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:
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4590:
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4563:
4559:
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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:
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1877:
1873:
1869:
1865:
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1836:
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1793:
1786:
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1733:
1726:
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1714:
1710:
1709:
1705:
1702:
1700:
1696:
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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:
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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:
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199:
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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:
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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
1220:AS
1216:AS
1212:AA
1208:AA
1204:SA
1200:SA
1196:AS
1192:AS
1188:SS
1184:SS
486:.
260:(4
217:12
166:.
146:.
122:.
10662:.
10650::
7344:e
7337:t
7330:v
7303:.
7291::
7268:.
7264::
7241:.
7227::
7187:.
7175::
7152:.
7132::
7124::
7101:.
7081::
7073::
7050:.
7036::
7028::
7020::
6997:.
6985::
6962:.
6948::
6940::
6917:.
6903::
6876:.
6872::
6849:.
6837::
6814:.
6802::
6748:2
6744:2
6732:.
6728::
6682:.
6616:.
6589:.
6585::
6562:.
6558::
6552:8
6486:a
6482:s
6468:.
6456::
6450:6
6433:.
6421::
6388:Z
6386:,
6384:Z
6380:1
6376:Z
6374:,
6372:Z
6352:.
6348::
6313:.
6299::
6291::
6268:.
6248::
6240::
6217:.
6205::
6199:6
6182:.
6170::
6147:.
6135::
6112:.
6100::
6094:4
6077:.
6073::
6047:.
6043::
6005:(
5990:(
5961:8
5770:1
5715:2
5710:|
5705:)
5702:r
5699:(
5685:|
5676:2
5671:|
5666:)
5663:r
5660:(
5646:|
5636:N
5628:)
5625:r
5622:(
5619:f
5610:=
5607:)
5604:r
5601:(
5596:)
5593:2
5590:(
5586:f
5562:0
5554:)
5551:2
5548:(
5544:f
5523:0
5515:)
5512:2
5509:(
5505:f
5481:N
5473:)
5470:r
5467:(
5455:=
5452:)
5449:r
5446:(
5443:f
5423:N
5403:)
5400:r
5397:(
5369:2
5365:N
5356:)
5353:r
5350:(
5342:2
5331:=
5328:)
5325:r
5322:(
5317:)
5314:2
5311:(
5307:f
5272:n
5268:n
5236:n
5232:n
5204:n
5200:n
5151:n
5147:j
5143:n
5139:j
5132:n
5128:j
5124:n
5120:j
5112:j
5108:j
5092:]
5076:n
5068:n
5066:4
5059:n
5051:n
5043:n
5041:4
5016:]
4965:]
4946:n
4942:n
4933:s
4930:q
4926:a
4923:p
4919:a
4916:q
4912:s
4909:p
4904:a
4901:q
4897:a
4894:p
4890:s
4887:q
4883:s
4880:p
4874:n
4872:4
4866:a
4863:q
4859:a
4856:p
4852:s
4849:q
4845:s
4842:p
4837:s
4834:q
4830:a
4827:p
4823:a
4820:q
4816:s
4813:p
4808:n
4806:4
4762:2
4759:=
4754:i
4750:p
4744:i
4718:2
4715:=
4710:i
4706:n
4700:i
4669:i
4665:p
4656:i
4652:n
4637:□
4604:i
4600:p
4591:i
4587:n
4564:i
4560:p
4556:+
4551:i
4547:n
4541:i
4512:)
4509:2
4502:d
4499:o
4496:m
4492:(
4486:}
4481:i
4477:p
4468:i
4464:n
4456:|
4449:)
4446:i
4443:,
4438:i
4434:p
4430:,
4425:i
4421:n
4417:(
4414:{
4408:=
4405:1
4398:i
4394:p
4385:i
4381:n
4372:=
4367:i
4363:p
4359:+
4354:i
4350:n
4342:i
4338:p
4329:i
4325:n
4311:i
4307:p
4303:+
4298:i
4294:n
4288:i
4258:i
4254:p
4245:i
4241:n
4220:1
4213:i
4209:p
4200:i
4196:n
4170:1
4167:=
4162:i
4158:p
4154:+
4149:i
4145:n
4122:i
4118:p
4109:i
4105:n
4082:i
4078:p
4074:+
4069:i
4065:n
4059:i
4032:i
4028:p
4024:=
4019:i
4015:n
3994:)
3991:2
3984:d
3981:o
3978:m
3974:(
3968:0
3960:i
3956:p
3952:+
3947:i
3943:n
3920:i
3916:p
3912:=
3907:i
3903:n
3880:i
3876:p
3872:+
3867:i
3863:n
3857:i
3849:=
3844:i
3840:p
3834:i
3826:+
3821:i
3817:n
3811:i
3784:i
3780:p
3774:i
3747:i
3743:n
3737:i
3698:i
3694:p
3688:i
3660:i
3656:n
3650:i
3624:}
3621:)
3618:i
3615:,
3610:i
3606:p
3602:,
3597:i
3593:n
3589:(
3586:{
3552:i
3548:p
3542:i
3526:q
3510:i
3506:n
3500:i
3485:n
3481:n
3460:i
3456:p
3447:i
3443:n
3419:}
3416:)
3413:i
3410:,
3405:i
3401:p
3397:,
3392:i
3388:n
3384:(
3381:{
3347:.
