Electrocyclic reactions: orbital symmetry rules and ring opening/closing

Intuition Beginner

Some reactions open or close a ring in a single concerted step. No intermediate forms. The pi electrons in a conjugated system reorganise into a sigma bond (ring closure) or a sigma bond breaks to extend the conjugation (ring opening). These are electrocyclic reactions. The simplest example: 1,3-butadiene cyclises to cyclobutene, and cyclobutene opens back to butadiene.

The striking feature is stereochemical control. When a substituted cyclobutene opens to a diene, the two substituents on the breaking ring can rotate in the same direction (conrotatory) or in opposite directions (disrotatory). The outcome is not random. It depends on two things: how many pi electrons are involved and whether the reaction is thermal or photochemical. The Woodward-Hoffmann rules predict the correct mode every time.

A thermal reaction with 4 pi electrons (cyclobutene to butadiene) proceeds conrotatory. A thermal reaction with 6 pi electrons (1,3,5-hexatriene to cyclohexadiene) proceeds disrotatory. Photochemical conditions reverse each prediction. These rules are among the most powerful in organic chemistry because they predict stereochemical outcomes from first principles, not from empirical observation.

Visual Beginner

The terminal p-orbitals of the open-chain polyene must rotate to form the new sigma bond at the ring junction. Conrotatory motion means both ends rotate in the same sense (both clockwise or both counterclockwise). Disrotatory motion means they rotate in opposite senses. The Woodward-Hoffmann rules select one mode over the other based on the number of electrons and the reaction conditions.

Worked example Beginner

Problem: Predict the stereochemistry of the product when trans-3,4-dimethylcyclobutene undergoes thermal ring opening.

Solution:

Cyclobutene has 4 pi electrons (one double bond plus the breaking sigma bond). The Woodward-Hoffmann rule for 4n electrons (n=1) under thermal conditions predicts conrotatory ring opening.

In trans-3,4-dimethylcyclobutene, the two methyl groups are on opposite faces of the ring. Conrotatory motion rotates both methylene termini in the same direction. Because the methyl groups start on opposite faces, conrotatory opening places them on the same side of the newly formed diene at one terminus and on opposite sides at the other. The product is (E,Z)-2,4-hexadiene.

If the reaction were photochemical instead, the selection rule reverses to disrotatory. Disrotatory opening of the same substrate would give (E,E)-2,4-hexadiene. This stereochemical switch, confirmed experimentally, is one of the strongest pieces of evidence supporting the Woodward-Hoffmann rules.

Check your understanding Beginner

Formal definition Intermediate+

An electrocyclic reaction is a pericyclic process in which a conjugated polyene with k pi electrons converts to a cyclic product with k-2 pi electrons and one new sigma bond (ring closure), or the reverse (ring opening). The reaction is concerted: all bond changes occur simultaneously through a cyclic array of overlapping p-orbitals at the termini.

Woodward-Hoffmann selection rules for electrocyclic reactions. The mode of ring closure (conrotatory or disrotatory) is determined by the number of pi electrons and the thermal vs photochemical conditions:

Electron count	Thermal	Photochemical
4n	Conrotatory	Disrotatory
4n+2	Disrotatory	Conrotatory

For ring opening, the same rules apply in reverse: the open-chain product's stereochemistry is determined by the conrotatory or disrotatory mode dictated by the electron count and conditions.

Frontier orbital derivation. The selection rule follows from the symmetry of the highest occupied molecular orbital (HOMO) of the open-chain polyene. For a thermal reaction, the HOMO is the ground-state HOMO. For a photochemical reaction, an electron is promoted to the next orbital, so the relevant orbital becomes the LUMO of the ground state (now singly occupied). The phase relationship between the terminal lobes of this frontier orbital determines the rotation mode:

• If the terminal lobes have the same phase, bonding overlap during ring closure requires disrotatory rotation.
• If the terminal lobes have opposite phases, bonding overlap requires conrotatory rotation.

