Kenichi (1982). "Role of Frontier Orbitals in Chemical Reactions".

5864:

denied the claim: he quotes Woodward from a lecture given in 1966 saying:

5379:{\displaystyle f^{(2)}(r)={\frac {\partial ^{2}\rho (r)}{\partial N^{2}}}} 5028: 1606:

The other prevalent class of sigmatropic rearrangements are , notably the

1404:). The two highest energy MOs are formed from linear combinations of the σ 559:

The Woodward–Hoffmann rules can be stated succinctly as a single sentence:

497:

The Woodward-Hoffmann rules explain these results through orbital overlap:

8070: 7716: 7686: 7451: 5022: 3001:

The following formulations of the Woodward–Hoffmann rules are equivalent:

2576: 2533:

of sulfur dioxide to 1,3-butadiene (a (4+1)-cheletropic addition) is + .

1274: 1270: 1153: 1078: 872:

orbital into the π orbital. Thus the two electrons in the ground-state Ψ

722: 695: 691: 372: 353: 259: 252: 7292: 7265: 7133: 7038: 6950: 6873: 6838: 6729: 6586: 6422: 6301: 6101: 6074: 6044: 5933:

The principle of orbital symmetry conservation is generally credited to

5032:

The Diels-Alder reaction is suprafacial with respect to both components.

2760:

are both even or both odd, then the sum of the four terms is 0 (mod 4).

1369:

Transfer of a pair of hydrogen atoms from ethane to perdeuterioethylene.

1115: 719:

axis, and antisymmetric with respect to reflection in the mirror plane.

344:. By that time, Woodward had died, and so was ineligible for the prize. 10354: 9881: 9231: 7007: 6491: 6257: 5777: 2657:

Alternatively, the general statement can be formulated in terms of the

2523: 2417: 1145: 764: 547: 7176: 7029: 6941: 6292: 4779:

yields the same conclusion (as it must): the reaction is not allowed.

1629:

The selection rules for an -sigmatropic rearrangement are as follows:

1123: 715:

of 1,3-butadiene is symmetric with respect to 180 rotation about the C

5270:+ 2 and the transition state is Hückel, or if the electron count is 4 4990:

double bond enables this generally kinetically unfavorable process.

2763:

The generalized statement of the Woodward–Hoffmann rules states that

2395: 6889:"Five decades of mechanistic and exploratory organic photochemistry" 625:+ 2)-electrons with Möbius topology is antiaromatic and forbidden. 162:

direction (both clockwise or both counterclockwise), the process is

7761: 7431: 5736: 1365: 1261: 1077:π-electrons. Cycloaddition reactions are further characterized as 883: 500: 320:) results in either an aromatic or antiaromatic transition state. 5221: 5194:

of Zimmerman, which was first stated in 1966 and is also known as

534:

to become the HOMO and the reaction mechanism must be disrotatory.

7421: 6927: 6792:

Theoretical Chemistry Accounts: Theory, Computation, and Modeling

6278: 5787:

Anti-WH product via disrotatory mechanism induced by ring strain.

5252:

hybrid orbitals, or a single phase in the case of an s orbital.

5214:

number of phase inversions whereas a Hückel topology involves an

4970: 3567:

gives the number of antarafacial components, we can also restate

2664:

First, consider the case where the total number of electrons is 4

1214:. Due to conservation of orbital symmetry, the bonding orbital π 537: 228: 2846:

must be odd in the allowed case and even in the forbidden case.

1144:

is the mirror plane between the components perpendicular to the

5757:, entitled "Violations," Woodward and Hoffmann famously stated: 3887:{\textstyle \sum _{i}n_{i}+\sum _{i}p_{i}=\sum _{i}n_{i}+p_{i}} 2568:

of 1,3-cyclooctadien-5-ide anion (a 6π-electrocyclization) is .

706:

of symmetry and in the disrotatory transition state there is a

3528:+ 2)-electron components) is odd or even, respectively, while 5097: 4974:

A thermally-allowed supra-antara -dimerization of a strained

4232:

simply enumerates the number of components with the property

2519: 1888:

For a supra/antara cycloaddition, it is thermally allowed if

1603:+ 2, then supra/supra or antara/antara is thermally allowed. 6672:

Perspectives on Structure and Mechanism in Organic Chemistry

5489:{\displaystyle f(r)={\frac {\partial \rho (r)}{\partial N}}} 4578:

and the number of symbols in a collection with the property

2783:

is odd in this case, the number of antarafacial components,

2543:

The -alkyl migration with inversion at carbon discovered by

2101:

For supra/supra or antara/antara double group transfers, if

5967:

has claimed priority in proposing the key insight in 1965 (

3342: 3265: 963: 959: 930: 926: 761:

axis and antisymmetric with respect to the σ mirror plane.

248: 7111: 5290:

Reinterpretation with conceptual density functional theory

5164: 5118:

1)/2 π-bond plus the σ bond involved in the reaction. If

2803:

even in this case, the number of antarafacial components,

273:

an electron in the HOMO of the reactant is promoted to an

6572: 2652: 2561:

of cyclobutene (a reverse 4π-electrocyclization) is or .

1633:

For supra/supra or antara/antara -sigmatropic shifts, if

1579:

is odd. That means one terminus of the σ-bond migrates (

1065:

The Woodward–Hoffmann rules can also explain bimolecular

169: 3999:{\displaystyle n_{i}+p_{i}\equiv 0\ (\mathrm {mod} \ 2)} 467:: electrocyclic ring opening leads to the formation of ( 220:. Chemists knew that such reactions exhibited striking 2370:

are subsumed by the bond topology (or faciality) terms

4737: 4693: 4534: 4188: 4052: 3804: 3767: 3730: 3681: 3643: 3535: 3493: 1539: 896:

of 1,3-butadiene, as shown above, has 2 electrons in Ψ

304:

proposed an equally general conceptual framework: the

102:. Consequently, any symmetry-violating reaction must 5583: 5541: 5502: 5441: 5421: 5392: 5304: 4649: 4584: 4281: 4238: 4142: 4102: 4012: 3940: 3900: 3584: 3440: 3379: 3150: 3095: 3037: 1218:

is forced to correlate with the antibonding orbital σ

1166:

To determine symmetry and asymmetry with respect to σ

513: 10496:

Erlenmeyer–Plöchl azlactone and amino-acid synthesis

4006:

holds; hence, omission of symbols with the property

2834:

In the case where the total number of electrons is 4

2458:

of a component can be suprafacial and antarafacial:

3362:We have a mathematically equivalent restatement of 2989: 674:

The transition state of a conrotatory closure has C

91:. The rules originate in certain symmetries of the 6789: 6160:Angewandte Chemie International Edition in English 5721: 5566: 5527: 5488: 5427: 5407: 5378: 5282:of the number of inversions (number of inversions 4766: 4722: 4675: 4610: 4570: 4516: 4264: 4224: 4174: 4128: 4088: 4038: 3998: 3926: 3886: 3790: 3753: 3704: 3666: 3636:is thermally allowed if and only if exactly one of 3628: 3558: 3516: 3466: 3423: 3351: 3133: 3067: 1152:splits the molecules in half perpendicular to the 526: 459:directions to form the new σ-bond. Thermolysis of 9557:Divinylcyclopropane-cycloheptadiene rearrangement 2435:The electron count of a conjugated π system with 1595:, then supra/antara is thermally allowed, and if 985:correlates with σ. Thus the orbitals making up Ψ 805:and σ, and the symmetric (S) molecular orbitals Ψ 332:disfavorable and considered symmetry-forbidden. 114:on its occurrence, and such reactions are called 75:to rationalize or predict certain aspects of the 10670: 6886: 6859: 6715: 6599: 6545: 6060: 6030: 5386:, the second derivative of the electron density 5065: 4046:from a collection will not change the parity of 1085:(a) with respect to each of the π components. ( 7350: 2554:of 1,3-butadiene (a 4π-electrocyclization) is . 1482:Additionally, the correlation diagram for any 4 16:Set of rules pertaining to pericyclic reactions 9817:Thermal rearrangement of aromatic hydrocarbons 8451:Thermal rearrangement of aromatic hydrocarbons 7060: 5184:Hypothetical Huckel versus Mobius aromaticity. 3089:the electron count and topology parity symbol 797:, which is symmetric (S) with respect to the C 10546:Lectka enantioselective beta-lactam synthesis 7806: 7336: 7278: 7251: 6541: 6539: 6537: 6535: 6533: 6531: 6529: 6527: 6525: 6523: 6521: 6519: 5081: 2381: 2073: 584:(i.e., irradiating the system, symbolized by 133: 10325:Inverse electron-demand Diels–Alder reaction 8146:Heterogeneous metal catalyzed cross-coupling 6824: 6711: 6709: 6707: 6517: 6515: 6513: 6511: 6509: 6507: 6505: 6503: 6501: 6499: 5818: 5040: 4485: 4413: 3623: 3585: 3418: 3380: 2771:is odd if the reaction is allowed. Now, if 2128:For supra/antara double group transfers, if 1845: 1560:− 1) atoms away from its original position. 1445: 1387: 1384:Conserved mirror plane in transfer reaction. 1352: 1314: 1158: 1036: 839: 811: 763: 721: 546: 536: 499: 488: 168: 9667:Lobry de Bruyn–Van Ekenstein transformation 6666: 6335: 6026: 6024: 6022: 5169: 2156:This is summarized in the following table: 1916:This is summarized in the following table: 1688:This is summarized in the following table: 1493:This is summarized in the following table: 1360: 1119:The cycloaddition retains stereochemistry. 289:+ 2 components and number of antarafacial 4 7343: 7329: 7163:Corey, E. J. (2004). "Impossible Dreams". 6921: 6664: 6662: 6660: 6658: 6656: 6654: 6652: 6650: 6648: 6646: 6408: 6272: 4618:have the same parity. Since formulations 1408:antibonds – highest is the antisymmetric σ 1060: 665: 463:follows the same stereochemical course as 356:irradiation) conditions is illustrative. 10157:Petrenko-Kritschenko piperidone synthesis 9612:Fritsch–Buttenberg–Wiechell rearrangement 7228: 7037: 6949: 6904: 6704: 6600:Woodward, R. B.; Hoffmann, Roald (1971). 6496: 6300: 6087: 5126:− 1 then it must be antarafacial, and if 1660:For supra/antara -sigmatropic shifts, if 852:because it transforms the electrons from 282: 10320:Intramolecular Diels–Alder cycloaddition 7281:Journal of the American Chemical Society 7254:Journal of the American Chemical Society 7210: 6827:Journal of the American Chemical Society 6575:Journal of the American Chemical Society 6566: 6411:Journal of the American Chemical Society 6063:Journal of the American Chemical Society 6033:Journal of the American Chemical Society 6019: 5799:Similarly, a recent paper describes how 5790: 5782: 5735: 5415:with respect to the number of electrons 5220: 5179: 5096: 5027: 4969: 2484: 2340: 2088: 1620: 1566: 1473: 1379: 1364: 1260: 1127:Symmetry elements of the cycloaddition. 1122: 1114: 887:First excited state (ES-1) of butadiene. 882: 681: 669: 613:+ 2) electrons with Hückel topology or 4 347: 18: 7217:Angewandte Chemie International Edition 6643: 5808:-WH product is predicted to be formed. 5535:, the region is electrophilic, and for 5165:Equivalence of other theoretical models 1400:), followed by the antisymmetric sum (σ 1269:A cycloaddition is exemplified by the 785:is asymmetric (A) with respect to the C 745:are antisymmetric with respect to the C 628: 383:) afforded only one geometric isomer, ( 130:, and each step conforms to the rules. 10671: 10340:Metal-centered cycloaddition reactions 9992:Debus–Radziszewski imidazole synthesis 7936:Bodroux–Chichibabin aldehyde synthesis 6443: 6317: 5242:Procedure for Dewar-Zimmerman analysis 2653:Derivation of an alternative statement 2332: 1645:+ 2 they are thermally allowed and if 833:and π form a correlation pair, as do Ψ 566:Generalized pericyclic selection rule. 10486:Diazoalkane 1,3-dipolar cycloaddition 10390:Vinylcyclopropane (5+2) cycloaddition 10295:Diazoalkane 1,3-dipolar cycloaddition 10067:Hurd–Mori 1,2,3-thiadiazole synthesis 9562:Dowd–Beckwith ring-expansion reaction 8729:Hurd–Mori 1,2,3-thiadiazole synthesis 7805: 7642:LFER solvent coefficients (data page) 7324: 7162: 6763: 6761: 6227: 6192: 6157: 6122: 4940:If the total number of electrons is 4 4225:{\textstyle \sum _{n_{i}\neq p_{i}}1} 2587: 1222:. Thus a high barrier is predicted. 868:orbital into the σ orbital, and the Ψ 651:molecular orbital correlation diagram 621:-electrons with Hückel topology or (4 87:, an important class of reactions in 9297:Sharpless asymmetric dihydroxylation 8534:Methoxymethylenetriphenylphosphorane 7197:Johnson, Carolyn Y. (March 1, 2005) 7105: 6603:The Conservation of Orbital Symmetry 6492:https://archive.org/details/whdz_red 6056: 6054: 5854:In a 2004 rebuttal published in the 5755:The Conservation of Orbital Symmetry 4683:, so the reaction is not allowed by 2450:The electron count of a σ bond is 2. 2113:+ 2 it is thermally allowed, and if 1684:+ 2 they are photochemically allowed 655:electronic state correlation diagram 415:-1,2,3,4-tetramethyl-1-cyclobutene ( 379:-1,2,3,4-tetramethyl-1-cyclobutene ( 10631: 9422:Allen–Millar–Trippett rearrangement 7063:The Journal of Physical Chemistry A 7010:The Journal of Physical Chemistry A 6966: 6626:P. R. Bunker and P. Jensen (2005), 3629:{\displaystyle \{(n_{i},p_{i},i)\}} 3479:Since the total electron count is 4 3424:{\displaystyle \{(n_{i},p_{i},i)\}} 2522:and an olefin in the first step of 1874:+ 2 and photochemically allowed if 1672:they are thermally allowed, and if 1540:Sigmatropic rearrangement reactions 916:is asymmetric with respect to the C 757:are symmetric with respect to the C 235:In an open-chain system containing 190:, and each component is said to be 13: 10561:Nitrone-olefin (3+2) cycloaddition 10556:Niementowski quinazoline synthesis 10345:Nitrone-olefin (3+2) cycloaddition 10270:Azide-alkyne Huisgen cycloaddition 10132:Niementowski quinazoline synthesis 9887:Azide-alkyne Huisgen cycloaddition 9192:Meerwein–Ponndorf–Verley reduction 8744:Leimgruber–Batcho indole synthesis 6758: 6628:Fundamentals of Molecular Symmetry 5632: 5615: 5477: 5460: 5360: 5337: 4501: 4498: 4495: 4410: 3983: 3980: 3977: 3277: 3274: 3271: 3249: 3246: 3243: 3202: 3199: 3196: 2974:-electron Möbius transition states 1431: 1245: 1092: 1047: 515: 14: 10700: 10385:Trimethylenemethane cycloaddition 10087:Johnson–Corey–Chaykovsky reaction 9952:Cadogan–Sundberg indole synthesis 9932:Bohlmann–Rahtz pyridine synthesis 9892:Baeyer–Emmerling indole synthesis 8699:Cadogan–Sundberg indole synthesis 8191:Johnson–Corey–Chaykovsky reaction 6338:Justus Liebigs Annalen der Chemie 6324:The Nobel Prize in Chemistry 1981 6051: 5005: 4954: 4571:{\textstyle \sum _{i}n_{i}+p_{i}} 4089:{\textstyle \sum _{i}n_{i}+p_{i}} 3141:according to the following rules: 2630:+ 2)-electron and antarafacial (4 2152:+ 2 it is photochemically allowed 2082:π electrons and a component with 249:highest occupied molecule orbital 10481:Cook–Heilbron thiazole synthesis 10310:Hexadehydro Diels–Alder reaction 10137:Niementowski quinoline synthesis 9967:Cook–Heilbron thiazole synthesis 9912:Bischler–Möhlau indole synthesis 9822:Tiffeneau–Demjanov rearrangement 9452:Baker–Venkataraman rearrangement 8610:Horner–Wadsworth–Emmons reaction 8281:Mizoroki-Heck vs. Reductive Heck 8166:Horner–Wadsworth–Emmons reaction 7677:Neighbouring group participation 7165:The Journal of Organic Chemistry 5984:aromatic transition state theory 5882: 5196:aromatic transition state theory 5086:-sigmatropic rearrangement": --> 2990:Alternative proof of equivalence 2775:is even, then this implies that 2140:it is thermally allowed, and if 1657:they are photochemically allowed 1073:π-electrons, and the other with 310:aromatic transition state theory 67:) are a set of rules devised by 10017:Fiesselmann thiophene synthesis 9847:Westphalen–Lettré rearrangement 9827:Vinylcyclopropane rearrangement 9657:Kornblum–DeLaMare rearrangement 9302:Epoxidation of allylic alcohols 9212:Noyori asymmetric hydrogenation 9147:Kornblum–DeLaMare rearrangement 8822:Gallagher–Hollander degradation 7272: 7245: 7204: 7191: 7156: 7054: 7001: 6880: 6853: 6818: 6783: 6736: 6685: 6620: 6593: 6472: 6437: 6402: 6356: 6329: 5969:see 'Controversy' section below 5244:(examples shown on the right): 4676:{\displaystyle n_{i}\neq p_{i}} 4611:{\displaystyle n_{i}\neq p_{i}} 4265:{\displaystyle n_{i}\neq p_{i}} 4129:{\displaystyle n_{i}\neq p_{i}} 3724:are equivalent. Exactly one of 3467:{\displaystyle n_{i}\neq p_{i}} 3281: 3269: 3134:{\displaystyle (n_{i},p_{i},i)} 3068:{\displaystyle i=1,2,\ldots ,k} 3031:-component pericyclic reaction 2540:(a -sigmatropic shift) is or . 