3332:i
3327:,
3324:1
3312:i
3307:,
3304:0
3298:{
3293:=
3288:i
3284:p
3278:d
3275:n
3272:a
3260:)
3257:4
3250:d
3247:o
3244:m
3240:(
3234:2
3228:N
3223:,
3220:1
3213:)
3210:4
3203:d
3200:o
3197:m
3193:(
3187:0
3181:N
3176:,
3173:0
3167:{
3162:=
3157:i
3153:n
3129:)
3126:i
3123:,
3118:i
3114:p
3110:,
3105:i
3101:n
3097:(
3084:N
3077:i
3063:k
3060:,
3054:,
3051:2
3048:,
3045:1
3042:=
3039:i
3029:k
2972:)
2970:n
2962:n
2951:n
2947:n
2945:4
2922:n
2920:4
2903:n
2901:4
2872:d
2868:a
2864:n
2860:n
2856:d
2852:b
2844:d
2840:b
2836:n
2829:d
2825:b
2821:n
2817:b
2813:a
2809:d
2805:b
2801:b
2797:d
2793:a
2789:d
2785:b
2781:b
2777:d
2773:a
2769:d
2765:a
2758:b
2754:a
2750:b
2746:a
2742:d
2738:c
2734:b
2730:a
2724:,
2722:a
2720:)
2718:r
2714:d
2710:s
2708:)
2706:t
2702:c
2698:a
2694:p
2690:b
2686:s
2682:q
2678:a
2674:n
2672:4
2666:n
2632:r
2628:q
2624:a
2622:)
2620:r
2616:s
2612:q
2603:a
2599:s
2498:N
2445:n
2441:n
2437:n
2402:-
2315:q
2306:s
2303:q
2299:a
2296:p
2292:a
2289:q
2285:s
2282:p
2277:a
2274:q
2270:a
2267:p
2263:s
2260:q
2256:s
2253:p
2247:n
2245:4
2239:a
2236:q
2232:a
2229:p
2225:s
2222:q
2218:s
2215:p
2210:s
2207:q
2203:a
2200:p
2196:a
2193:q
2189:s
2186:p
2181:n
2179:4
2167:q
2163:p
2150:n
2146:q
2142:p
2138:n
2134:q
2130:p
2123:n
2119:q
2115:p
2111:n
2107:q
2103:p
2084:q
2080:p
2066:s
2063:q
2059:a
2056:p
2052:a
2049:q
2045:s
2042:p
2037:a
2034:q
2030:a
2027:p
2023:s
2020:q
2016:s
2013:p
2007:n
2005:4
1999:a
1996:q
1992:a
1989:p
1985:s
1982:q
1978:s
1975:p
1970:s
1967:q
1963:a
1960:p
1956:a
1953:q
1949:s
1946:p
1941:n
1939:4
1927:q
1923:p
1910:n
1906:q
1902:p
1898:n
1894:q
1890:p
1884:n
1880:q
1876:p
1872:n
1868:q
1864:p
1856:q
1852:p
1838:s
1835:j
1831:a
1828:i
1824:a
1821:j
1817:s
1814:i
1809:a
1806:j
1802:a
1799:i
1795:s
1792:j
1788:s
1785:i
1779:n
1777:4
1771:a
1768:j
1764:a
1761:i
1757:s
1754:j
1750:s
1747:i
1742:s
1739:j
1735:a
1732:i
1728:a
1725:j
1721:s
1718:i
1713:n
1711:4
1699:j
1695:i
1682:n
1678:j
1674:i
1670:n
1666:j
1662:i
1655:n
1651:j
1647:i
1643:n
1639:j
1635:i
1616:2
1601:n
1597:j
1593:n
1589:j
1585:j
1581:j
1577:j
1558:j
1554:i
1550:j
1546:i
1525:n
1523:4
1511:n
1509:4
1488:n
1484:n
1469:n
1467:4
1464:n
1462:4
1456:n
1452:n
1414:A
1410:A
1402:A
1398:S
1344:A
1342:σ
1340:S
1336:2
1332:1
1330:Ψ
1310:4
1306:3
1302:2
1298:1
1294:4
1290:3
1286:2
1282:1
1256:]
1180:2
1176:1
1172:2
1168:1
1150:2
1142:1
1138:2
1134:1
1132:σ
1103:]
1075:q
1071:p
1028:4
1026:Ψ
1024:2
1022:Ψ
1020:1
1016:3
1014:Ψ
1012:2
1010:Ψ
1008:1
1004:3
1000:2
996:1
994:Ψ
991:2
989:Ψ
987:1
983:2
979:1
975:2
973:Ψ
971:1
955:3
951:2
947:1
943:3
941:Ψ
939:2
937:Ψ
935:1
922:2
918:2
914:1
910:2
908:Ψ
906:1
902:2
898:1
874:2
870:2
866:1
862:2
858:1
835:4
831:2
827:3
823:1
821:Ψ
807:4
803:3
799:2
795:2
791:2
787:2
783:1
781:Ψ
774:2
772:C
759:2
755:4
751:2
747:2
743:3
739:1
735:3
731:1
729:Ψ
717:2
713:2
702:2
700:C
676:2
623:n
619:n
615:n
611:n
589:ν
587:h
578:Δ
520:3
484:5
477:7
473:Z
471:,
469:E
465:3
461:6
453:6
445:5
441:E
439:,
437:E
429:4
425:Z
423:,
421:E
417:3
409:Z
407:,
405:E
401:Z
399:,
397:Z
393:2
389:E
387:,
385:E
381:1
318:n
314:n
291:r
287:q
262:n
239:n
237:4
55:.
53:4
49:Z
47:,
45:E
41:3
37:2
33:E
31:,
29:E
25:1
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