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doi 10 1016 s0040 4020 01 82171 2 issn 0040 4020 dewar michael j s 1971 11 01 aromaticity and pericyclic reactions angewandte chemie international edition in english 10 11 761 776 doi 10 1002 anie 197107611 issn 1521 3773 fukui kenichi 1965 01 01 stereoselectivity associated with noncycloaddition to unsaturated bonds tetrahedron letters 6 28 2427 2432 doi 10 1016 s0040 4039 00 90203 x issn 0040 4039 fukui kenichi 1982 role of frontier orbitals in chemical reactions science 218 4574 747 754 bibcode 1982sci 218 747f doi 10 1126 science 218 4574 747 jstor 1689733 pmid 17771019 1 2 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 accounts of chemical research 45 5 683 95 doi 10 1021 ar200192t hdl 10533 131820 pmid 22283422 the nobel prize in chemistry 1981 nobelprize org corey e j 2004 impossible dreams the journal of organic chemistry 69 9 2917 9 doi 10 1021 jo049925d pmid 15104426 johnson carolyn y march 1 2005 whose idea was it boston globe 1 2 hoffmann roald 2004 a claim on the development of the frontier orbital explanation of electrocyclic reactions angewandte chemie international edition 43 48 6586 90 doi 10 1002 anie 200461440 pmid 15558636 corey e j hortmann alfred g 1963 total synthesis of dihydrocostunolide journal of the american chemical society 85 24 4033 bibcode 1963jachs 85 4033c doi 10 1021 ja00907a030 corey e j hortmann alfred g 1965 the total synthesis of dihydrocostunolide journal of the american chemical society 87 24 5736 42 bibcode 1965jachs 87 5736c doi 10 1021 ja00952a037 pmid 5845424 the original statement given by woodward and hoffmann is somewhat more elaborate a ground state pericyclic change is symmetry allowed when the total number of 4q 2 s and 4r a components is odd however the statement given here is mathematically equivalent for a proof see https ia601607 us archive org 11 items woodhoff2025 woodhoff2025 pdf 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 woodward r b hoffmann roald 1969 the conservation of orbital symmetry angew chem int ed 8 11 781 853 doi 10 1002 anie 196907811 criegee rudolf noll klaus 1959 umsetzungen in der reihe des 1 2 3 4 tetramethyl cyclobutans justus liebigs annalen der chemie 627 1 14 doi 10 1002 jlac 19596270102 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 conrotation vs disrotation the formation of the z z isomer from ring opening of 1 both ends rotating counterclockwise is therefore also symmetry allowed that the z z 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 see torquoselectivity srinivasan r 1968 07 01 mechanism of the photochemical valence tautomerization of 1 3 butadienes journal of the american chemical society 90 16 4498 4499 bibcode 1968jachs 90 4498s doi 10 1021 ja01018a080 issn 0002 7863 winter rudolph ernst k 1965 01 01 the preparation and isomerization of cis and trans 3 4 dimethylcyclobutene tetrahedron letters 6 17 1207 1212 doi 10 1016 s0040 4039 01 83997 6 issn 0040 4039 longuet higgins h c abrahamson e w 1965 the electronic mechanism of electrocyclic reactions journal of the american chemical society 87 9 2045 doi 10 1021 ja01087a033 woodward r b hoffmann roald 1971 the conservation of orbital symmetry 3rd printing 1st ed weinheim brd verlag chemie gmbh brd and academic press usa pp 1 178 isbn 978 1483256153 p r bunker and p jensen 2005 fundamentals of molecular symmetry crc press isbn 0 7503 0941 5 see section 10 4 1 2 3 4 5 6 7 8 9 10 11 carroll felix 1998 perspectives on structure and mechanism in organic chemistry brooks cole pp 710 794 isbn 0534249485 1 2 3 hoffmann roald woodward r b 1965 selection rules for concerted cycloaddition reactions j am chem soc 87 9 2046 bibcode 1965jachs 87 2046h doi 10 1021 ja01087a034 because so 2 has orthogonal lone pair and antibonding orbitals the allyl like antibonding orbital of so 2 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 both of the separate orbital interactions have to allowed for the reaction to be allowed the fmo approach probably gives the most intuitive picture here 1 2 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 component so that no phase inversion takes place within it one draws in the dewar zimmerman connections between components based on the bond topology supra or antara 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 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 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 