1900:and photochemically allowed if 296:In the intervening four years, 10476:Chichibabin pyridine synthesis 9962:Chichibabin pyridine synthesis 9922:Blum–Ittah aziridine synthesis 9757:Ring expansion and contraction 8026:Cross dehydrogenative coupling 6378:) isomer from ring opening of 6221: 6186: 6151: 6116: 6081: 5927: 5906:for calculating UV absorptions 5826: 5709: 5704: 5698: 5684: 5670: 5665: 5659: 5645: 5627: 5621: 5606: 5600: 5595: 5589: 5553: 5547: 5514: 5508: 5472: 5466: 5451: 5445: 5402: 5396: 5355: 5349: 5327: 5321: 5316: 5310: 4511: 4491: 4455: 4448: 4416: 3993: 3973: 3620: 3588: 3415: 3383: 3259: 3239: 3212: 3192: 3128: 3096: 3079:with Woodward-Hoffmann symbol 2642:(not explicitly stated above, 2406:(unfilled or filled, symbol ω) 1006:correlates with σ, the state Ψ 933:, and thus is represented as Ψ 391:)-3,4-dimethyl-2,4-hexadiene ( 1: 10640:Chemistry: A European Journal 10446:Bischler–Napieralski reaction 10404:Heterocycle forming reactions 10057:Hemetsberger indole synthesis 9917:Bischler–Napieralski reaction 9832:Wagner–Meerwein rearrangement 9802:Sommelet–Hauser rearrangement 9782:Seyferth–Gilbert homologation 9647:Ireland–Claisen rearrangement 9642:Hofmann–Martius rearrangement 9402:2,3-sigmatropic rearrangement 9017:Corey–Winter olefin synthesis 8942:Barton–McCombie deoxygenation 8585:Corey–Winter olefin synthesis 8539:Seyferth–Gilbert homologation 8406:Seyferth–Gilbert homologation 6975:Chemistry: A European Journal 6930:Accounts of Chemical Research 6458:10.1016/S0040-4039(01)83997-6 6281:Accounts of Chemical Research 6207:10.1016/S0040-4039(00)90203-X 6137:10.1016/S0040-4020(01)82171-2 6090:Accounts of Chemical Research 5920: 5748: 4767:{\textstyle \sum _{i}p_{i}=2} 4723:{\textstyle \sum _{i}n_{i}=2} 4175:{\displaystyle n_{i}+p_{i}=1} 2125:it is photochemically allowed 1412:, preceded by the symmetric σ 451:-3,4-dimethyl-1-cyclobutene ( 10551:Lehmstedt–Tanasescu reaction 10511:Gabriel–Colman rearrangement 10466:Bucherer carbazole synthesis 10461:Borsche–Drechsel cyclization 10441:Bernthsen acridine synthesis 10426:Bamberger triazine synthesis 10411:Algar–Flynn–Oyamada reaction 10122:Nazarov cyclization reaction 9987:De Kimpe aziridine synthesis 9942:Bucherer carbazole synthesis 9937:Borsche–Drechsel cyclization 9707:Nazarov cyclization reaction 9687:Meyer–Schuster rearrangement 9617:Gabriel–Colman rearrangement 9367:Wolffenstein–Böters reaction 9252:Reduction of nitro compounds 9102:Grundmann aldehyde synthesis 8907:Algar–Flynn–Oyamada reaction 8316:Olefin conversion technology 8311:Nozaki–Hiyama–Kishi reaction 8106:Gabriel–Colman rearrangement 7996:Claisen-Schmidt condensation 7941:Bouveault aldehyde synthesis 6674:, Brooks/Cole, pp. 710–794, 6250:10.1126/science.218.4574.747 5838:Journal of Organic Chemistry 5567:{\displaystyle f^{(2)}<0} 5528:{\displaystyle f^{(2)}>0} 5021:The synchronous 6π-electron 2526:(a (3+2)-cycloaddition) is . 2511:(a (4+2)-cycloaddition) is . 2353:bond topologies. The terms 2351:antarafacial and suprafacial 1439:antarafacial and suprafacial 856:orbitals of the reactants (Ψ 93:molecule's orbital structure 7: 10526:Hantzsch pyridine synthesis 10305:Enone–alkene cycloadditions 10127:Nenitzescu indole synthesis 10047:Hantzsch pyridine synthesis 10012:Ferrario–Ackermann reaction 9662:Kowalski ester homologation 9627:Halogen dance rearrangement 9472:Benzilic acid rearrangement 8897:Akabori amino-acid reaction 8857:Von Braun amide degradation 8802:Barbier–Wieland degradation 8754:Nenitzescu indole synthesis 8734:Kharasch–Sosnovsky reaction 8625:Julia–Kocienski olefination 8529:Kowalski ester homologation 8226:Kowalski ester homologation 8201:Julia–Kocienski olefination 7956:Cadiot–Chodkiewicz coupling 7881:Aza-Baylis–Hillman reaction 7826:Acetoacetic ester synthesis 7537:Dynamic binding (chemistry) 7527:Conrotatory and disrotatory 7502:Charge remote fragmentation 5954:Angew. Chem. Int. Ed. Engl. 5897: 5218:number of phase inversions. 5057:By the above rules, for a 4 4782: 4096:. On the other hand, when 4039:{\displaystyle n_{i}=p_{i}} 3927:{\displaystyle n_{i}=p_{i}} 3791:{\textstyle \sum _{i}p_{i}} 3754:{\textstyle \sum _{i}n_{i}} 3705:{\textstyle \sum _{i}p_{i}} 3667:{\textstyle \sum _{i}n_{i}} 3559:{\textstyle \sum _{i}p_{i}} 3517:{\textstyle \sum _{i}n_{i}} 2579:(a -sigmatropic shift) is . 2547:(a -sigmatropic shift) is . 904:, so it is represented as Ψ 258:In open systems containing 10: 10705: 10684:Physical organic chemistry 10591:Robinson–Gabriel synthesis 10541:Kröhnke pyridine synthesis 10375:Retro-Diels–Alder reaction 10315:Imine Diels–Alder reaction 10102:Kröhnke pyridine synthesis 9717:Newman–Kwart rearrangement 9692:Mislow–Evans rearrangement 9602:Fischer–Hepp rearrangement 9547:Di-π-methane rearrangement 9327:Stephen aldehyde synthesis 9062:Eschweiler–Clarke reaction 8779:Williamson ether synthesis 8096:Fujiwara–Moritani reaction 8001:Combes quinoline synthesis 7966:Carbonyl olefin metathesis 7667:More O'Ferrall–Jencks plot 7592:Grunwald–Winstein equation 7562:Electron-withdrawing group 7497:Catalytic resonance theory 6696:correlation diagrams, the 5173: 5082:-sigmatropic rearrangement 5070:+ 2 electrocyclic reaction 3027:Index the components of a 2638:(stated above) as well as 2566:electrocyclic ring closing 2559:electrocyclic ring opening 2552:electrocyclic ring closing 2382:Woodward-Hoffmann notation 1854:π-electrons, and one with 204: 134:Background and terminology 65:pericyclic selection rules 10601:Urech hydantoin synthesis 10581:Pomeranz–Fritsch reaction 10506:Fischer oxazole synthesis 10403: 10240:1,3-Dipolar cycloaddition 10230: 10212:Urech hydantoin synthesis 10182:Reissert indole synthesis 10167:Pomeranz–Fritsch reaction 10097:Knorr quinoline synthesis 10027:Fischer oxazole synthesis 9957:Camps quinoline synthesis 9877:1,3-Dipolar cycloaddition 9865: 9777:Semipinacol rearrangement 9752:Ramberg–Bäcklund reaction 9737:Piancatelli rearrangement 9677:McFadyen–Stevens reaction 9432:Alpha-ketol rearrangement 9380: 9187:McFadyen–Stevens reaction 9132:Kiliani–Fischer synthesis 9052:Elbs persulfate oxidation 8977:Bouveault–Blanc reduction 8937:Baeyer–Villiger oxidation 8875: 8792: 8769:Schotten–Baumann reaction 8672: 8645:Ramberg–Bäcklund reaction 8552: 8524:Kiliani–Fischer synthesis 8504: 8366:Ramberg–Bäcklund reaction 8351:Pinacol coupling reaction 8346:Piancatelli rearrangement 8241:Liebeskind–Srogl coupling 8091:Fujimoto–Belleau reaction 7814: 7808:List of organic reactions 7672:Negative hyperconjugation 7417: 7359: 6887:Zimmerman, H. E. (2006). 6370:). The formation of the ( 5296:density functional theory 3716:It suffices to show that 2858:and the electron count (4 2791:, is even. Likewise, if 2516:1,3-dipolar cycloaddition 527:{\displaystyle \Psi _{3}} 10679:Eponymous chemical rules 10576:Pictet–Spengler reaction 10491:Einhorn–Brunner reaction 10456:Boger pyridine synthesis 10350:Oxo-Diels–Alder reaction 10265:Aza-Diels–Alder reaction 10162:Pictet–Spengler reaction 10062:Hofmann–Löffler reaction 10052:Hegedus indole synthesis 10022:Fischer indole synthesis 9897:Bartoli indole synthesis 9852:Willgerodt rearrangement 9682:McLafferty rearrangement 9592:Ferrier carbocyclization 9407:2,3-Wittig rearrangement 9397:1,2-Wittig rearrangement 9237:Parikh–Doering oxidation 9227:Oxygen rebound mechanism 8892:Adkins–Peterson reaction 8784:Yamaguchi esterification 8724:Hegedus indole synthesis 8689:Bartoli indole synthesis 8560:Bamford–Stevens reaction 8476:Weinreb ketone synthesis 8436:Stork enamine alkylation 8211:Knoevenagel condensation 8081:Ferrier carbocyclization 7971:Castro–Stephens coupling 7597:Hammett acidity function 7587:Free-energy relationship 7532:Curtin–Hammett principle 7517:Conformational isomerism 7211:Hoffmann, Roald (2004). 7083:10.1021/acs.jpca.6b10365 6350:10.1002/jlac.19596270102 5915: 5831:It has been stated that 5408:{\displaystyle \rho (r)} 5170:Dewar–Zimmerman analysis 4801:Photochemically allowed 3578:A collection of symbols 3373:A collection of symbols 2866:) implies the parity of 2174:Photochemically allowed 2074:Group transfer reactions 1934:Photochemically allowed 1706:Photochemically allowed 1504:Photochemically allowed 1361:Group transfer reactions 1002:correlates with σ, and Ψ 878:excited electronic state 640:of a given reaction. A 447:) was exposed to light, 342:Nobel Prize in Chemistry 338:molecular orbital theory 281:In 1969, they would use 10536:Knorr pyrrole synthesis 10471:Bucherer–Bergs reaction 10416:Allan–Robinson reaction 10395:Wagner-Jauregg reaction 10187:Ring-closing metathesis 10112:Larock indole synthesis 10092:Knorr pyrrole synthesis 9947:Bucherer–Bergs reaction 9812:Stieglitz rearrangement 9792:Skattebøl rearrangement 9762:Ring-closing metathesis 9622:Group transfer reaction 9587:Favorskii rearrangement 9527:Cornforth rearrangement 9457:Bamberger rearrangement 9362:Wolff–Kishner reduction 9182:Markó–Lam deoxygenation 9077:Fleming–Tamao oxidation 9072:Fischer–Tropsch process 8759:Oxymercuration reaction 8739:Knorr pyrrole synthesis 8565:Barton–Kellogg reaction 8471:Wagner-Jauregg reaction 8391:Ring-closing metathesis 8381:Reimer–Tiemann reaction 8371:Rauhut–Currier reaction 8286:Nef isocyanide reaction 8246:Malonic ester synthesis 8216:Knorr pyrrole synthesis 8151:High dilution principle 8086:Friedel–Crafts reaction 8021:Cross-coupling reaction 7946:Bucherer–Bergs reaction 7931:Blanc chloromethylation 7921:Blaise ketone synthesis 7896:Baylis–Hillman reaction 7891:Barton–Kellogg reaction 7866:Allan–Robinson reaction 7772:Woodward–Hoffmann rules 7507:Charge-transfer complex 6906:10.1351/pac200678122193 4626:are equivalent, so are 2626:refer to suprafacial (4 1846:Cycloaddition reactions 1446:Electrocyclic reactions 1061:Cycloaddition reactions 981:correlates with π and Ψ 666:Electrocyclic reactions 554: 293:components is odd. . 211:electrocyclic reactions 118:. Their opposites are 61:Woodward–Hoffmann rules 10652:10.1002/chem.200700365 10501:Feist–Benary synthesis 10275:Bradsher cycloaddition 10245:4+4 Photocycloaddition 10202:Simmons–Smith reaction 10147:Paternò–Büchi reaction 10007:Feist–Benary synthesis 9997:Dieckmann condensation 9747:Pummerer rearrangement 9727:Oxy-Cope rearrangement 9702:Myers allene synthesis 9652:Jacobsen rearrangement 9567:Electrocyclic reaction 9542:Demjanov rearrangement 9497:Buchner ring expansion 9467:Beckmann rearrangement 9447:Aza-Cope rearrangement 9442:Arndt–Eistert reaction 9417:Alkyne zipper reaction 9337:Transfer hydrogenation 9312:Sharpless oxyamination 9287:Selenoxide elimination 9172:Lombardo methylenation 9097:Griesbaum coozonolysis 9007:Corey–Itsuno reduction 8982:Boyland–Sims oxidation 8922:Angeli–Rimini reaction 8570:Boord olefin synthesis 8514:Arndt–Eistert reaction 8506:Homologation reactions 8306:Nitro-Mannich reaction 8221:Kolbe–Schmitt reaction 8031:Cross-coupling partner 7951:Buchner ring expansion 7871:Arndt–Eistert reaction 7637:Kinetic isotope effect 7384:Rearrangement reaction 7230:10.1002/anie.200461440 6987:10.1002/chem.200700365 6670:Carroll, Felix (1998) 6560:10.1002/anie.196907811 6172:10.1002/anie.197107611 5823: 5796: 5788: 5765: 5741: 5723: 5568: 5529: 5490: 5429: 5409: 5380: 5257:electrocyclization.) 5226: 5185: 5102: 5045:Electrocyclic Reaction 5033: 4979: 4768: 4724: 4677: 4612: 4572: 4526: 4518: 4266: 4226: 4176: 4130: 4090: 4040: 4000: 3928: 3888: 3798:is odd if and only if 3792: 3755: 3706: 3668: 3630: 3560: 3518: 3468: 3425: 3360: 3353: 3135: 3069: 2987: 2883: 2608: 2490: 2346: 2094: 2086:π electrons as shown. 