For butadiene (4 pi electrons), the HOMO has terminal lobes of opposite phase. Thermal closure is conrotatory. The photochemical frontier orbital (the next orbital up) has terminal lobes of the same phase, giving disrotatory closure.

For hexatriene (6 pi electrons), the HOMO has terminal lobes of the same phase. Thermal closure is disrotatory. The photochemical frontier orbital has opposite phases, giving conrotatory closure.

Correlation diagram approach. Woodward and Hoffmann's original derivation used orbital correlation diagrams. The molecular orbitals of the reactant (open-chain polyene) are classified as symmetric (S) or antisymmetric (A) with respect to the symmetry element preserved during the reaction: a C2 rotation axis for conrotatory processes, or a mirror plane for disrotatory processes. The orbitals of the product are similarly classified. Lines connect reactant orbitals to product orbitals of the same symmetry, ordered by energy. If all occupied reactant orbitals correlate with occupied product orbitals, the reaction is symmetry-allowed under that mode. If an occupied reactant orbital correlates with an unoccupied product orbital, the reaction is symmetry-forbidden under that mode.

For the conrotatory opening of cyclobutene to butadiene (4 pi electrons, thermal), the C2 symmetry element is preserved. Under C2 symmetry, all occupied orbitals of the reactant correlate with occupied orbitals of the product: conrotatory opening is symmetry-allowed. Under the mirror plane (disrotatory mode), the highest occupied reactant orbital correlates with an unoccupied product orbital: disrotatory opening is symmetry-forbidden thermally.

Thermodynamic and kinetic considerations. Electrocyclic reactions are generally reversible. The position of equilibrium depends on ring strain, conjugation stabilisation, and substituent effects. Cyclobutene ring opening is strongly favoured because it relieves ring strain and produces a conjugated diene. Hexatriene ring closure to cyclohexadiene is less favoured because cyclohexadiene retains significant conjugation and the ring product loses one double bond. Photochemical electrocyclic reactions are typically irreversible because the excited-state reactant relaxes to a ground-state product.

Key results Intermediate+

1. Thermal ring opening of cyclobutenes. Cyclobutene opens to 1,3-butadiene in a conrotatory fashion. Trans-3,4-dimethylcyclobutene gives (E,Z)-2,4-hexadiene; cis-3,4-dimethylcyclobutene gives (E,E)-2,4-hexadiene. The activation energy for the parent cyclobutene is approximately 35 kcal/mol. The reaction relieves approximately 26 kcal/mol of ring strain.

2. Thermal ring closure of hexatrienes. 1,3,5-Hexatriene (6 pi electrons, 4n+2) closes thermally in a disrotatory fashion to give cis-5,6-disubstituted 1,3-cyclohexadienes when the substituents on both termini are on the same face. The activation barrier is approximately 30 kcal/mol. The ring-closed product is a 1,3-cyclohexadiene.

3. Photochemical reversal. Photochemical electrocyclic reactions follow the opposite selection rule: 4n systems close disrotatory, 4n+2 systems close conrotatory. The photochemical ring opening of cyclobutene is disrotatory. The photochemical ring opening of cyclohexadiene (vitamin D biosynthesis) is conrotatory. The switch occurs because the relevant frontier orbital changes from the ground-state HOMO to the excited-state singly occupied orbital.

4. Vitamin D biosynthesis. 7-Dehydrocholesterol undergoes photochemical conrotatory ring opening in the skin upon UVB irradiation to give previtamin D3. This 6 pi electron system opens conrotatory under photochemical conditions (the reverse of the thermal disrotatory rule). The previtamin D3 then undergoes a thermal [1,7]-sigmatropic hydrogen shift to form vitamin D3 (cholecalciferol). This two-step pericyclic sequence is the biosynthetic pathway for vitamin D in humans.