yamabe shinichi kuwata kayoko minato tsutomu 1999 frontier orbital analyses of ketene 2 2 cycloadditions theoretical chemistry accounts theory computation and modeling 102 1 6 139 146 doi 10 1007 s002140050484 s2cid 206899145 berson jerome a nelson george l 1967 10 01 inversion of configuration in the migrating group of a thermal 1 3 sigmatropic rearrangement journal of the american chemical society 89 21 5503 5504 bibcode 1967jachs 89 5503b doi 10 1021 ja00997a065 issn 0002 7863 zimmerman h e 1966 on molecular orbital correlation diagrams möbius systems and factors controlling ground and excited state reactions ii j am chem soc 88 7 1566 156 bibcode 1966jachs 88 1566z doi 10 1021 ja00959a053 zimmerman h e 2006 five decades of mechanistic and exploratory organic photochemistry pure appl chem 78 12 2193 2203 doi 10 1351 pac200678122193 s2cid 37436155 ayers paul w morell christophe de proft frank geerlings paul 5 october 2007 understanding the woodward hoffmann rules by using changes in electron density chemistry a european journal 13 29 8240 8247 doi 10 1002 chem 200700365 pmid 17639522 morell christophe grand andré toro labbé alejandro 1 january 2005 new dual descriptor for chemical reactivity the journal of physical chemistry a 109 1 205 212 bibcode 2005jpca 109 205m doi 10 1021 jp046577a hdl 10533 176692 pmid 16839107 farahani pooria baader wilhelm j 2017 02 16 unimolecular decomposition mechanism of 1 2 dioxetanedione concerted or biradical that is the question the journal of physical chemistry a 121 6 1189 1194 bibcode 2017jpca 121 1189f doi 10 1021 acs jpca 6b10365 issn 1089 5639 pmid 28094939 hickenboth charles r moore jeffrey s white scott r sottos nancy r baudry jerome wilson scott r 2007 biasing reaction pathways with mechanical force nature 446 7134 423 7 bibcode 2007natur 446 423h doi 10 1038 nature05681 pmid 17377579 s2cid 4427747 journal articles understanding the woodward hoffmann rules by using changes in electron density 1 v t e topics in organic reactions addition reaction elimination reaction polymerization reagents rearrangement reaction redox reaction regioselectivity stereoselectivity stereospecificity substitution reaction a value alpha effect annulene anomeric effect antiaromaticity aromatic ring current aromaticity baird s rule baker nathan effect baldwin s rules bema hapothle beta silicon effect bicycloaromaticity bredt s rule bürgi dunitz angle catalytic resonance theory charge remote fragmentation charge transfer complex clar s rule conformational isomerism conjugated system conrotatory and disrotatory curtin hammett principle dynamic binding chemistry edwards equation effective molarity electromeric effect electron rich electron withdrawing group electronic effect electrophile evelyn effect flippin lodge angle free energy relationship grunwald winstein equation hammett acidity function hammett equation george s hammond hammond s postulate homoaromaticity hückel s rule hyperconjugation inductive effect kinetic isotope effect lfer solvent coefficients data page marcus theory markovnikov s rule möbius aromaticity möbius hückel concept more o ferrall jencks plot negative hyperconjugation neighbouring group participation 2 norbornyl cation nucleophile kennedy j p orton passive binding phosphaethynolate polar effect polyfluorene ring strain σ aromaticity spherical aromaticity spiroaromaticity steric effects superaromaticity swain lupton equation taft equation thorpe ingold effect vinylogy walsh diagram woodward hoffmann rules woodward s rules y aromaticity yukawa tsuno equation zaitsev s rule σ bishomoaromaticity list of organic reactions carbon carbon bond forming reactions acetoacetic ester synthesis acyloin condensation aldol condensation aldol reaction alkane metathesis alkyne metathesis alkyne trimerisation alkynylation allan robinson reaction arndt eistert reaction auwers synthesis aza baylis hillman reaction barbier reaction barton kellogg reaction baylis hillman reaction benary reaction bergman cyclization biginelli reaction bingel reaction blaise ketone synthesis blaise reaction blanc chloromethylation bodroux chichibabin aldehyde synthesis bouveault aldehyde synthesis bucherer bergs reaction buchner ring expansion cadiot chodkiewicz coupling carbonyl allylation carbonyl olefin metathesis castro stephens coupling chan rearrangement chan lam coupling claisen condensation claisen rearrangement claisen schmidt condensation