1626: 1572: 1479: 1392: 1385: 1370: 1357: 1319: 1266: 1163: 1128: 1120: 1053: 1042: 888: 845: 817: 768: 726: 687: 679: 603: 574: 572: 551: 541: 528: 504: 494: 271:photochemical reaction 173: 56: 10360:Pauson–Khand reaction 10197:Sharpless epoxidation 10152:Pechmann condensation 10032:Friedländer synthesis 9982:Davis–Beirut reaction 9837:Wallach rearrangement 9807:Stevens rearrangement 9742:Pinacol rearrangement 9722:Overman rearrangement 9637:Hofmann rearrangement 9632:Hayashi rearrangement 9597:Ferrier rearrangement 9552:Dimroth rearrangement 9537:Curtius rearrangement 9532:Criegee rearrangement 9512:Claisen rearrangement 9502:Carroll rearrangement 9437:Amadori rearrangement 9427:Allylic rearrangement 9307:Sharpless epoxidation 9042:Dess–Martin oxidation 8967:Bohn–Schmidt reaction 8827:Hofmann rearrangement 8630:Kauffmann olefination 8553:Olefination reactions 8491:Wurtz–Fittig reaction 8326:Palladium–NHC complex 8206:Kauffmann olefination 8161:Homologation reaction 8011:Corey–House synthesis 7991:Claisen rearrangement 7787:Yukawa–Tsuno equation 7747:Swain–Lupton equation 7727:Spherical aromaticity 7662:Möbius–Hückel concept 7447:Aromatic ring current 7409:Substitution reaction 6804:10.1007/s002140050484 5982:, 146). In addition, 5935:Robert Burns Woodward 5822: 5794: 5786: 5759: 5739: 5724: 5569: 5530: 5491: 5430: 5410: 5381: 5224: 5191:Möbius-Hückel concept 5183: 5176:Möbius–Hückel concept 5100: 5031: 4973: 4769: 4725: 4678: 4613: 4573: 4519: 4274: 4267: 4227: 4177: 4131: 4091: 4041: 4001: 3929: 3889: 3793: 3756: 3707: 3669: 3631: 3561: 3519: 3469: 3426: 3354: 3143: 3136: 3075:and assign component 3070: 3024:Proof of equivalence: 2981: 2958:reactions proceed via 2877: 2823:+ 2. Contrariwise,, 2594: 2573:Wagner-Meerwein shift 2488: 2344: 2092: 1624: 1570: 1552:. Thus it migrates ( 1477: 1391: 1383: 1368: 1356: 1318: 1264: 1162: 1126: 1118: 1051: 1040: 1032:avoided crossing rule 886: 843: 815: 767: 725: 685: 673: 653:one can construct an 597: 563: 561: 550: 540: 529: 503: 492: 367:photostationary state 348:Illustrative examples 306:Möbius-Hückel concept 172: 97:molecular Hamiltonian 69:Robert Burns Woodward 23:Thermolysis converts 22: 10566:Paal–Knorr synthesis 10436:Barton–Zard reaction 10380:Staudinger synthesis 10330:Ketene cycloaddition 10300:Diels–Alder reaction 10280:Cheletropic reaction 10260:Alkyne trimerisation 10142:Paal–Knorr synthesis 10107:Kulinkovich reaction 10082:Jacobsen epoxidation 10002:Diels–Alder reaction 9797:Smiles rearrangement 9787:Sigmatropic reaction 9672:Lossen rearrangement 9522:Corey–Fuchs reaction 9487:Boekelheide reaction 9482:Bergmann degradation 9412:Achmatowicz reaction 9197:Methionine sulfoxide 8997:Clemmensen reduction 8957:Bergmann degradation 8887:Acyloin condensation 8852:Strecker degradation 8807:Bergmann degradation 8774:Ullmann condensation 8640:Peterson olefination 8615:Hydrazone iodination 8595:Elimination reaction 8496:Zincke–Suhl reaction 8416:Sonogashira coupling 8376:Reformatsky reaction 8336:Peterson olefination 8301:Nierenstein reaction 8231:Kulinkovich reaction 8046:Diels–Alder reaction 8006:Corey–Fuchs reaction 7986:Claisen condensation 7856:Alkyne trimerisation 7831:Acyloin condensation 7797:Σ-bishomoaromaticity 7757:Thorpe–Ingold effect 7369:Elimination reaction 6548:Angew. Chem. Int. Ed 5581: 5539: 5500: 5439: 5419: 5390: 5302: 5000:ketene cycloaddition 4735: 4691: 4647: 4582: 4532: 4279: 4236: 4186: 4140: 4100: 4050: 4010: 3938: 3898: 3802: 3765: 3728: 3679: 3641: 3582: 3533: 3491: 3438: 3377: 3148: 3093: 3035: 2531:cheletropic addition 2509:Diels-Alder reaction 2473:The relationship is 2462:The relationship is 1250:cycloadditions": --> 1097:Cycloadditions": --> 998:correlates with π, Ψ 900:and 2 electrons in Ψ 629:Correlation diagrams 593:intersystem crossing 511: 283:correlation diagrams 215:synthesize vitamin B 85:pericyclic reactions 10586:Prilezhaev reaction 10571:Pellizzari reaction 10250:(4+3) cycloaddition 10217:Van Leusen reaction 10192:Robinson annulation 10177:Pschorr cyclization 10172:Prilezhaev reaction 9902:Bergman cyclization 9857:Wolff rearrangement 9842:Weerman degradation 9732:Pericyclic reaction 9712:Neber rearrangement 9607:Fries rearrangement 9492:Brook rearrangement 9477:Bergman cyclization 9322:Staudinger reaction 9267:Rosenmund reduction 9257:Reductive amination 9222:Oppenauer oxidation 9012:Corey–Kim oxidation 8987:Cannizzaro reaction 8862:Weerman degradation 8837:Isosaccharinic acid 8749:Mukaiyama hydration 8605:Hofmann elimination 8590:Dehydrohalogenation 8575:Chugaev elimination 8396:Robinson annulation 8341:Pfitzinger reaction 8111:Gattermann reaction 8056:Wulff–Dötz reaction 8036:Dakin–West reaction 7961:Carbonyl allylation 7906:Bergman cyclization 7692:Kennedy J. P. Orton 7612:Hammond's postulate 7582:Flippin–Lodge angle 7552:Electromeric effect 7477:Beta-silicon effect 7462:Baker–Nathan effect 7293:10.1021/ja00952a037 7266:10.1021/ja00907a030 7134:10.1038/nature05681 7126:2007Natur.446..423H 7075:2017JPCA..121.1189F 7022:2005JPCA..109..205M 6874:10.1021/ja00959a053 6839:10.1021/ja00997a065 6730:10.1021/ja01087a034 6587:10.1021/ja01087a033 6446:Tetrahedron Letters 6423:10.1021/ja01018a080 6242:1982Sci...218..747F 6195:Tetrahedron Letters 6102:10.1021/ar50044a002 6075:10.1021/ja00959a052 6045:10.1021/ja01080a054 5774:dioxetane-1,2-dione 5114:+ 1) as there are ( 5010:Cycloaddition": --> 4959:Cycloaddition": --> 2966:-electron Hückel or 2887: 2411:conjugated π system 2333:General formulation 1308:is symmetric, and Ψ 1304:is antisymmetric, Ψ 793:axis. Similarly, Ψ 638:correlation diagram 302:Michael J. S. Dewar 35:) geometric isomer 10335:McCormack reaction 10285:Conia-ene reaction 10117:Madelung synthesis 9907:Biginelli reaction 9697:Mumm rearrangement 9582:Favorskii reaction 9517:Cope rearrangement 9507:Chan rearrangement 9272:Rubottom oxidation 9202:Miyaura borylation 9167:Lipid peroxidation 9162:Lindgren oxidation 9142:Kornblum oxidation 9137:Kolbe electrolysis 9082:Fukuyama reduction 8992:Carbonyl reduction 8842:Marker degradation 8704:Diazonium compound 8694:Boudouard reaction 8673:Carbon-heteroatom 8600:Grieco elimination 8386:Rieche formylation 8331:Passerini reaction 8261:Meerwein arylation 8181:Hydroxymethylation 8076:Favorskii reaction 7976:Chan rearrangement 7911:Biginelli reaction 7836:Aldol condensation 7682:2-Norbornyl cation 7657:Möbius aromaticity 7652:Markovnikov's rule 7547:Effective molarity 7492:Bürgi–Dunitz angle 7482:Bicycloaromaticity 7199:Whose idea was it? 6488:components is odd. 5878:of the synthesis. 5824: 5797: 5789: 5742: 5719: 5564: 5525: 5486: 5425: 5405: 5376: 5227: 5186: 5103: 5034: 4980: 4775:are both even, so 4764: 4747: 4720: 4703: 4673: 4608: 4568: 4544: 4514: 4403: 4347: 4291: 4262: 4222: 4218: 4172: 4126: 4086: 4062: 4036: 3996: 3924: 3884: 3860: 3837: 3814: 3788: 3777: 3751: 3740: 3702: 3691: 3664: 3653: 3626: 3556: 3545: 3514: 3503: 3464: 3421: 3349: 3341: 3264: 3131: 3065: 2955:Thermal pericyclic 2885: 2605:components is odd. 2588:Original statement 2538:Cope rearrangement 2491: 2347: 2095: 1627: 1573: 1480: 1393: 1386: 1371: 1358: 1320: 1267: 1164: 1129: 1121: 1054: 1043: 969:The ground state Ψ 889: 846: 818: 769: 727: 688: 680: 552: 542: 524: 505: 495: 174: 116:symmetry-forbidden 110:; this imposes an 57: 10646:(29): 8240–8247. 10627: 10626: 10623: 10622: 10619: 10618: 10611:Wohl–Aue reaction 10255:6+4 Cycloaddition 10072:Iodolactonization 9392:1,2-rearrangement 9357:Wohl–Aue reaction 9277:Sabatier reaction 9242:Pinnick oxidation 9207:Mozingo reduction 9152:Leuckart reaction 9107:Haloform reaction 9022:Criegee oxidation 9002:Collins oxidation 8952:Benkeser reaction 8947:Bechamp reduction 8917:Andrussow process 8902:Alcohol oxidation 8812:Edman degradation 8719:Haloform reaction 8668: 8667: 8655:Takai olefination 8620:Julia olefination 8446:Takai olefination 8321:Olefin metathesis 8196:Julia olefination 8121:Grignard reaction 8101:Fukuyama coupling 8016:Coupling reaction 7981:Chan–Lam coupling 7851:Alkyne metathesis 7846:Alkane metathesis 7702:Phosphaethynolate 7607:George S. Hammond 7567:Electronic effect 7522:Conjugated system 7404:Stereospecificity 7399:Stereoselectivity 7364:Addition reaction 7353:organic reactions 7177:10.1021/jo049925d 7030:10.1021/jp046577a 6981:(29): 8240–8247. 6942:10.1021/ar200192t 6899:(12): 2193–2203. 6833:(21): 5503–5504. 6452:(17): 1207–1212. 6417:(16): 4498–4499. 6396:torquoselectivity 6326:. Nobelprize.org. 6293:10.1021/ar200192t 6236:(4574): 747–754. 6201:(28): 2427–2432. 5992:J. Am. Chem. Soc. 5973:Tetrahedron Lett. 5963:, 781). However, 5943:J. Am. Chem. Soc. 5910:Torquoselectivity 5876:stereospecificity 5857:Angewandte Chemie 5833:Elias James Corey 5801:mechanical stress 5753:In Chapter 12 of 5695: 5656: 5639: 5484: 5428:{\displaystyle N} 5374: 5286:2) is unchanged. 4938: 4937: 4798:Thermally allowed 4738: 4694: 4535: 4507: 4490: 4461: 4453: 4374: 4318: 4282: 4189: 4053: 3989: 3972: 3851: 3828: 3805: 3768: 3731: 3682: 3644: 3536: 3524:(the number of (4 3494: 3337: 3317: 3255: 3238: 3208: 3191: 2938: 2937: 2439:double bonds is 2 2311: 2310: 2171:Thermally allowed 2071: 2070: 1931:Thermally allowed 1843: 1842: 1703:Thermally allowed 1537: 1536: 1501:Thermally allowed 1210:correlates with σ 1202:correlates with σ 1194:correlates with σ 1186:correlates with σ 582:ultraviolet light 475:)-2,4-hexadiene ( 443:)-2,4-hexadiene ( 419:) afforded only ( 329:frontier orbitals 222:stereospecificity 89:organic chemistry 81:activation energy 10696: 10664: 10663: 10635: 10606:Wenker synthesis 10596:Stollé synthesis 10451:Bobbitt reaction 10421:Auwers synthesis 10365:Povarov reaction 10290:Cyclopropanation 10228: 10227: 10222:Wenker synthesis 9977:Darzens reaction 9927:Bobbitt reaction 9772:Schmidt reaction 9577:Enyne metathesis 9352:Whiting reaction 9347:Wharton reaction 9292:Shapiro reaction 9282:Sarett oxidation 9247:Prévost reaction 9057:Emde degradation 8867:Wohl degradation 8847:Ruff degradation 8817:Emde degradation 8714:Grignard reagent 8650:Shapiro reaction 8635:McMurry reaction 8502: 8501: 8466:Ullmann reaction 8431:Stollé synthesis 8421:Stetter reaction 8411:Shapiro reaction 8401:Sakurai reaction 8296:Negishi coupling 8276:Minisci reaction 8271:Michael reaction 8256:McMurry reaction 8251:Mannich reaction 8131:Hammick reaction 8126:Grignard reagent 8066:Enyne metathesis 8051:Doebner reaction 8041:Darzens reaction 7886:Barbier reaction 7876:Auwers synthesis 7803: 7802: 7777:Woodward's rules 7742:Superaromaticity 7732:Spiroaromaticity 7632:Inductive effect 7627:Hyperconjugation 7602:Hammett equation 7542:Edwards equation 7394:Regioselectivity 7345: 7338: 7331: 7322: 7321: 7312:Journal Articles 7305: 7304: 7276: 7270: 7269: 7249: 7243: 7242: 7232: 7208: 7202: 7195: 7189: 7188: 7160: 7154: 7153: 7109: 7103: 7102: 7069:(6): 1189–1194. 7058: 7052: 7051: 7041: 7005: 6999: 6998: 6970: 6964: 6963: 6953: 6925: 6919: 6918: 6908: 6884: 6878: 6877: 6862:J. Am. Chem. Soc 6857: 6851: 6850: 6822: 6816: 6815: 6798:(1–6): 139–146. 6787: 6781: 6765: 6756: 6740: 6734: 6733: 6718:J. Am. Chem. Soc 6713: 6702: 6689: 6683: 6668: 6641: 6640:see Section 10.4 6624: 6618: 6617: 6597: 6591: 6590: 6570: 6564: 6563: 6543: 6494: 6476: 6470: 6469: 6441: 6435: 6434: 6406: 6400: 6360: 6354: 6353: 6333: 6327: 6321: 6315: 6314: 6304: 6276: 6270: 6269: 6225: 6219: 6218: 6190: 6184: 6183: 6155: 6149: 6148: 6120: 6114: 6113: 6085: 6079: 6078: 6069:(7): 1564–1565. 