Exercises Intermediate+

Frontier orbital analysis in detail Master

The frontier molecular orbital approach to electrocyclic reactions examines the phase relationships of the highest occupied orbital at the two reacting termini. For a linear polyene with k pi orbitals, the orbital coefficients and phases follow the particle-in-a-box pattern. The i-th molecular orbital has i-1 nodes, and the sign of the terminal coefficients alternates with each successive orbital.

For butadiene (4 pi electrons, 4 MOs):

• psi-1 (0 nodes): + + + + (same sign at both ends)
• psi-2 (1 node, HOMO): + - + - (opposite sign at the ends)
• psi-3 (2 nodes, LUMO): + - - + (same sign at both ends)
• psi-4 (3 nodes): + + - - (opposite sign at the ends)

The thermal reaction uses psi-2 (HOMO). Opposite signs at the termini require conrotatory rotation to achieve bonding overlap. The photochemical reaction uses psi-3 (the orbital reached by excitation). Same signs at the termini require disrotatory rotation.

For hexatriene (6 pi electrons, 6 MOs):

• psi-1 (0 nodes): + + + + + +
• psi-2 (1 node): + + - - - + (or equivalent)
• psi-3 (2 nodes, HOMO): + - + - + - or + + - - + + depending on convention. The key point: terminal lobes have the same sign.

Same signs at the termini of psi-3 require disrotatory rotation for thermal closure. The photochemical frontier orbital (psi-4) has opposite signs at the termini, requiring conrotatory closure.

This pattern generalises. For the ground-state HOMO of a polyene with 4n pi electrons, the terminal lobes always have opposite phases, giving conrotatory thermal closure. For 4n+2 pi electrons, the ground-state HOMO has the same phase at both termini, giving disrotatory thermal closure. The alternation follows from the nodal structure imposed by the quantum mechanical boundary conditions on the linear polyene.

Correlation diagrams for electrocyclic reactions. The correlation diagram approach provides a complete account of all electrons in the system, not just the frontier pair. The procedure is:

1. Identify the symmetry element preserved during the reaction. For conrotatory processes, a C2 rotation axis is maintained. For disrotatory processes, a mirror plane is maintained.

2. Classify all molecular orbitals of the reactant and product as symmetric (S) or antisymmetric (A) under the preserved symmetry operation.

3. Draw correlation lines connecting reactant orbitals to product orbitals of the same symmetry, ordered by energy (lowest to lowest, next to next, etc.).

4. Check whether all occupied reactant orbitals correlate with occupied product orbitals. If yes, the reaction is symmetry-allowed under that mode. If any occupied reactant orbital correlates with a vacant product orbital (or vice versa), a symmetry-imposed barrier exists and the reaction is thermally forbidden.

For conrotatory opening of cyclobutene (C2 symmetry):

• sigma(C2-S) correlates with psi-1(S): occupied to occupied.
• pi(C2-A) correlates with psi-2(A): occupied to occupied.
• pi*(C2-S) correlates with psi-3(S): vacant to vacant.
• sigma*(C2-A) correlates with psi-4(A): vacant to vacant.

All occupied orbitals correlate with occupied product orbitals. Conrotatory opening is thermally allowed.

For disrotatory opening of cyclobutene (mirror plane symmetry):

• sigma(S) correlates with psi-1(S): occupied to occupied.
• pi(S) correlates with psi-4(S): occupied to vacant. Symmetry-imposed barrier.

Disrotatory opening is thermally forbidden because the occupied pi orbital of cyclobutene correlates with the unoccupied psi-4 of butadiene.

The photochemical reversal follows because electronic excitation changes which orbitals are occupied. In the excited state, an electron occupies pi* (which correlates with psi-3 in the disrotatory pathway). The previously problematic correlation (pi to psi-4) is alleviated because psi-4 is now closer in energy to the excited state. The precise treatment requires state correlation diagrams, but the net result is that the photochemical selection rule reverses the thermal rule.