combes quinoline synthesis corey fuchs reaction corey house synthesis coupling reaction cross coupling reaction cross dehydrogenative coupling cross coupling partner dakin west reaction darzens reaction diels alder reaction doebner reaction wulff dötz reaction ene reaction enyne metathesis ethenolysis favorskii reaction ferrier carbocyclization friedel crafts reaction fujimoto belleau reaction fujiwara moritani reaction fukuyama coupling gabriel colman rearrangement gattermann reaction glaser coupling grignard reaction grignard reagent hammick reaction heck reaction henry reaction heterogeneous metal catalyzed cross coupling high dilution principle hiyama coupling homologation reaction horner wadsworth emmons reaction hydrocyanation hydrovinylation hydroxymethylation ivanov reaction johnson corey chaykovsky reaction julia olefination julia kocienski olefination kauffmann olefination knoevenagel condensation knorr pyrrole synthesis kolbe schmitt reaction kowalski ester homologation kulinkovich reaction kumada coupling liebeskind srogl coupling malonic ester synthesis mannich reaction mcmurry reaction meerwein arylation methylenation michael reaction minisci reaction mizoroki heck vs reductive heck nef isocyanide reaction nef synthesis negishi coupling nierenstein reaction nitro mannich reaction nozaki hiyama kishi reaction olefin conversion technology olefin metathesis palladium nhc complex passerini reaction peterson olefination pfitzinger reaction piancatelli rearrangement pinacol coupling reaction prins reaction quelet reaction ramberg bäcklund reaction rauhut currier reaction reformatsky reaction reimer tiemann reaction rieche formylation ring closing metathesis robinson annulation sakurai reaction seyferth gilbert homologation shapiro reaction sonogashira coupling stetter reaction stille reaction stollé synthesis stork enamine alkylation suzuki reaction takai olefination thermal rearrangement of aromatic hydrocarbons thorpe reaction ugi reaction ullmann reaction wagner jauregg reaction weinreb ketone synthesis wittig reaction wurtz reaction wurtz fittig reaction zincke suhl reaction homologation reactions arndt eistert reaction hooker reaction kiliani fischer synthesis kowalski ester homologation methoxymethylenetriphenylphosphorane seyferth gilbert homologation wittig reaction olefination reactions bamford stevens reaction barton kellogg reaction boord olefin synthesis chugaev elimination cope reaction corey winter olefin synthesis dehydrohalogenation elimination reaction grieco elimination hofmann elimination horner wadsworth emmons reaction hydrazone iodination julia olefination julia kocienski olefination kauffmann olefination mcmurry reaction peterson olefination ramberg bäcklund reaction shapiro reaction takai olefination wittig reaction carbon heteroatom bond forming reactions azo coupling bartoli indole synthesis boudouard reaction cadogan sundberg indole synthesis diazonium compound esterification grignard reagent haloform reaction hegedus indole synthesis hurd mori 1 2 3 thiadiazole synthesis kharasch sosnovsky reaction knorr pyrrole synthesis leimgruber batcho indole synthesis mukaiyama hydration nenitzescu indole synthesis oxymercuration reaction reed reaction schotten baumann reaction ullmann condensation williamson ether synthesis yamaguchi esterification degradation reactions barbier wieland degradation bergmann degradation edman degradation emde degradation gallagher hollander degradation hofmann rearrangement hooker reaction isosaccharinic acid marker degradation ruff degradation strecker degradation von braun amide degradation weerman degradation wohl degradation organic redox reactions acyloin condensation adkins peterson reaction akabori amino acid reaction alcohol oxidation algar flynn oyamada reaction amide reduction andrussow process angeli rimini reaction aromatization autoxidation baeyer villiger oxidation barton mccombie deoxygenation bechamp reduction benkeser reaction bergmann degradation birch reduction bohn schmidt reaction bosch reaction bouveault blanc reduction boyland sims oxidation cannizzaro reaction carbonyl reduction clemmensen reduction collins oxidation corey itsuno reduction corey kim oxidation corey winter olefin synthesis criegee oxidation dakin oxidation davis oxidation deoxygenation dess martin oxidation dna oxidation elbs persulfate oxidation emde degradation eschweiler clarke reaction étard reaction fischer tr...