6058: 6049: 6048: 6028: 6017: 5931: 5904:Woodward's rules 5886: 5728: 5726: 5725: 5720: 5718: 5717: 5712: 5697: 5696: 5693: 5687: 5679: 5678: 5673: 5658: 5657: 5654: 5648: 5640: 5638: 5630: 5613: 5599: 5598: 5573: 5571: 5570: 5565: 5557: 5556: 5534: 5532: 5531: 5526: 5518: 5517: 5495: 5493: 5492: 5487: 5485: 5483: 5475: 5458: 5434: 5432: 5431: 5426: 5414: 5412: 5411: 5406: 5385: 5383: 5382: 5377: 5375: 5373: 5372: 5371: 5358: 5345: 5344: 5334: 5320: 5319: 5208:phase inversions 5094: 5093: 5089: 5018: 5017: 5013: 4967: 4966: 4962: 4790: 4789: 4773: 4771: 4770: 4765: 4757: 4756: 4746: 4729: 4727: 4726: 4721: 4713: 4712: 4702: 4682: 4680: 4679: 4674: 4672: 4671: 4659: 4658: 4617: 4615: 4614: 4609: 4607: 4606: 4594: 4593: 4577: 4575: 4574: 4569: 4567: 4566: 4554: 4553: 4543: 4523: 4521: 4520: 4515: 4505: 4504: 4488: 4484: 4483: 4471: 4470: 4459: 4458: 4451: 4441: 4440: 4428: 4427: 4402: 4401: 4400: 4388: 4387: 4370: 4369: 4357: 4356: 4346: 4345: 4344: 4332: 4331: 4314: 4313: 4301: 4300: 4290: 4271: 4269: 4268: 4263: 4261: 4260: 4248: 4247: 4231: 4229: 4228: 4223: 4217: 4216: 4215: 4203: 4202: 4181: 4179: 4178: 4173: 4165: 4164: 4152: 4151: 4135: 4133: 4132: 4127: 4125: 4124: 4112: 4111: 4095: 4093: 4092: 4087: 4085: 4084: 4072: 4071: 4061: 4045: 4043: 4042: 4037: 4035: 4034: 4022: 4021: 4005: 4003: 4002: 3997: 3987: 3986: 3970: 3963: 3962: 3950: 3949: 3933: 3931: 3930: 3925: 3923: 3922: 3910: 3909: 3893: 3891: 3890: 3885: 3883: 3882: 3870: 3869: 3859: 3847: 3846: 3836: 3824: 3823: 3813: 3797: 3795: 3794: 3789: 3787: 3786: 3776: 3760: 3758: 3757: 3752: 3750: 3749: 3739: 3711: 3709: 3708: 3703: 3701: 3700: 3690: 3673: 3671: 3670: 3665: 3663: 3662: 3652: 3635: 3633: 3632: 3627: 3613: 3612: 3600: 3599: 3565: 3563: 3562: 3557: 3555: 3554: 3544: 3523: 3521: 3520: 3515: 3513: 3512: 3502: 3473: 3471: 3470: 3465: 3463: 3462: 3450: 3449: 3430: 3428: 3427: 3422: 3408: 3407: 3395: 3394: 3358: 3356: 3355: 3350: 3345: 3344: 3338: 3335: 3318: 3315: 3291: 3290: 3280: 3268: 3267: 3253: 3252: 3236: 3206: 3205: 3189: 3160: 3159: 3140: 3138: 3137: 3132: 3121: 3120: 3108: 3107: 3074: 3072: 3071: 3066: 2888: 2884: 2799:is even. Since 2564:The disrotatory 2557:The conrotatory 2550:The conrotatory 2159: 2158: 1919: 1918: 1691: 1690: 1496: 1495: 1258: 1257: 1253: 1105: 1104: 1100: 642:symmetry element 533: 531: 530: 525: 523: 522: 298:Howard Zimmerman 264:+ 2) π electrons 245:orbital symmetry 179:orbital topology 140:transition state 120:symmetry-allowed 10704: 10703: 10699: 10698: 10697: 10695: 10694: 10693: 10669: 10668: 10667: 10636: 10632: 10628: 10615: 10516:Gewald reaction 10399: 10226: 10207:Skraup reaction 10042:Graham reaction 10037:Gewald reaction 9868: 9861: 9383: 9376: 9332:Swern oxidation 9317:Stahl oxidation 9262:Riley oxidation 9217:Omega oxidation 9177:Luche reduction 9127:Jones oxidation 9092:Glycol cleavage 9087:Ganem oxidation 9032:Davis oxidation 9027:Dakin oxidation 8962:Birch reduction 8912:Amide reduction 8878: 8871: 8832:Hooker reaction 8794: 8788: 8676: 8674: 8664: 8660:Wittig reaction 8548: 8544:Wittig reaction 8519:Hooker reaction 8500: 8481:Wittig reaction 8456:Thorpe reaction 8441:Suzuki reaction 8426:Stille reaction 8361:Quelet reaction 8236:Kumada coupling 8186:Ivanov reaction 8176:Hydrovinylation 8156:Hiyama coupling 8116:Glaser coupling 7926:Blaise reaction 7916:Bingel reaction 7901:Benary reaction 7818: 7816: 7810: 7801: 7697:Passive binding 7617:Homoaromaticity 7467:Baldwin's rules 7442:Antiaromaticity 7437:Anomeric effect 7413: 7355: 7349: 7309: 7308: 7287:(24): 5736–42. 7277: 7273: 7250: 7246: 7223:(48): 6586–90. 7209: 7205: 7196: 7192: 7161: 7157: 7120:(7134): 423–7. 7110: 7106: 7059: 7055: 7006: 7002: 6971: 6967: 6926: 6922: 6893:Pure Appl. Chem 6885: 6881: 6868:(7): 1566–156. 6858: 6854: 6823: 6819: 6788: 6784: 6766: 6759: 6749: 6745: 6741: 6737: 6714: 6705: 6690: 6686: 6669: 6644: 6625: 6621: 6614: 6598: 6594: 6571: 6567: 6554:(11): 781–853. 6544: 6497: 6487: 6483: 6477: 6473: 6442: 6438: 6407: 6403: 6361: 6357: 6334: 6330: 6322: 6318: 6277: 6273: 6226: 6222: 6191: 6187: 6166:(11): 761–776. 6156: 6152: 6121: 6117: 6086: 6082: 6059: 6052: 6029: 6020: 5988:H. E. Zimmerman 5932: 5928: 5923: 5918: 5900: 5872:total synthesis 5829: 5751: 5713: 5708: 5707: 5692: 5688: 5683: 5674: 5669: 5668: 5653: 5649: 5644: 5631: 5614: 5612: 5588: 5584: 5582: 5579: 5578: 5546: 5542: 5540: 5537: 5536: 5507: 5503: 5501: 5498: 5497: 5476: 5459: 5457: 5440: 5437: 5436: 5420: 5417: 5416: 5391: 5388: 5387: 5367: 5363: 5359: 5340: 5336: 5335: 5333: 5309: 5305: 5303: 5300: 5299: 5292: 5178: 5172: 5167: 5095: 5091: 5087: 5085: 5084: 5072: 5047: 5019: 5015: 5011: 5009: 5008: 4968: 4964: 4960: 4958: 4957: 4934: 4927: 4920: 4913: 4905: 4898: 4891: 4884: 4867: 4860: 4853: 4846: 4838: 4831: 4824: 4817: 4785: 4752: 4748: 4742: 4736: 4733: 4732: 4708: 4704: 4698: 4692: 4689: 4688: 4667: 4663: 4654: 4650: 4648: 4645: 4644: 4639: 4634:, as claimed. 4602: 4598: 4589: 4585: 4583: 4580: 4579: 4562: 4558: 4549: 4545: 4539: 4533: 4530: 4529: 4494: 4479: 4475: 4466: 4462: 4454: 4436: 4432: 4423: 4419: 4396: 4392: 4383: 4379: 4378: 4365: 4361: 4352: 4348: 4340: 4336: 4327: 4323: 4322: 4309: 4305: 4296: 4292: 4286: 4280: 4277: 4276: 4256: 4252: 4243: 4239: 4237: 4234: 4233: 4211: 4207: 4198: 4194: 4193: 4187: 4184: 4183: 4160: 4156: 4147: 4143: 4141: 4138: 4137: 4120: 4116: 4107: 4103: 4101: 4098: 4097: 4080: 4076: 4067: 4063: 4057: 4051: 4048: 4047: 4030: 4026: 4017: 4013: 4011: 4008: 4007: 3976: 3958: 3954: 3945: 3941: 3939: 3936: 3935: 3918: 3914: 3905: 3901: 3899: 3896: 3895: 3878: 3874: 3865: 3861: 3855: 3842: 3838: 3832: 3819: 3815: 3809: 3803: 3800: 3799: 3782: 3778: 3772: 3766: 3763: 3762: 3745: 3741: 3735: 3729: 3726: 3725: 3696: 3692: 3686: 3680: 3677: 3676: 3658: 3654: 3648: 3642: 3639: 3638: 3608: 3604: 3595: 3591: 3583: 3580: 3579: 3550: 3546: 3540: 3534: 3531: 3530: 3508: 3504: 3498: 3492: 3489: 3488: 3487:precisely when 3458: 3454: 3445: 3441: 3439: 3436: 3435: 3403: 3399: 3390: 3386: 3378: 3375: 3374: 3340: 3339: 3336: is antara 3334: 3329: 3320: 3319: 3314: 3309: 3296: 3295: 3286: 3282: 3270: 3263: 3262: 3242: 3225: 3216: 3215: 3195: 3178: 3165: 3164: 3155: 3151: 3149: 3146: 3145: 3116: 3112: 3103: 3099: 3094: 3091: 3090: 3088: 3082: 3036: 3033: 3032: 2992: 2933: 2928: 2914: 2909: 2779:is odd. Since 2752:is odd, for if 2723: 2711: 2699: 2687: 2655: 2625: 2617: 2604: 2600: 2590: 2502: 2496: 2384: 2335: 2307: 2300: 2293: 2286: 2278: 2271: 2264: 2257: 2240: 2233: 2226: 2219: 2211: 2204: 2197: 2190: 2076: 2067: 2060: 2053: 2046: 2038: 2031: 2024: 2017: 2000: 1993: 1986: 1979: 1971: 1964: 1957: 1950: 1848: 1839: 1832: 1825: 1818: 1810: 1803: 1796: 1789: 1772: 1765: 1758: 1751: 1743: 1736: 1729: 1722: 1617: 1542: 1448: 1434: 1432:Selection rules 1423: 1419: 1415: 1411: 1407: 1403: 1399: 1363: 1345: 1341: 1337: 1333: 1311: 1307: 1303: 1300:is symmetric, Ψ 1299: 1295: 1291: 1287: 1283: 1259: 1255: 1251: 1249: 1248: 1240: 1236: 1232: 1228: 1221: 1217: 1213: 1209: 1206:, and finally π 1205: 1201: 1197: 1193: 1189: 1185: 1181: 1177: 1173: 1169: 1151: 1143: 1139: 1135: 1106: 1102: 1098: 1096: 1095: 1063: 1029: 1025: 1021: 1017: 1013: 1009: 1005: 1001: 997: 992: 988: 984: 980: 976: 972: 956: 952: 948: 944: 940: 936: 923: 919: 915: 911: 907: 903: 899: 875: 871: 867: 863: 859: 836: 832: 828: 824: 808: 804: 800: 796: 792: 788: 784: 775: 760: 756: 752: 748: 744: 740: 736: 732: 718: 714: 703: 677: 668: 634:Longuet-Higgins 631: 573: 557: 518: 514: 512: 509: 508: 350: 218: 207: 136: 108:the environment 106:extensively to 77:stereochemistry 17: 12: 11: 5: 10702: 10692: 10691: 10689:Cycloadditions 10686: 10681: 10666: 10665: 10629: 10625: 10624: 10621: 10620: 10617: 10616: 10614: 10613: 10608: 10603: 10598: 10593: 10588: 10583: 10578: 10573: 10568: 10563: 10558: 10553: 10548: 10543: 10538: 10533: 10528: 10523: 10521:Hantzsch ester 10518: 10513: 10508: 10503: 10498: 10493: 10488: 10483: 10478: 10473: 10468: 10463: 10458: 10453: 10448: 10443: 10438: 10433: 10431:Banert cascade 10428: 10423: 10418: 10413: 10407: 10405: 10401: 10400: 10398: 10397: 10392: 10387: 10382: 10377: 10372: 10370:Prato reaction 10367: 10362: 10357: 10352: 10347: 10342: 10337: 10332: 10327: 10322: 10317: 10312: 10307: 10302: 10297: 10292: 10287: 10282: 10277: 10272: 10267: 10262: 10257: 10252: 10247: 10242: 10236: 10234: 10225: 10224: 10219: 10214: 10209: 10204: 10199: 10194: 10189: 10184: 10179: 10174: 10169: 10164: 10159: 10154: 10149: 10144: 10139: 10134: 10129: 10124: 10119: 10114: 10109: 10104: 10099: 10094: 10089: 10084: 10079: 10074: 10069: 10064: 10059: 10054: 10049: 10044: 10039: 10034: 10029: 10024: 10019: 10014: 10009: 10004: 9999: 9994: 9989: 9984: 9979: 9974: 9969: 9964: 9959: 9954: 9949: 9944: 9939: 9934: 9929: 9924: 9919: 9914: 9909: 9904: 9899: 9894: 9889: 9884: 9879: 9873: 9871: 9863: 9862: 9860: 9859: 9854: 9849: 9844: 9839: 9834: 9829: 9824: 9819: 9814: 9809: 9804: 9799: 9794: 9789: 9784: 9779: 9774: 9769: 9764: 9759: 9754: 9749: 9744: 9739: 9734: 9729: 9724: 9719: 9714: 9709: 9704: 9699: 9694: 9689: 9684: 9679: 9674: 9669: 9664: 9659: 9654: 9649: 9644: 9639: 9634: 9629: 9624: 9619: 9614: 9609: 9604: 9599: 9594: 9589: 9584: 9579: 9574: 9569: 9564: 9559: 9554: 9549: 9544: 9539: 9534: 9529: 9524: 9519: 9514: 9509: 9504: 9499: 9494: 9489: 9484: 9479: 9474: 9469: 9464: 9462:Banert cascade 9459: 9454: 9449: 9444: 9439: 9434: 9429: 9424: 9419: 9414: 9409: 9404: 9399: 9394: 9388: 9386: 9382:Rearrangement 9378: 9377: 9375: 9374: 9372:Zinin reaction 9369: 9364: 9359: 9354: 9349: 9344: 9342:Wacker process 9339: 9334: 9329: 9324: 9319: 9314: 9309: 9304: 9299: 9294: 9289: 9284: 9279: 9274: 9269: 9264: 9259: 9254: 9249: 9244: 9239: 9234: 9229: 9224: 9219: 9214: 9209: 9204: 9199: 9194: 9189: 9184: 9179: 9174: 9169: 9164: 9159: 9154: 9149: 9144: 9139: 9134: 9129: 9124: 9119: 9117:Hydrogenolysis 9114: 9109: 9104: 9099: 9094: 9089: 9084: 9079: 9074: 9069: 9067:Étard reaction 9064: 9059: 9054: 9049: 9044: 9039: 9034: 9029: 9024: 9019: 9014: 9009: 9004: 8999: 8994: 8989: 8984: 8979: 8974: 8972:Bosch reaction 8969: 8964: 8959: 8954: 8949: 8944: 8939: 8934: 8929: 8924: 8919: 8914: 8909: 8904: 8899: 8894: 8889: 8883: 8881: 8877:Organic redox 8873: 8872: 8870: 8869: 8864: 8859: 8854: 8849: 8844: 8839: 8834: 8829: 8824: 8819: 8814: 8809: 8804: 8798: 8796: 8790: 8789: 8787: 8786: 8781: 8776: 8771: 8766: 8761: 8756: 8751: 8746: 8741: 8736: 8731: 8726: 8721: 8716: 8711: 8709:Esterification 8706: 8701: 8696: 8691: 8686: 8680: 8678: 8670: 8669: 8666: 8665: 8663: 8662: 8657: 8652: 8647: 8642: 8637: 8632: 8627: 8622: 8617: 8612: 8607: 8602: 8597: 8592: 8587: 8582: 8577: 8572: 8567: 8562: 8556: 8554: 8550: 8549: 8547: 8546: 8541: 8536: 8531: 8526: 8521: 8516: 8510: 8508: 8499: 8498: 8493: 8488: 8486:Wurtz reaction 8483: 8478: 8473: 8468: 8463: 8458: 8453: 8448: 8443: 8438: 8433: 8428: 8423: 8418: 8413: 8408: 8403: 8398: 8393: 8388: 8383: 8378: 8373: 8368: 8363: 8358: 8356:Prins reaction 8353: 8348: 8343: 8338: 8333: 8328: 8323: 8318: 8313: 8308: 8303: 8298: 8293: 8288: 8283: 8278: 8273: 8268: 8263: 8258: 8253: 8248: 8243: 8238: 8233: 8228: 8223: 8218: 8213: 8208: 8203: 8198: 8193: 8188: 8183: 8178: 8173: 8171:Hydrocyanation 8168: 8163: 8158: 8153: 8148: 8143: 8141:Henry reaction 8138: 8133: 8128: 8123: 8118: 8113: 8108: 8103: 8098: 8093: 8088: 8083: 8078: 8073: 8068: 8063: 8058: 8053: 8048: 8043: 8038: 8033: 8028: 8023: 8018: 8013: 8008: 8003: 7998: 7993: 7988: 7983: 7978: 7973: 7968: 7963: 7958: 7953: 7948: 7943: 7938: 7933: 7928: 7923: 7918: 7913: 7908: 7903: 7898: 7893: 7888: 7883: 7878: 7873: 7868: 7863: 7858: 7853: 7848: 7843: 7841:Aldol reaction 7838: 7833: 7828: 7822: 7820: 7815:Carbon-carbon 7812: 7811: 7800: 7799: 7794: 7792:Zaitsev's rule 7789: 7784: 7779: 7774: 7769: 7764: 7759: 7754: 7749: 7744: 7739: 7737:Steric effects 7734: 7729: 7724: 7719: 7714: 7709: 7704: 7699: 7694: 7689: 7684: 7679: 7674: 7669: 7664: 7659: 7654: 7649: 7644: 7639: 7634: 7629: 7624: 7619: 7614: 7609: 7604: 7599: 7594: 7589: 7584: 7579: 7574: 7569: 7564: 7559: 7554: 7549: 7544: 7539: 7534: 7529: 7524: 7519: 7514: 7509: 7504: 7499: 7494: 7489: 7484: 7479: 7474: 7469: 7464: 7459: 7454: 7449: 7444: 7439: 7434: 7429: 7424: 7418: 7415: 7414: 7412: 7411: 7406: 7401: 7396: 7391: 7389:Redox reaction 7386: 7381: 7376: 7374:Polymerization 7371: 7366: 7360: 7357: 7356: 7348: 7347: 7340: 7333: 7325: 7319: 7318: 7314: 7313: 7307: 7306: 7271: 7244: 7203: 7201:. Boston Globe 7190: 7155: 7104: 7053: 7016:(1): 205–212. 