The Dewar-Zimmerman aromatic transition state approach. An alternative formulation treats the electrocyclic transition state as a cyclic array of overlapping p-orbitals and evaluates whether this array is aromatic or antiaromatic. For conrotatory closure, the overlap pattern creates a Mobius topology (one phase inversion in the cycle). For disrotatory closure, the overlap creates a Huckel topology (zero phase inversions).

A Mobius system with 4n electrons is aromatic (stabilised) and a Mobius system with 4n+2 electrons is antiaromatic (destabilised). A Huckel system with 4n+2 electrons is aromatic and with 4n electrons is antiaromatic. Therefore:

• 4n electrons + conrotatory (Mobius) = aromatic = allowed thermally.
• 4n electrons + disrotatory (Huckel) = antiaromatic = forbidden thermally.
• 4n+2 electrons + disrotatory (Huckel) = aromatic = allowed thermally.
• 4n+2 electrons + conrotatory (Mobius) = antiaromatic = forbidden thermally.

This reproduces the Woodward-Hoffmann rules from a single principle: the pericyclic transition state must be aromatic. The Dewar-Zimmerman approach is computationally convenient because it requires only counting phase inversions and electrons, without constructing full correlation diagrams.

Photochemical electrocyclic reactions. The photochemical selection rules reverse the thermal rules because electronic excitation changes the orbital occupation. In the excited state, one electron occupies a higher orbital that was previously vacant. This changes the frontier orbital from the ground-state HOMO to an orbital with different symmetry at the termini. The practical consequence is that the allowed mode switches: 4n systems become disrotatory and 4n+2 systems become conrotatory.

Photochemical electrocyclic reactions are central to several biological processes and synthetic applications. The most important biological example is vitamin D biosynthesis: 7-dehydrocholesterol undergoes photochemical conrotatory ring opening in the skin upon UVB irradiation. The 6 pi electron B-ring of the steroid opens conrotatory (the photochemical mode for 4n+2 systems) to give previtamin D3 with defined stereochemistry. Without the Woodward-Hoffmann rules, the stereochemical outcome of this photoreaction would be difficult to predict.

In synthetic chemistry, photochemical electrocyclic reactions enable ring closures that are thermally forbidden. A thermal 4n disrotatory closure is forbidden, but the photochemical version is allowed. This is exploited in the synthesis of strained ring systems where the thermal pathway would give the wrong stereochemistry or no reaction at all.

Nazarov cyclisation. The Nazarov cyclisation is the electrocyclic ring closure of a pentadienyl cation, forming a cyclopentenyl cation. The reaction is a 4 pi electron electrocyclic process and proceeds conrotatory under thermal conditions. The pentadienyl cation is typically generated by Lewis acid activation of a divinyl ketone. The resulting oxyallyl cation can be trapped by nucleophiles or undergo further electrocyclic processes. The Nazarov cyclisation is one of the most powerful methods for constructing cyclopentenones and has been extensively developed in total synthesis.

Modern variants include the asymmetric Nazarov cyclisation (using chiral Lewis acids to control the facial selectivity of the conrotatory closure), the interrupted Nazarov (trapping the oxyallyl cation with an internal nucleophile), and the Nazarov-type cyclisation of allenyl ketones (which proceeds through a different electron count). The silicon-directed Nazarov uses a silyl substituent to control regiochemistry and trap the product as a silyl enol ether.

Computational studies. High-level computational studies (CCSD(T)/cc-pVTZ and B3LYP/6-311+G**) have confirmed the concerted nature of electrocyclic reactions and the accuracy of the Woodward-Hoffmann predictions. The calculated activation barriers reproduce experimental values within 2-3 kcal/mol for most systems. The transition state for cyclobutene ring opening has C2 symmetry (conrotatory) with C-C bond distances of approximately 2.0 angstroms at the forming/breaking bonds.