7000: 6965: 6920: 6879: 6852: 6817: 6782: 6757: 6747: 6743: 6735: 6703: 6684: 6642: 6619: 6613:978-1483256153 6612: 6592: 6565: 6495: 6485: 6481: 6471: 6436: 6401: 6355: 6328: 6316: 6271: 6220: 6185: 6150: 6115: 6096:(8): 272–280. 6080: 6050: 6018: 6003:M. J. S. Dewar 5986:, advanced by 5939:Roald Hoffmann 5925: 5924: 5922: 5919: 5917: 5914: 5913: 5912: 5907: 5899: 5896: 5888: 5887: 5862:Roald Hoffmann 5828: 5825: 5750: 5747: 5730: 5729: 5716: 5711: 5706: 5703: 5700: 5691: 5686: 5682: 5677: 5672: 5667: 5664: 5661: 5652: 5647: 5643: 5637: 5634: 5629: 5626: 5623: 5620: 5617: 5611: 5608: 5605: 5602: 5597: 5594: 5591: 5587: 5563: 5560: 5555: 5552: 5549: 5545: 5524: 5521: 5516: 5513: 5510: 5506: 5482: 5479: 5474: 5471: 5468: 5465: 5462: 5456: 5453: 5450: 5447: 5444: 5424: 5404: 5401: 5398: 5395: 5370: 5366: 5362: 5357: 5354: 5351: 5348: 5343: 5339: 5332: 5329: 5326: 5323: 5318: 5315: 5312: 5308: 5291: 5288: 5174:Main article: 5171: 5168: 5166: 5163: 5083: 5080: 5071: 5064: 5046: 5039: 5007: 5004: 4956: 4953: 4936: 4935: 4932: 4925: 4918: 4911: 4906: 4903: 4896: 4889: 4882: 4877: 4869: 4868: 4865: 4858: 4851: 4844: 4839: 4836: 4829: 4822: 4815: 4810: 4803: 4802: 4799: 4796: 4784: 4781: 4763: 4760: 4755: 4751: 4745: 4741: 4719: 4716: 4711: 4707: 4701: 4697: 4670: 4666: 4662: 4657: 4653: 4635: 4605: 4601: 4597: 4592: 4588: 4565: 4561: 4557: 4552: 4548: 4542: 4538: 4513: 4510: 4503: 4500: 4497: 4493: 4487: 4482: 4478: 4474: 4469: 4465: 4457: 4450: 4447: 4444: 4439: 4435: 4431: 4426: 4422: 4418: 4415: 4412: 4409: 4406: 4399: 4395: 4391: 4386: 4382: 4377: 4373: 4368: 4364: 4360: 4355: 4351: 4343: 4339: 4335: 4330: 4326: 4321: 4317: 4312: 4308: 4304: 4299: 4295: 4289: 4285: 4272:. Therefore, 4259: 4255: 4251: 4246: 4242: 4221: 4214: 4210: 4206: 4201: 4197: 4192: 4171: 4168: 4163: 4159: 4155: 4150: 4146: 4123: 4119: 4115: 4110: 4106: 4083: 4079: 4075: 4070: 4066: 4060: 4056: 4033: 4029: 4025: 4020: 4016: 3995: 3992: 3985: 3982: 3979: 3975: 3969: 3966: 3961: 3957: 3953: 3948: 3944: 3921: 3917: 3913: 3908: 3904: 3881: 3877: 3873: 3868: 3864: 3858: 3854: 3850: 3845: 3841: 3835: 3831: 3827: 3822: 3818: 3812: 3808: 3785: 3781: 3775: 3771: 3748: 3744: 3738: 3734: 3699: 3695: 3689: 3685: 3661: 3657: 3651: 3647: 3625: 3622: 3619: 3616: 3611: 3607: 3603: 3598: 3594: 3590: 3587: 3553: 3549: 3543: 3539: 3511: 3507: 3501: 3497: 3461: 3457: 3453: 3448: 3444: 3420: 3417: 3414: 3411: 3406: 3402: 3398: 3393: 3389: 3385: 3382: 3348: 3343: 3333: 3330: 3328: 3325: 3322: 3321: 3316: is supra 3313: 3310: 3308: 3305: 3302: 3301: 3299: 3294: 3289: 3285: 3279: 3276: 3273: 3266: 3261: 3258: 3251: 3248: 3245: 3241: 3235: 3232: 3229: 3226: 3224: 3221: 3218: 3217: 3214: 3211: 3204: 3201: 3198: 3194: 3188: 3185: 3182: 3179: 3177: 3174: 3171: 3170: 3168: 3163: 3158: 3154: 3130: 3127: 3124: 3119: 3115: 3111: 3106: 3102: 3098: 3086: 3080: 3064: 3061: 3058: 3055: 3052: 3049: 3046: 3043: 3040: 2991: 2988: 2936: 2935: 2930: 2929:anti-aromatic 2925: 2917: 2916: 2915:anti-aromatic 2911: 2906: 2898: 2897: 2894: 2891: 2726: 2725: 2721: 2709: 2697: 2685: 2654: 2651: 2647:if and only if 2623: 2615: 2602: 2598: 2589: 2586: 2581: 2580: 2569: 2562: 2555: 2548: 2541: 2534: 2527: 2512: 2500: 2494: 2483: 2482: 2471: 2452: 2451: 2448: 2433: 2426:electron count 2422: 2421: 2414: 2407: 2383: 2380: 2334: 2331: 2309: 2308: 2305: 2298: 2291: 2284: 2279: 2276: 2269: 2262: 2255: 2250: 2242: 2241: 2238: 2231: 2224: 2217: 2212: 2209: 2202: 2195: 2188: 2183: 2176: 2175: 2172: 2169: 2154: 2153: 2126: 2075: 2072: 2069: 2068: 2065: 2058: 2051: 2044: 2039: 2036: 2029: 2022: 2015: 2010: 2002: 2001: 1998: 1991: 1984: 1977: 1972: 1969: 1962: 1955: 1948: 1943: 1936: 1935: 1932: 1929: 1914: 1913: 1886: 1847: 1844: 1841: 1840: 1837: 1830: 1823: 1816: 1811: 1808: 1801: 1794: 1787: 1782: 1774: 1773: 1770: 1763: 1756: 1749: 1744: 1741: 1734: 1727: 1720: 1715: 1708: 1707: 1704: 1701: 1686: 1685: 1658: 1615: 1541: 1538: 1535: 1534: 1531: 1528: 1520: 1519: 1516: 1513: 1506: 1505: 1502: 1499: 1447: 1444: 1433: 1430: 1421: 1417: 1413: 1409: 1405: 1401: 1397: 1362: 1359: 1343: 1339: 1335: 1331: 1309: 1305: 1301: 1297: 1293: 1289: 1285: 1281: 1247: 1246:cycloadditions 1244: 1238: 1234: 1230: 1226: 1219: 1215: 1211: 1207: 1203: 1199: 1195: 1191: 1187: 1183: 1179: 1175: 1171: 1167: 1149: 1141: 1137: 1133: 1094: 1093:Cycloadditions 1091: 1062: 1059: 1027: 1023: 1019: 1015: 1011: 1007: 1003: 999: 995: 990: 986: 982: 978: 974: 970: 954: 950: 946: 942: 938: 934: 921: 917: 913: 909: 905: 901: 897: 873: 869: 865: 861: 857: 834: 830: 826: 822: 806: 802: 798: 794: 790: 786: 782: 773: 758: 754: 750: 746: 742: 738: 734: 730: 716: 712: 708:σ mirror plane 701: 675: 667: 664: 630: 627: 562: 556: 553: 521: 517: 349: 346: 279: 278: 267: 256: 216: 206: 203: 135: 132: 112:energy barrier 73:Roald Hoffmann 15: 9: 6: 4: 3: 2: 10701: 10690: 10687: 10685: 10682: 10680: 10677: 10676: 10674: 10661: 10657: 10653: 10649: 10645: 10641: 10634: 10630: 10612: 10609: 10607: 10604: 10602: 10599: 10597: 10594: 10592: 10589: 10587: 10584: 10582: 10579: 10577: 10574: 10572: 10569: 10567: 10564: 10562: 10559: 10557: 10554: 10552: 10549: 10547: 10544: 10542: 10539: 10537: 10534: 10532: 10531:Herz reaction 10529: 10527: 10524: 10522: 10519: 10517: 10514: 10512: 10509: 10507: 10504: 10502: 10499: 10497: 10494: 10492: 10489: 10487: 10484: 10482: 10479: 10477: 10474: 10472: 10469: 10467: 10464: 10462: 10459: 10457: 10454: 10452: 10449: 10447: 10444: 10442: 10439: 10437: 10434: 10432: 10429: 10427: 10424: 10422: 10419: 10417: 10414: 10412: 10409: 10408: 10406: 10402: 10396: 10393: 10391: 10388: 10386: 10383: 10381: 10378: 10376: 10373: 10371: 10368: 10366: 10363: 10361: 10358: 10356: 10353: 10351: 10348: 10346: 10343: 10341: 10338: 10336: 10333: 10331: 10328: 10326: 10323: 10321: 10318: 10316: 10313: 10311: 10308: 10306: 10303: 10301: 10298: 10296: 10293: 10291: 10288: 10286: 10283: 10281: 10278: 10276: 10273: 10271: 10268: 10266: 10263: 10261: 10258: 10256: 10253: 10251: 10248: 10246: 10243: 10241: 10238: 10237: 10235: 10233: 10232:Cycloaddition 10229: 10223: 10220: 10218: 10215: 10213: 10210: 10208: 10205: 10203: 10200: 10198: 10195: 10193: 10190: 10188: 10185: 10183: 10180: 10178: 10175: 10173: 10170: 10168: 10165: 10163: 10160: 10158: 10155: 10153: 10150: 10148: 10145: 10143: 10140: 10138: 10135: 10133: 10130: 10128: 10125: 10123: 10120: 10118: 10115: 10113: 10110: 10108: 10105: 10103: 10100: 10098: 10095: 10093: 10090: 10088: 10085: 10083: 10080: 10078: 10077:Isay reaction 10075: 10073: 10070: 10068: 10065: 10063: 10060: 10058: 10055: 10053: 10050: 10048: 10045: 10043: 10040: 10038: 10035: 10033: 10030: 10028: 10025: 10023: 10020: 10018: 10015: 10013: 10010: 10008: 10005: 10003: 10000: 9998: 9995: 9993: 9990: 9988: 9985: 9983: 9980: 9978: 9975: 9973: 9972:Cycloaddition 9970: 9968: 9965: 9963: 9960: 9958: 9955: 9953: 9950: 9948: 9945: 9943: 9940: 9938: 9935: 9933: 9930: 9928: 9925: 9923: 9920: 9918: 9915: 9913: 9910: 9908: 9905: 9903: 9900: 9898: 9895: 9893: 9890: 9888: 9885: 9883: 9880: 9878: 9875: 9874: 9872: 9870: 9867:Ring forming 9864: 9858: 9855: 9853: 9850: 9848: 9845: 9843: 9840: 9838: 9835: 9833: 9830: 9828: 9825: 9823: 9820: 9818: 9815: 9813: 9810: 9808: 9805: 9803: 9800: 9798: 9795: 9793: 9790: 9788: 9785: 9783: 9780: 9778: 9775: 9773: 9770: 9768: 9767:Rupe reaction 9765: 9763: 9760: 9758: 9755: 9753: 9750: 9748: 9745: 9743: 9740: 9738: 9735: 9733: 9730: 9728: 9725: 9723: 9720: 9718: 9715: 9713: 9710: 9708: 9705: 9703: 9700: 9698: 9695: 9693: 9690: 9688: 9685: 9683: 9680: 9678: 9675: 9673: 9670: 9668: 9665: 9663: 9660: 9658: 9655: 9653: 9650: 9648: 9645: 9643: 9640: 9638: 9635: 9633: 9630: 9628: 9625: 9623: 9620: 9618: 9615: 9613: 9610: 9608: 9605: 9603: 9600: 9598: 9595: 9593: 9590: 9588: 9585: 9583: 9580: 9578: 9575: 9573: 9570: 9568: 9565: 9563: 9560: 9558: 9555: 9553: 9550: 9548: 9545: 9543: 9540: 9538: 9535: 9533: 9530: 9528: 9525: 9523: 9520: 9518: 9515: 9513: 9510: 9508: 9505: 9503: 9500: 9498: 9495: 9493: 9490: 9488: 9485: 9483: 9480: 9478: 9475: 9473: 9470: 9468: 9465: 9463: 9460: 9458: 9455: 9453: 9450: 9448: 9445: 9443: 9440: 9438: 9435: 9433: 9430: 9428: 9425: 9423: 9420: 9418: 9415: 9413: 9410: 9408: 9405: 9403: 9400: 9398: 9395: 9393: 9390: 9389: 9387: 9385: 9379: 9373: 9370: 9368: 9365: 9363: 9360: 9358: 9355: 9353: 9350: 9348: 9345: 9343: 9340: 9338: 9335: 9333: 9330: 9328: 9325: 9323: 9320: 9318: 9315: 9313: 9310: 9308: 9305: 9303: 9300: 9298: 9295: 9293: 9290: 9288: 9285: 9283: 9280: 9278: 9275: 9273: 9270: 9268: 9265: 9263: 9260: 9258: 9255: 9253: 9250: 9248: 9245: 9243: 9240: 9238: 9235: 9233: 9230: 9228: 9225: 9223: 9220: 9218: 9215: 9213: 9210: 9208: 9205: 9203: 9200: 9198: 9195: 9193: 9190: 9188: 9185: 9183: 9180: 9178: 9175: 9173: 9170: 9168: 9165: 9163: 9160: 9158: 9157:Ley oxidation 9155: 9153: 9150: 9148: 9145: 9143: 9140: 9138: 9135: 9133: 9130: 9128: 9125: 9123: 9122:Hydroxylation 9120: 9118: 9115: 9113: 9112:Hydrogenation 9110: 9108: 9105: 9103: 9100: 9098: 9095: 9093: 9090: 9088: 9085: 9083: 9080: 9078: 9075: 9073: 9070: 9068: 9065: 9063: 9060: 9058: 9055: 9053: 9050: 9048: 9047:DNA oxidation 9045: 9043: 9040: 9038: 9037:Deoxygenation 9035: 9033: 9030: 9028: 9025: 9023: 9020: 9018: 9015: 9013: 9010: 9008: 9005: 9003: 9000: 8998: 8995: 8993: 8990: 8988: 8985: 8983: 8980: 8978: 8975: 8973: 8970: 8968: 8965: 8963: 8960: 8958: 8955: 8953: 8950: 8948: 8945: 8943: 8940: 8938: 8935: 8933: 8930: 8928: 8927:Aromatization 8925: 8923: 8920: 8918: 8915: 8913: 8910: 8908: 8905: 8903: 8900: 8898: 8895: 8893: 8890: 8888: 8885: 8884: 8882: 8880: 8874: 8868: 8865: 8863: 8860: 8858: 8855: 8853: 8850: 8848: 8845: 8843: 8840: 8838: 8835: 8833: 8830: 8828: 8825: 8823: 8820: 8818: 8815: 8813: 8810: 8808: 8805: 8803: 8800: 8799: 8797: 8791: 8785: 8782: 8780: 8777: 8775: 8772: 8770: 8767: 8765: 8764:Reed reaction 8762: 8760: 8757: 8755: 8752: 8750: 8747: 8745: 8742: 8740: 8737: 8735: 8732: 8730: 8727: 8725: 8722: 8720: 8717: 8715: 8712: 8710: 8707: 8705: 8702: 8700: 8697: 8695: 8692: 8690: 8687: 8685: 8682: 8681: 8679: 8675:bond forming 8671: 8661: 8658: 8656: 8653: 8651: 8648: 8646: 8643: 8641: 8638: 8636: 8633: 8631: 8628: 8626: 8623: 8621: 8618: 8616: 8613: 8611: 8608: 8606: 8603: 8601: 8598: 8596: 8593: 8591: 8588: 8586: 8583: 8581: 8580:Cope reaction 8578: 8576: 8573: 8571: 8568: 8566: 8563: 8561: 8558: 8557: 8555: 8551: 8545: 8542: 8540: 8537: 8535: 8532: 8530: 8527: 8525: 8522: 8520: 8517: 8515: 8512: 8511: 8509: 8507: 8503: 8497: 8494: 8492: 8489: 8487: 8484: 8482: 8479: 8477: 8474: 8472: 8469: 8467: 8464: 8462: 8459: 8457: 8454: 8452: 8449: 8447: 8444: 8442: 8439: 8437: 8434: 8432: 8429: 8427: 8424: 8422: 8419: 8417: 8414: 8412: 8409: 8407: 8404: 8402: 8399: 8397: 8394: 8392: 8389: 8387: 8384: 8382: 8379: 8377: 8374: 8372: 8369: 8367: 8364: 8362: 8359: 8357: 8354: 8352: 8349: 8347: 8344: 8342: 8339: 8337: 8334: 8332: 8329: 8327: 8324: 8322: 8319: 8317: 8314: 8312: 8309: 8307: 8304: 8302: 8299: 8297: 8294: 8292: 8291:Nef synthesis 8289: 8287: 8284: 8282: 8279: 8277: 8274: 8272: 8269: 8267: 8266:Methylenation 8264: 8262: 8259: 8257: 8254: 8252: 8249: 8247: 8244: 8242: 8239: 8237: 8234: 8232: 8229: 8227: 8224: 8222: 8219: 8217: 8214: 8212: 8209: 8207: 8204: 8202: 8199: 8197: 8194: 8192: 8189: 8187: 8184: 8182: 8179: 8177: 8174: 8172: 8169: 8167: 8164: 8162: 8159: 8157: 8154: 8152: 8149: 8147: 8144: 8142: 8139: 8137: 8136:Heck reaction 8134: 8132: 8129: 8127: 8124: 8122: 8119: 8117: 8114: 8112: 8109: 8107: 8104: 8102: 8099: 8097: 8094: 8092: 8089: 8087: 8084: 8082: 8079: 8077: 8074: 8072: 8069: 8067: 8064: 8062: 8059: 8057: 8054: 8052: 8049: 8047: 8044: 8042: 8039: 8037: 8034: 8032: 8029: 8027: 8024: 8022: 8019: 8017: 8014: 8012: 8009: 8007: 8004: 8002: 7999: 7997: 7994: 7992: 7989: 7987: 7984: 7982: 7979: 7977: 7974: 7972: 7969: 7967: 7964: 7962: 7959: 7957: 7954: 7952: 7949: 7947: 7944: 7942: 7939: 7937: 7934: 7932: 7929: 7927: 7924: 7922: 7919: 7917: 7914: 7912: 7909: 7907: 7904: 7902: 7899: 7897: 7894: 7892: 7889: 7887: 7884: 7882: 7879: 7877: 7874: 7872: 7869: 7867: 7864: 7862: 7859: 7857: 7854: 7852: 7849: 7847: 7844: 7842: 7839: 7837: 7834: 7832: 7829: 7827: 7824: 7823: 7821: 7817:bond forming 7813: 7809: 7804: 7798: 7795: 7793: 7790: 7788: 7785: 7783: 7782:Y-aromaticity 7780: 7778: 7775: 7773: 7770: 7768: 7767:Walsh diagram 7765: 7763: 7760: 7758: 7755: 7753: 7752:Taft equation 7750: 7748: 7745: 7743: 7740: 7738: 7735: 7733: 7730: 7728: 7725: 7723: 7722:Σ-aromaticity 7720: 7718: 7715: 7713: 7710: 7708: 7705: 7703: 7700: 7698: 7695: 7693: 7690: 7688: 7685: 7683: 7680: 7678: 7675: 7673: 7670: 7668: 7665: 7663: 7660: 7658: 7655: 7653: 7650: 7648: 7647:Marcus theory 7645: 7643: 7640: 7638: 7635: 7633: 7630: 7628: 7625: 7623: 7622:Hückel's rule 7620: 7618: 7615: 7613: 7610: 7608: 7605: 7603: 7600: 7598: 7595: 7593: 7590: 7588: 7585: 7583: 7580: 7578: 7577:Evelyn effect 7575: 7573: 7570: 7568: 7565: 7563: 7560: 7558: 7557:Electron-rich 7555: 7553: 7550: 7548: 7545: 7543: 7540: 7538: 7535: 7533: 7530: 7528: 7525: 7523: 7520: 7518: 7515: 7513: 7510: 7508: 7505: 7503: 7500: 7498: 7495: 7493: 7490: 7488: 7485: 7483: 7480: 7478: 7475: 7473: 7472:Bema Hapothle 7470: 7468: 7465: 7463: 7460: 7458: 7455: 7453: 7450: 7448: 7445: 7443: 7440: 7438: 7435: 7433: 7430: 7428: 7425: 7423: 7420: 7419: 7416: 7410: 7407: 7405: 7402: 7400: 7397: 7395: 7392: 7390: 7387: 7385: 7382: 7380: 7377: 7375: 7372: 7370: 7367: 7365: 7362: 7361: 7358: 7354: 7346: 7341: 7339: 7334: 7332: 7327: 7326: 7323: 7316: 7315: 7311: 7310: 7302: 7298: 7294: 7290: 7286: 7282: 7275: 7267: 7263: 7259: 7255: 7248: 7240: 7236: 7231: 7226: 7222: 7218: 7214: 7207: 7200: 7194: 7186: 7182: 7178: 7174: 7171:(9): 2917–9. 7170: 7166: 7159: 7151: 7147: 7143: 7139: 7135: 7131: 7127: 7123: 7119: 7115: 7108: 7100: 7096: 7092: 7088: 7084: 7080: 7076: 7072: 7068: 7064: 7057: 7049: 7045: 7040: 7035: 7031: 7027: 7023: 7019: 7015: 7011: 7004: 6996: 6992: 6988: 6984: 6980: 6976: 6969: 6961: 6957: 6952: 6947: 6943: 6939: 6936:(5): 683–95. 6935: 6931: 6924: 6916: 6912: 6907: 6902: 6898: 6894: 6890: 6883: 6875: 6871: 6867: 6863: 6856: 6848: 6844: 6840: 6836: 6832: 6828: 6821: 6813: 6809: 6805: 6801: 6797: 6793: 6786: 6779: 6775: 6771: 6764: 6762: 6754: 6739: 6731: 6727: 6723: 6719: 6712: 6710: 6708: 6699: 6695: 6688: 6681: 6677: 6673: 6667: 6665: 6663: 6661: 6659: 6657: 6655: 6653: 6651: 6649: 6647: 6639: 6637: 6636:0-7503-0941-5 6633: 6629: 6623: 6615: 6609: 6605: 6604: 6596: 6588: 6584: 6580: 6576: 6569: 6561: 6557: 6553: 6549: 6542: 6540: 6538: 6536: 6534: 6532: 6530: 6528: 6526: 6524: 6522: 6520: 6518: 6516: 6514: 6512: 6510: 6508: 6506: 6504: 6502: 6500: 6493: 6489: 6475: 6467: 6463: 6459: 6455: 6451: 6447: 6440: 6432: 6428: 6424: 6420: 6416: 6412: 6405: 6398: 6397: 6393: 6389: 6385: 6381: 6377: 6373: 6369: 6365: 6359: 6351: 6347: 6343: 6339: 6332: 6325: 6320: 6312: 6308: 6303: 6298: 6294: 6290: 6287:(5): 683–95. 6286: 6282: 6275: 6267: 6263: 6259: 6255: 6251: 6247: 6243: 6239: 6235: 6231: 6224: 6216: 6212: 6208: 6204: 6200: 6196: 6189: 6181: 6177: 6173: 6169: 6165: 6161: 6154: 6146: 6142: 6138: 6134: 6130: 6126: 6119: 6111: 6107: 6103: 6099: 6095: 6091: 6084: 6076: 6072: 6068: 6064: 6057: 6055: 6046: 6042: 6038: 6034: 6027: 6025: 6023: 6015: 6011: 6008: 6004: 6000: 5996: 5993: 5989: 5985: 5981: 5977: 5974: 5970: 5966: 5962: 5958: 5955: 5951: 5947: 5944: 5940: 5936: 5930: 5926: 5911: 5908: 5905: 5902: 5901: 5895: 5893: 5892:photochemical 5885: 5881: 5880: 5879: 5877: 5873: 5868: 5867: 5863: 5859: 5858: 5852: 5850: 5846: 5842: 5840: 5839: 5834: 5821: 5817: 5814: 5809: 5807: 5802: 5793: 5785: 5781: 5779: 5775: 5771: 5764: 5763: 5758: 5756: 5746: 5738: 5734: 5714: 5701: 5689: 5680: 5675: 5662: 5650: 5641: 5635: 5624: 5618: 5609: 5603: 5592: 5585: 5577: 5576: 5575: 5561: 5558: 5550: 5543: 5522: 5519: 5511: 5504: 5480: 5469: 5463: 5454: 5448: 5442: 5422: 5399: 5393: 5368: 5364: 5352: 5346: 5341: 5330: 5324: 5313: 5306: 5297: 5287: 5285: 5281: 5275: 5273: 5269: 5265: 5260: 5255: 5251: 5247: 5243: 5239: 5237: 5233: 5223: 5219: 5217: 5213: 5209: 5205: 5201: 5197: 5193: 5192: 5182: 5177: 5162: 5159: 5154: 5152: 5148: 5144: 5140: 5135: 5133: 5129: 5125: 5121: 5117: 5113: 5109: 5099: 5090: 5079: 5077: 5069: 5063: 5060: 5055: 5052: 5044: 5038: 5030: 5026: 5024: 5014: 5006:Cycloaddition 5003: 5001: 4997: 4993: 4989: 4984: 4977: 4972: 4963: 4955:Cycloaddition 4952: 4949: 4947: 4943: 4931: 4924: 4917: 4910: 4907: 4902: 4895: 4888: 4881: 4878: 4875: 4871: 4870: 4864: 4857: 4850: 4843: 4840: 4835: 4828: 4821: 4814: 4811: 4809: 4805: 4804: 4800: 4797: 4795: 4792: 4791: 4788: 4780: 4778: 4774: 4761: 4758: 4753: 4749: 4743: 4739: 4717: 4714: 4709: 4705: 4699: 4695: 4687:. Likewise, 4686: 4668: 4664: 4660: 4655: 4651: 4640: 4638: 4633: 4629: 4625: 4621: 4603: 4599: 4595: 4590: 4586: 4563: 4559: 4555: 4550: 4546: 4540: 4536: 4525: 4508: 4480: 4476: 4472: 4467: 4463: 4445: 4442: 4437: 4433: 4429: 4424: 4420: 4407: 4404: 4397: 4393: 4389: 4384: 4380: 4375: 4371: 4366: 4362: 4358: 4353: 4349: 4341: 4337: 4333: 4328: 4324: 4319: 4315: 4310: 4306: 4302: 4297: 4293: 4287: 4283: 4273: 4257: 4253: 4249: 4244: 4240: 4219: 4212: 4208: 4204: 4199: 4195: 4190: 4169: 4166: 4161: 4157: 4153: 4148: 4144: 4121: 4117: 4113: 4108: 4104: 4081: 4077: 4073: 4068: 4064: 4058: 4054: 4031: 4027: 4023: 4018: 4014: 3990: 3967: 3964: 3959: 3955: 3951: 3946: 3942: 3919: 3915: 3911: 3906: 3902: 3879: 3875: 3871: 3866: 3862: 3856: 3852: 3848: 3843: 3839: 3833: 3829: 3825: 3820: 3816: 3810: 3806: 3783: 3779: 3773: 3769: 3746: 3742: 3736: 3732: 3723: 3719: 3714: 3713: 3697: 3693: 3687: 3683: 3659: 3655: 3649: 3645: 3637: 3617: 3614: 3609: 3605: 3601: 3596: 3592: 3576: 3572: 3570: 3566: 3551: 3547: 3541: 3537: 3527: 3509: 3505: 3499: 3495: 3486: 3482: 3477: 3476: 3459: 3455: 3451: 3446: 3442: 3434: 3431: 3412: 3409: 3404: 3400: 3396: 3391: 3387: 3371: 3367: 3365: 3359: 3346: 3331: 3326: 3323: 3311: 3306: 3303: 3297: 3292: 3287: 3283: 3256: 3233: 3230: 3227: 3222: 3219: 3209: 3186: 3183: 3180: 3175: 3172: 3166: 3161: 3156: 3152: 3142: 3125: 3122: 3117: 3113: 3109: 3104: 3100: 3085: 3078: 3062: 3059: 3056: 3053: 3050: 3047: 3044: 3041: 3038: 3030: 3026: 3025: 3020: 3019: 3015: 3011: 3010: 3007: 3003: 3002: 2999: 2995: 2986: 2985: 2980: 2977: 2975: 2971: 2967: 2963: 2959: 2956: 2952: 2948: 2942: 2931: 2926: 2923: 2919: 2918: 2912: 2907: 2904: 2900: 2899: 2895: 2892: 2890: 2889: 2882: 2881: 2876: 2873: 2869: 2865: 2861: 2857: 2853: 2847: 2845: 2841: 2837: 2832: 2830: 2826: 2822: 2818: 2814: 2810: 2806: 2802: 2798: 2795:is odd, then 2794: 2790: 2786: 2782: 2778: 2774: 2770: 2766: 2761: 2759: 2755: 2751: 2747: 2743: 2739: 2735: 2731: 2719: 2715: 2707: 2703: 2695: 2691: 2683: 2679: 2675: 2671: 2670: 2669: 2667: 2662: 2660: 2650: 2648: 2645: 2641: 2637: 2633: 2629: 2621: 2613: 2607: 2606: 2593: 2585: 2578: 2574: 2570: 2567: 2563: 2560: 2556: 2553: 2549: 2546: 2542: 2539: 2535: 2532: 2528: 2525: 2521: 2517: 2513: 2510: 2506: 2505: 2504: 2499: 2487: 2480: 2476: 2472: 2469: 2465: 2461: 2460: 2459: 2457: 2456:bond topology 2449: 2446: 2442: 2438: 2434: 2431: 2430: 2429: 2427: 2419: 2415: 2412: 2408: 2405: 2403: 2397: 2393: 2392: 2391: 2389: 2379: 2377: 2373: 2369: 2365: 2360: 2356: 2352: 2343: 2339: 2330: 2328: 2323: 2318: 2316: 2304: 2297: 2290: 2283: 2280: 2275: 2268: 2261: 2254: 2251: 2248: 2244: 2243: 2237: 2230: 2223: 2216: 2213: 2208: 2201: 2194: 2187: 2184: 2182: 2178: 2177: 2173: 2170: 2168: 2164: 2161: 2160: 2157: 2151: 2147: 2143: 2139: 2135: 2131: 2127: 2124: 2120: 2116: 2112: 2108: 2104: 2100: 2099: 2098: 2091: 2087: 2085: 2081: 2064: 2057: 2050: 2043: 2040: 2035: 2028: 2021: 2014: 2011: 2008: 2004: 2003: 1997: 1990: 1983: 1976: 1973: 1968: 1961: 1954: 1947: 1944: 1942: 1938: 1937: 1933: 1930: 1928: 1924: 1921: 1920: 1917: 1911: 1907: 1903: 1899: 1895: 1891: 1887: 1885: 1881: 1877: 1873: 1869: 1865: 1861: 1860: 1859: 1857: 1853: 1836: 1829: 1822: 1815: 1812: 1807: 1800: 1793: 1786: 1783: 1780: 1776: 1775: 1769: 1762: 1755: 1748: 1745: 1740: 1733: 1726: 1719: 1716: 1714: 1710: 1709: 1705: 1702: 1700: 1696: 1693: 1692: 1689: 1683: 1679: 1675: 1671: 1667: 1663: 1659: 1656: 1652: 1648: 1644: 1640: 1636: 1632: 1631: 1630: 1623: 1619: 1613: 1609: 1604: 1602: 1598: 1594: 1590: 1586: 1582: 1578: 1569: 1565: 1561: 1559: 1555: 1551: 1547: 1532: 1529: 1526: 1522: 1521: 1517: 1514: 1512: 1508: 1507: 1503: 1500: 1498: 1497: 1494: 1491: 1489: 1485: 1476: 1472: 1470: 1465: 1459: 1457: 1453: 1443: 1440: 1429: 1425: 1390: 1382: 1378: 1375: 1367: 1355: 1351: 1347: 1327: 1323: 1317: 1313: 1278: 1276: 1272: 1263: 1254: 1243: 1223: 1161: 1157: 1155: 1147: 1125: 1117: 1113: 1109: 1101: 1090: 1088: 1084: 1080: 1076: 1072: 1068: 1067:cycloaddition 1058: 1050: 1046: 1039: 1035: 1033: 967: 965: 961: 932: 928: 895: 885: 881: 879: 855: 851: 842: 838: 814: 810: 778: 766: 762: 724: 720: 709: 705: 697: 693: 684: 672: 663: 659: 656: 652: 647: 643: 639: 635: 626: 624: 620: 616: 612: 607: 602: 601: 596: 594: 590: 588: 583: 579: 571: 570: 567: 560: 549: 545: 539: 535: 519: 502: 498: 491: 487: 485: 482: 478: 474: 470: 466: 462: 458: 454: 450: 446: 442: 438: 434: 430: 426: 422: 418: 414: 410: 406: 402: 398: 394: 390: 386: 382: 378: 374: 369: 368: 362: 357: 355: 345: 343: 339: 333: 330: 327:analyzed the 326: 325:Kenichi Fukui 321: 319: 315: 311: 307: 303: 299: 294: 292: 288: 284: 276: 275:excited state 272: 268: 265: 263: 257: 254: 250: 246: 242: 240: 234: 233: 232: 230: 227: 223: 219: 212: 202: 199: 195: 194: 189: 184: 180: 171: 167: 165: 161: 156: 152: 147: 145: 141: 131: 129: 123: 121: 117: 113: 109: 105: 101: 98: 94: 90: 86: 82: 78: 74: 70: 66: 62: 54: 50: 46: 42: 38: 34: 30: 26: 21: 10643: 10639: 10633: 9572:Ene reaction 8932:Autoxidation 8793:Degradation 8684:Azo coupling 8461:Ugi reaction 8061:Ene reaction 7861:Alkynylation 7771: 7712:Polyfluorene 7707:Polar effect 7572:Electrophile 7487:Bredt's rule 7457:Baird's rule 7427:Alpha effect 7284: 7280: 7274: 7260:(24): 4033. 