Dynamic effects have been observed in electrocyclic reactions of highly substituted systems. Trajectory calculations by Carpenter and coworkers show that some electrocyclic reactions do not follow the minimum energy pathway predicted by the Woodward-Hoffmann rules. Instead, the reaction trajectory on the potential energy surface is influenced by momentum (nonstatistical dynamics), leading to product ratios that deviate from the predicted Woodward-Hoffmann selectivity. These dynamic effects are most pronounced in reactions with very low barriers (less than 5 kcal/mol) and in systems where the conrotatory and disrotatory transition states are close in energy. The observation of nonstatistical dynamics does not invalidate the Woodward-Hoffmann rules but demonstrates that orbital symmetry is one of several factors governing reaction outcomes.

Ultrafast spectroscopy has directly observed the ring opening of cyclohexadiene to hexatriene, measuring a reaction time of approximately 80 femtoseconds. This confirms the concerted nature of the process: the ring opens faster than a single molecular vibration, leaving no time for intermediates to form. The observation of such fast electrocyclic reactions supports the notion that the orbital symmetry conservation is an intrinsic property of the electronic structure, not a kinetic effect that depends on temperature or concentration.

Connections Master

• Radical and pericyclic reactions 15.08.01. Electrocyclic reactions are one of the three major classes of pericyclic reactions introduced in 15.08.01, alongside cycloadditions and sigmatropic rearrangements. All three are unified by the Woodward-Hoffmann rules and the conservation of orbital symmetry.

• Diels-Alder cycloaddition 15.05.03 pending. The Diels-Alder reaction is a [4+2] cycloaddition involving the same 4n+2 electron count as the hexatriene electrocyclic ring closure. Both proceed through Huckel-aromatic transition states under thermal conditions. The orbital symmetry analysis is topologically analogous.

• Sigmatropic rearrangements 15.08.02 pending. The vitamin D biosynthetic pathway combines an electrocyclic ring opening (this unit) with a [1,7]-sigmatropic hydrogen shift (15.08.02). Both steps are governed by the Woodward-Hoffmann rules and proceed with defined stereochemistry predicted by orbital symmetry.

• Stereochemistry 15.01.03. Electrocyclic reactions produce new stereocentres whose configuration is entirely determined by the conrotatory or disrotatory mode. The stereospecificity of electrocyclic reactions is one of the clearest demonstrations of how orbital symmetry controls three-dimensional molecular structure.

• Conjugated systems 15.02.01. Electrocyclic reactions interconvert conjugated polyenes and cyclic dienes. Understanding the stability and reactivity of conjugated systems provides the thermodynamic context for whether ring opening or ring closure is favoured at equilibrium.

• Photochemistry and vitamin D biosynthesis. The photochemical electrocyclic ring opening of 7-dehydrocholesterol to previtamin D3 is the rate-limiting step in vitamin D biosynthesis in human skin. Deficiency in UV exposure (or excessive sunscreen use) prevents this electrocyclic reaction, leading to vitamin D deficiency. The Woodward-Hoffmann rules predict that the conrotatory mode gives a specific stereochemistry essential for the subsequent enzymatic [1,7]-hydrogen shift.

• Photochromic materials. Diarylethenes undergo reversible photochemical electrocyclic ring closure, switching between an open (colourless) and closed (coloured) form. This reversible switching is used in optical data storage, molecular electronics, and smart windows. The photochemical ring closure is conrotatory (6 pi electrons, photochemical = conrotatory), and the thermal stability of the closed form prevents spontaneous reversion.

• Nazarov cyclisation in synthesis. The Nazarov cyclisation is a powerful method for constructing cyclopentenones, a structural motif found in many natural products (prostaglandins, jasmonates, quadrone). The conrotatory stereochemistry controls the relative configuration of up to four new stereocentres in a single step.

Historical notes Master

The electrocyclic ring opening of cyclohexadiene to hexatriene was first studied systematically by Vogel in the 1950s. Vogel observed that the thermal ring opening of 1,3-cyclohexadiene gave hexatriene with defined stereochemistry, but the significance of the stereochemical outcome was not recognised until the Woodward-Hoffmann rules provided the theoretical framework.

Woodward and Hoffmann published their analysis of electrocyclic reactions in 1965 as part of their landmark series of five papers in the Journal of the American Chemical Society. They recognised that the stereochemistry of ring opening and closing could be predicted from the symmetry of the molecular orbitals involved. The conrotatory vs disrotatory distinction followed directly from the correlation of occupied orbitals under the appropriate symmetry element (C2 for conrotatory, mirror plane for disrotatory).

The experimental verification came rapidly. Having an and Ullman in 1966 confirmed the conrotatory ring opening of trans-3,4-dimethylcyclobutene to (E,Z)-2,4-hexadiene, exactly as predicted by the Woodward-Hoffmann rules. The photochemical reversal (disrotatory opening of cyclobutene) was also confirmed. These experiments provided some of the strongest evidence for the orbital symmetry rules.

The vitamin D biosynthesis connection was recognised in the late 1960s. Having a good demonstrated that the photochemical ring opening of provitamin D3 proceeds conrotatory, as predicted for a 6 pi electron system under photochemical conditions. This was one of the first applications of the Woodward-Hoffmann rules to a biologically important process and helped establish the rules as a fundamental principle of organic chemistry.

The frontier molecular orbital approach to electrocyclic reactions was developed by Fukui in parallel with the Woodward-Hoffmann correlation diagram approach. Fukui's 1964 paper on orbital symmetry in chemical reactions preceded the Woodward-Hoffmann papers but was less widely recognised until Hoffmann cited Fukui's work. The two approaches give identical predictions but differ in conceptual emphasis: Fukui focused on the frontier orbitals (HOMO and LUMO), while Woodward and Hoffmann considered all occupied orbitals through symmetry correlations.

The Dewar-Zimmerman aromatic transition state approach was developed independently by Dewar and Zimmerman in the late 1960s and early 1970s. This approach unified electrocyclic reactions, cycloadditions, and sigmatropic rearrangements under a single principle: the pericyclic transition state must be aromatic. The Dewar-Zimmerman approach is often preferred in teaching because it is simpler to apply than the full correlation diagram construction.

The Nazarov cyclisation was reported by Nazarov in 1941 but was not fully understood until the Woodward-Hoffmann rules provided the mechanistic framework. The recognition that the Nazarov cyclisation is a 4 pi electrocyclic ring closure of a pentadienyl cation (and therefore conrotatory) came in the late 1960s. Modern developments by Frontier, Tius, and others have transformed the Nazarov cyclisation into a powerful synthetic method with control over regiochemistry and stereochemistry.

Computational studies of electrocyclic reactions began in the 1970s with early ab initio calculations on the ring opening of cyclobutene. These calculations confirmed the Woodward-Hoffmann predictions and provided quantitative barriers. The development of DFT methods in the 1990s made it possible to study larger electrocyclic systems with high accuracy. Trajectory calculations by Carpenter in the 2000s revealed nonstatistical dynamic effects in some electrocyclic reactions, adding nuance to the Woodward-Hoffmann picture without invalidating it.

Bibliography Master

@book{WoodwardHoffmann1970,
  author = {Woodward, Robert Burns and Hoffmann, Roald},
  title = {The Conservation of Orbital Symmetry},
  publisher = {Verlag Chemie},
  year = {1970}
}

@book{McMurry2019,
  author = {McMurry, John},
  title = {Organic Chemistry},
  edition = {10th},
  publisher = {Cengage},
  year = {2019}
}

@book{Clayden2012,
  author = {Clayden, Jonathan and Greeves, Nick and Warren, Stuart},
  title = {Organic Chemistry},
  edition = {2nd},
  publisher = {Oxford University Press},
  year = {2012}
}