7257: 7253: 7247: 7220: 7216: 7206: 7193: 7168: 7164: 7158: 7117: 7113: 7107: 7066: 7062: 7056: 7039:10533/176692 7013: 7009: 7003: 6978: 6974: 6968: 6951:10533/131820 6933: 6929: 6923: 6896: 6892: 6882: 6865: 6861: 6855: 6830: 6826: 6820: 6795: 6791: 6785: 6777: 6773: 6769: 6752: 6738: 6721: 6717: 6697: 6693: 6687: 6671: 6630:(CRC Press) 6627: 6622: 6602: 6595: 6578: 6574: 6568: 6551: 6547: 6479: 6474: 6449: 6445: 6439: 6414: 6410: 6404: 6394: 6391: 6387: 6383: 6379: 6375: 6371: 6367: 6363: 6358: 6341: 6337: 6331: 6319: 6302:10533/131820 6284: 6280: 6274: 6233: 6229: 6223: 6198: 6194: 6188: 6163: 6159: 6153: 6128: 6124: 6118: 6093: 6089: 6083: 6066: 6062: 6036: 6032: 6013: 6009: 6006: 6001:, 1564) and 5998: 5994: 5991: 5979: 5975: 5972: 5968: 5960: 5956: 5953: 5949: 5945: 5942: 5929: 5889: 5869: 5865: 5855: 5853: 5848: 5847: 5843: 5836: 5830: 5812: 5810: 5805: 5798: 5769: 5766: 5761: 5760: 5754: 5752: 5743: 5731: 5293: 5276: 5271: 5267: 5263: 5258: 5253: 5250: 5245: 5241: 5240: 5235: 5231: 5228: 5215: 5211: 5207: 5203: 5199: 5195: 5189: 5187: 5155: 5150: 5146: 5142: 5138: 5136: 5131: 5127: 5123: 5119: 5115: 5111: 5107: 5104: 5075: 5073: 5067: 5058: 5056: 5050: 5048: 5042: 5035: 5020: 4995: 4991: 4987: 4985: 4981: 4975: 4950: 4945: 4941: 4939: 4929: 4922: 4915: 4908: 4900: 4893: 4886: 4879: 4873: 4862: 4855: 4848: 4841: 4833: 4826: 4819: 4812: 4807: 4793: 4786: 4776: 4731: 4684: 4641: 4631: 4627: 4623: 4619: 4527: 4275: 3894:is odd. If 3721: 3717: 3715: 3674: 3577: 3574: 3573: 3568: 3529: 3525: 3484: 3480: 3478: 3474: 3432: 3372: 3369: 3368: 3363: 3361: 3144: 3083: 3076: 3028: 3023: 3022: 3021: 3016: 3013: 3012: 3008: 3005: 3004: 3000: 2998:Proposition. 2997: 2996: 2993: 2983: 2982: 2978: 2973: 2969: 2965: 2961: 2957: 2954: 2950: 2946: 2943: 2939: 2921: 2902: 2879: 2878: 2871: 2867: 2863: 2859: 2855: 2851: 2848: 2843: 2839: 2835: 2833: 2828: 2824: 2820: 2816: 2812: 2808: 2804: 2800: 2796: 2792: 2788: 2784: 2780: 2776: 2772: 2768: 2764: 2762: 2757: 2753: 2749: 2745: 2741: 2737: 2733: 2729: 2727: 2717: 2713: 2705: 2701: 2693: 2689: 2681: 2677: 2673: 2665: 2663: 2658: 2656: 2643: 2639: 2635: 2631: 2627: 2619: 2611: 2609: 2596: 2595: 2591: 2582: 2497: 2492: 2478: 2475:antarafacial 2474: 2467: 2463: 2455: 2453: 2444: 2440: 2436: 2425: 2423: 2401: 2394:An isolated 2387: 2385: 2375: 2372:antarafacial 2371: 2367: 2363: 2358: 2354: 2348: 2336: 2326: 2322:ene reaction 2319: 2314: 2313:The case of 2312: 2302: 2295: 2288: 2281: 2273: 2266: 2259: 2252: 2246: 2235: 2228: 2221: 2214: 2206: 2199: 2192: 2185: 2180: 2166: 2162: 2155: 2149: 2145: 2141: 2137: 2133: 2129: 2122: 2118: 2114: 2110: 2106: 2102: 2096: 2083: 2079: 2077: 2062: 2055: 2048: 2041: 2033: 2026: 2019: 2012: 2006: 1995: 1988: 1981: 1974: 1966: 1959: 1952: 1945: 1940: 1926: 1922: 1915: 1909: 1905: 1901: 1897: 1893: 1889: 1883: 1879: 1875: 1871: 1867: 1863: 1855: 1851: 1849: 1834: 1827: 1820: 1813: 1805: 1798: 1791: 1784: 1778: 1767: 1760: 1753: 1746: 1738: 1731: 1724: 1717: 1712: 1698: 1694: 1687: 1681: 1677: 1673: 1669: 1665: 1661: 1654: 1650: 1646: 1642: 1638: 1634: 1628: 1605: 1600: 1596: 1592: 1588: 1584: 1580: 1576: 1574: 1562: 1557: 1553: 1549: 1545: 1543: 1533:conrotatory 1524: 1518:disrotatory 1510: 1492: 1487: 1483: 1481: 1468: 1463: 1460: 1455: 1451: 1449: 1435: 1426: 1394: 1376: 1372: 1348: 1328: 1324: 1321: 1279: 1268: 1224: 1165: 1130: 1110: 1107: 1086: 1083:antarafacial 1074: 1070: 1064: 1055: 1044: 968: 894:ground state 890: 854:ground-state 847: 819: 779: 770: 728: 689: 660: 654: 650: 637: 632: 622: 618: 614: 610: 608: 604: 599: 598: 586: 575: 568: 565: 564: 558: 543: 506: 496: 483: 480: 476: 472: 468: 464: 460: 456: 452: 448: 444: 440: 436: 432: 428: 424: 420: 416: 412: 408: 404: 400: 396: 392: 388: 384: 380: 376: 365: 358: 351: 334: 322: 317: 313: 295: 290: 286: 280: 261: 238: 208: 197: 193:antarafacial 191: 187: 182: 178: 175: 163: 159: 154: 150: 148: 137: 128:asynchronous 124: 119: 115: 64: 60: 58: 52: 48: 44: 40: 36: 32: 28: 24: 8071:Ethenolysis 7717:Ring strain 7687:Nucleophile 7512:Clar's rule 7452:Aromaticity 6724:(9): 2046. 6581:(9): 2045. 6368:disrotation 6364:conrotation 6125:Tetrahedron 6007:Tetrahedron 5965:E. J. Corey 5827:Controversy 5023:Diels-Alder 2577:carbocation 2464:suprafacial 2376:suprafacial 2368:disrotatory 2364:conrotatory 2359:disrotatory 2355:conrotatory 1530:disrotatory 1515:conrotatory 1424:of ethene. 1275:cyclohexene 1271:Diels-Alder 1079:suprafacial 953:is S, and Ψ 920:axis, and Ψ 696:disrotatory 692:conrotatory 403:) and the ( 373:Thermolysis 361:equilibrium 354:Ultraviolet 323:Meanwhile, 253:conrotatory 241:π electrons 213:might help 198:suprafacial 164:conrotatory 155:disrotatory 151:conrotatory 10673:Categories 10355:Ozonolysis 9882:Annulation 9232:Ozonolysis 7351:Topics in 6742:Because SO 6680:0534249485 6039:(2): 395. 5921:References 5778:glowsticks 5749:Exceptions 4136:, we have 3018:forbidden. 2636:sufficient 2524:ozonolysis 2420:(symbol σ) 2413:(symbol π) 1178:and then σ 1146:p-orbitals 777:rotation. 226:conjugated 149:The terms 9869:reactions 9384:reactions 8879:reactions 8795:reactions 8677:reactions 7819:reactions 7091:1089-5639 6847:0002-7863 6812:206899145 6466:0040-4039 6431:0002-7863 6215:0040-4039 6180:1521-3773 6145:0040-4020 6131:: 75–92. 6110:0001-4842 5690:ϕ 5681:− 5651:ϕ 5642:≅ 5633:∂ 5616:∂ 5478:∂ 5464:ρ 5461:∂ 5394:ρ 5361:∂ 5347:ρ 5338:∂ 4740:∑ 4696:∑ 4661:≠ 4596:≠ 4537:∑ 4473:≠ 4411:# 4390:≠ 4376:∑ 4334:≠ 4320:∑ 4316:≡ 4284:∑ 4250:≠ 4205:≠ 4191:∑ 4114:≠ 4055:∑ 3965:≡ 3853:∑ 3830:∑ 3807:∑ 3770:∑ 3733:∑ 3684:∑ 3646:∑ 3538:∑ 3496:∑ 3452:≠ 3231:≡ 3184:≡ 3057:… 2934:aromatic 2927:Forbidden 2913:Forbidden 2910:aromatic 2640:necessary 2388:component 2327:see below 516:Ψ 427:) isomer 188:component 183:faciality 100:conserves 95:that any 51:) isomer 10660:17639522 7762:Vinylogy 7432:Annulene 7379:Reagents 7239:15558636 7185:15104426 7142:17377579 7099:28094939 7048:16839107 6995:17639522 6960:22283422 6915:37436155 6484:and (4r) 6344:: 1–14. 6311:22283422 6266:17771019 6014:Suppl. 8 5898:See also 4783:Examples 3483:+ 2 or 4 2862:+ 2 or 4 2831:is odd. 2610:Here, (4 2601:and (4r) 646:symmetry 457:opposite 395:); the ( 316:+ 2 or 4 255:process. 229:polyenes 144:orbitals 63:(or the 7422:A value 7301:5845424 7150:4427747 7122:Bibcode 7071:Bibcode 7018:Bibcode 6694:orbital 6258:1689733 6238:Bibcode 6230:Science 5264:Step 4. 5259:Step 3. 5254:Step 2. 5246:Step 1. 4978:-olefin 3712:is odd. 3475:is odd. 2932:Allowed 2908:Allowed 2896:Möbius 2893:Hückel 2404:orbital 1612:Claisen 1599:+ 1 = 4 1591:+ 1 = 4 1556:− 1), ( 1154:σ-bonds 1081:(s) or 962:to the 949:is A, Ψ 945:. As Ψ 929:to the 850:barrier 837:and σ. 809:and π. 247:of the 205:History 10658: 7299: 7237: 7183: 7148: 7140: 7114:Nature 7097: 7089: 7046: 6993: 6958: 6913: 6845: 6810: 6774:antara 6678: 6634: 6610: 6464: 6429: 6309: 6264: 6256: 6213: 6178: 6143: 6108: 5284:modulo 5280:parity 5158:Berson 4528:Thus, 4506: 4489: 4460: 4452: 4182:, but 3988: 3971: 3254: 3237: 3207: 3190: 2740:, and 2728:where 2676:+ 2 = 2618:and (4 2545:Berson 2418:σ bond 479:) and 243:, the 104:couple 39:, but 7146:S2CID 6911:S2CID 6808:S2CID 6770:supra 6698:state 6254:JSTOR 5916:Notes 5890:This 4996:trans 4988:trans 4976:trans 4794:p + q 3081:σ/π/ω 2905:+2 e 2668:+ 2: 2659:total 2575:of a 2520:ozone 2495:σ/π/ω 2443:(or 2 1420:and π 1237:and σ 1229:and π 1170:and σ 1136:and σ 860:and Ψ 753:and Ψ 741:and Ψ 733:and Ψ 694:or a 377:trans 308:, or 269:In a 10656:PMID 7297:PMID 7235:PMID 7181:PMID 7138:PMID 7095:PMID 7087:ISSN 7044:PMID 6991:PMID 6956:PMID 6843:ISSN 6753:both 6676:ISBN 6632:ISBN 6608:ISBN 6462:ISSN 6427:ISSN 6366:vs. 6307:PMID 6262:PMID 6211:ISSN 6176:ISSN 6141:ISSN 6106:ISSN 6010:1966 5995:1966 5976:1961 5957:1969 5946:1965 5937:and 5806:anti 5694:HOMO 5655:LUMO 5559:< 5520:> 5216:even 5088:edit 5012:edit 4961:edit 4777:(B') 4730:and 4685:(A') 4630:and 4624:(B') 4622:and 4620:(A') 3722:(B') 3720:and 3718:(A') 3575:(B') 3370:(A') 2964:+ 2) 2815:and 2756:and 2696:+ 2) 2684:+ 2) 2644:see: 2614:+ 2) 2536:The 2529:The 2514:The 2507:The 2479:anti 2454:The 2424:The 2374:and 2366:and 2357:and 2320:The 1610:and 1608:Cope 1548:and 1252:edit 1140:. σ 1099:edit 964:LUMO 960:HOMO 931:LUMO 927:HOMO 704:axis 555:Rule 433:same 300:and 160:same 153:and 79:and 71:and 59:The 43:to ( 27:to ( 10648:doi 7289:doi 7262:doi 7225:doi 7173:doi 7130:doi 7118:446 7079:doi 7067:121 7034:hdl 7026:doi 7014:109 6983:doi 6946:hdl 6938:doi 6901:doi 6870:doi 6835:doi 6800:doi 6796:102 6772:or 6726:doi 6583:doi 6556:doi 6454:doi 6419:doi 6392:see 6346:doi 6342:627 6297:hdl 6289:doi 6246:doi 6234:218 6203:doi 6168:doi 6133:doi 6098:doi 6071:doi 6041:doi 5813:cis 5212:odd 5149:= 4 5141:= 4 5130:= 4 5122:= 4 5116:j − 5074:A 4 5049:A 4 4992:cis 4921:or 4892:or 4876:+ 2 4854:or 4825:or 4632:(B) 4628:(A) 3761:or 3675:or 3569:(B) 3364:(A) 3087:s/a 3014:(B) 3006:(A) 2748:or 2518:of 2501:s/a 2468:syn 2398:or 2329:). 2294:or 2265:or 2249:+ 2 2227:or 2198:or 2148:= 4 2136:= 4 2121:= 4 2109:= 4 2054:or 2025:or 2009:+ 2 1987:or 1958:or 1912:+ 2 1908:= 4 1896:= 4 1882:= 4 1870:= 4 1826:or 1797:or 1781:+ 2 1759:or 1730:or 1680:= 4 1668:= 4 1653:= 4 1641:= 4 1527:+ 2 1292:, Ψ 1288:, Ψ 1284:, Ψ 1198:, π 1190:, π 1148:; σ 1089:.) 481:not 449:cis 413:cis 375:of 196:or 181:or 83:of 10675:: 10654:. 10644:13 10642:. 7295:. 7285:87 7283:. 7258:85 7256:. 7233:. 7221:43 7219:. 7215:. 7179:. 7169:69 7167:. 7144:. 7136:. 7128:. 7116:. 7093:. 7085:. 7077:. 7065:. 7042:. 7032:. 7024:. 7012:. 6989:. 6979:13 6977:. 6954:. 6944:. 6934:45 6932:. 6909:. 6897:78 6895:. 6891:. 6866:88 6864:. 6841:. 6831:89 6829:. 6806:. 6794:. 6760:^ 6722:87 6720:. 6706:^ 6645:^ 6579:87 6577:. 6550:. 6498:^ 6460:. 6448:. 6425:. 6415:90 6413:. 6399:.) 6340:. 6305:. 6295:. 6285:45 6283:. 6260:. 6252:. 6244:. 6232:. 6209:. 6197:. 6174:. 6164:10 6162:. 6139:. 6129:22 6127:. 6104:. 6092:. 6067:88 6065:. 6053:^ 6037:87 6035:. 6021:^ 6012:, 5999:88 5997:, 5980:16 5978:, 5959:, 5950:87 5948:, 5860:, 5249:sp 4994:, 4928:+ 4914:+ 4899:+ 4885:+ 4861:+ 4847:+ 4832:+ 4818:+ 4524:. 3934:, 3571:: 3366:: 2976:. 2968:(4 2960:(4 2924:e 2870:+ 2854:+ 2842:+ 2827:+ 2807:+ 2787:+ 2767:+ 2736:, 2732:, 2716:(4 2712:+ 2704:(4 2700:+ 2692:(4 2688:+ 2680:(4 2649:) 2571:A 2416:A 2409:A 2400:sp 2396:p- 2386:A 2301:+ 2287:+ 2272:+ 2258:+ 2234:+ 2220:+ 2205:+ 2191:+ 2165:+ 2144:+ 2132:+ 2117:+ 2105:+ 2061:+ 2047:+ 2032:+ 2018:+ 1994:+ 1980:+ 1965:+ 1951:+ 1925:+ 1904:+ 1892:+ 1878:+ 1866:+ 1833:+ 1819:+ 1804:+ 1790:+ 1766:+ 1752:+ 1737:+ 1723:+ 1697:+ 1676:+ 1664:+ 1649:+ 1637:+ 1422:CC 1418:CC 1406:CH 1396:(σ 1334:πΨ 1277:. 1239:AS 1235:SS 1231:AS 1227:SS 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