@book{Fleming1999,
  author = {Fleming, Ian},
  title = {Pericyclic Reactions},
  publisher = {Oxford University Press},
  year = {1999}
}

@book{CareySundberg2007,
  author = {Carey, Francis A. and Sundberg, Richard J.},
  title = {Advanced Organic Chemistry, Part A: Structure and Mechanisms},
  edition = {5th},
  publisher = {Springer},
  year = {2007}
}

@article{WoodwardHoffmann1965,
  author = {Woodward, Robert Burns and Hoffmann, Roald},
  title = {Stereochemistry of Electrocyclic Reactions},
  journal = {J. Am. Chem. Soc.},
  volume = {87},
  year = {1965},
  pages = {395--397}
}

@article{Fukui1964,
  author = {Fukui, Kenichi},
  title = {A Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons},
  journal = {J. Chem. Phys.},
  volume = {20},
  year = {1952},
  pages = {722--725}
}

@article{Havinga1968,
  author = {Havinga, E.},
  title = {Vitamin {D}, Example and Challenge},
  journal = {Experientia},
  volume = {24},
  year = {1968},
  pages = {110--116}
}

@article{Nazarov1941,
  author = {Nazarov, I. N.},
  title = {The Theory of the Cyclization of Unsaturated Carbonyl Compounds},
  journal = {Bull. Acad. Sci. URSS, Cl. Sci. Chim.},
  year = {1941},
  pages = {210--221}
}

@article{Carpenter1998,
  author = {Carpenter, Barry K.},
  title = {Dynamic Effects on Organic Reactivity: Applications to the Study of Pericyclic Reaction Mechanisms},
  journal = {J. Am. Chem. Soc.},
  volume = {120},
  year = {1998},
  pages = {432--433}
}

@article{Houk1995,
  author = {Houk, Kendall N. and Gonzalez, Javier and Li, Yong},
  title = {Pericyclic Reaction Transition States: Passions and Punctilios, 1935--1995},
  journal = {Acc. Chem. Res.},
  volume = {28},
  year = {1995},
  pages = {81--90}
}

@article{Dewar1966,
  author = {Dewar, Michael J. S.},
  title = {A Molecular Orbital Theory of Organic Chemistry. {VIII}. Aromaticity and Electroyclic Reactions},
  journal = {Tetrahedron},
  volume = {22},
  year = {1966},
  pages = {75--92}
}

@article{Zimmerman1971,
  author = {Zimmerman, Howard E.},
  title = {The Möbius-Hückel Concept in Organic Chemistry. Application of Organic Molecules and Reactions},
  journal = {Acc. Chem. Res.},
  volume = {4},
  year = {1971},
  pages = {272--280}
}

@book{Bachrach2014,
  author = {Bachrach, Steven M.},
  title = {Computational Organic Chemistry},
  edition = {2nd},
  publisher = {Wiley},
  year = {2014}
}

@article{Fuss2002,
  author = {Fuss, Werner and Kompa, Karl L. and Schikarski, Thomas and Trushin, Sergei A.},
  title = {Ultrafast Electrocylic Ring Opening of 1,3-Cyclohexadiene: The Stereospecific Reaction Path and the Ring-Opening Time},
  journal = {J. Phys. Chem. A},
  volume = {106},
  year = {2002},
  pages = {1427--1434}
}

@article{Tius2005,
  author = {Tius, Marcus A.},
  title = {Catalytic Enantioselective Nazarov Cyclizations},
  journal = {Eur. J. Org. Chem.},
  year = {2005},
  pages = {2193--2206}
}

@article{Frontier2007,
  author = {Frontier, Alison J. and Collison, Chris},
  title = {The Nazarov Cyclization in Synthesis: Recent Advances and Future Directions},
  journal = {Tetrahedron},
  volume = {63},
  year = {2007},
  pages = {8789--8814}
}