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Química Orgânica Física · Orbitals and pericyclic reactions

Orbitais moleculares e regras de seleção pericíclicas

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  • 2-Pirona + DMAD

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O que você vai aprender

  • Build Hückel π molecular orbitals for chains and rings, count their nodes, and use their energies to judge delocalisation, aromaticity and antiaromaticity.
  • Predict whether an electrocyclic reaction is conrotatory or disrotatory from its electron count and whether it is run thermally or photochemically, and translate the rotation into product stereochemistry.
  • Apply Woodward–Hoffmann and frontier-orbital reasoning to cycloadditions: allowed and forbidden combinations, stereospecificity, the endo rule and regiochemistry from orbital coefficients.
  • Classify sigmatropic and cheletropic reactions by order and electron count and predict their suprafacial or antarafacial geometry and stereochemical outcome.

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Hückel molecular orbitals

In Hückel theory each sp² carbon contributes one p orbital, every orbital has the Coulomb energy α, and neighbouring orbitals interact with the resonance integral β (β < 0, so α + β lies below α). An open chain of N carbons has levels α + 2β cos(kπ/(N + 1)), k = 1…N. Ethylene gives α ± β; the allyl system gives α + √2β, α and α − √2β; butadiene gives α ± 1.618β and α ± 0.618β. The k-th orbital has k − 1 nodes, so each step up in energy adds one node. Delocalisation energy is the π energy of the conjugated system minus that of isolated π bonds: the allyl cation has 2(α + √2β) against 2(α + β) for an ethylene plus an empty p orbital, a gain of 0.83|β|.

Rings: aromatic, antiaromatic, nonaromatic

A ring of N carbons has levels α + 2β cos(2πk/N). Drawing the polygon point-down inside a circle (the Frost circle) shows one lowest orbital and then degenerate pairs. Filling them, 4n + 2 π electrons close a shell with every bonding orbital full: the cyclic array is aromatic (benzene 6α + 8β, 2|β| below three ethylenes). With 4n electrons the last two electrons sit singly in a degenerate nonbonding pair: square cyclobutadiene has 4α + 4β, no better than two ethylenes, and is antiaromatic. The rule applies only to planar, fully conjugated rings; a ring that can pucker, such as tub-shaped cyclooctatetraene, escapes and is nonaromatic. The cyclopropenyl cation (2 π electrons) and the cyclopentadienyl anion (6) are aromatic; the cyclopentadienyl cation (4) is antiaromatic.

Frontier orbitals and the selection rules

A concerted pericyclic reaction is allowed when its frontier orbitals overlap in phase where new bonds form. In the ground state (thermal reaction) the controlling orbital is the HOMO; light promotes one electron to the former LUMO, which becomes the new HOMO and has the opposite symmetry at the termini. The compact Woodward–Hoffmann statement: a thermal reaction is allowed when the total number of suprafacial 4q + 2 components plus antarafacial 4r components is odd. Light reverses every prediction. Always state both the electron count and the conditions (heat, Δ, or light, hν) before deciding the geometry.

Electrocyclic reactions

Count the π electrons that take part. Thermal: 4n electrons rotate conrotatory, 4n + 2 disrotatory. Photochemical: 4n disrotatory, 4n + 2 conrotatory. Then follow the terminal substituents: when both terminal groups point outward (an E,…,E polyene), conrotation puts them trans on the new ring and disrotation puts them cis. Heating (2E,4Z,6E)-octa-2,4,6-triene (6 electrons, disrotatory) gives cis-5,6-dimethylcyclohexa-1,3-diene; heating trans-3,4-dimethylcyclobutene (4 electrons, conrotatory) gives (2E,4E)-hexa-2,4-diene. When two conrotatory or two disrotatory senses are possible, substituents choose: donors rotate outward, π-acceptors such as CHO can rotate inward (torquoselectivity). Cations and anions count the same way: the pentadienyl cation of the Nazarov cyclisation is a 4-electron, thermally conrotatory system.

Cycloadditions: allowed pairs, endo and regiochemistry

With both components reacting on one face (suprafacial), a [4 + 2] cycloaddition (6 electrons) and a [3 + 2] dipolar cycloaddition (6 electrons) are thermally allowed, and a [2 + 2] (4 electrons) is thermally forbidden but photochemically allowed. Ketenes are the classic exception: they add to alkenes thermally, classically explained by the ketene acting as the antarafacial partner ([π2s + π2a]). In a Diels–Alder reaction both partners react suprafacially, so geometry is kept: a trans dienophile gives trans ring substituents. In normal-demand reactions the diene HOMO meets the dienophile LUMO; electron-withdrawing groups on the dienophile and donors on the diene narrow the gap and speed the reaction, and a Lewis acid on the dienophile carbonyl lowers its LUMO further. The terminus with the larger HOMO coefficient bonds to the dienophile carbon with the larger LUMO coefficient: 1-donor dienes give 'ortho' (1,2) and 2-donor dienes 'para' (1,4) adducts. Kinetic Diels–Alder products are usually endo, the activating group tucked under the diene, favoured by secondary orbital and electrostatic interactions even though the exo adduct is more stable.

Sigmatropic and cheletropic shifts

A [i,j] sigmatropic shift moves a σ bond across i and j atoms; count the electrons in the cyclic array. Hydrogen can only migrate suprafacially in short chains, so the thermal [1,5]-H shift (6 electrons) is fast while the thermal [1,3]-H shift (4 electrons, would need antarafacial) is not seen; the [1,7]-H shift (8 electrons) is thermally antarafacial, possible because the triene coils into a helix. [3,3] shifts (Cope, Claisen) are 6-electron, suprafacial on both allyl units and prefer a chair transition state that converts alkene geometry into predictable stereochemistry; [2,3] shifts (Wittig, Mislow–Evans) pass through a five-membered envelope. Cheletropic extrusion of SO₂ from a 3-sulfolene is the reverse of a cycloaddition onto one atom and is thermally allowed with disrotatory motion of the diene termini.

What to carry forward

Every pericyclic prediction has three inputs: the number of electrons in the cyclic array, whether the reaction is thermal or photochemical, and the suprafacial or antarafacial geometry each component can reach. Hückel orbitals tell you the phases at the termini, and frontier-orbital energies and coefficients then explain rate, regiochemistry and the endo preference.

Problemas de prática (40)

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Desenhe o mecanismo 12

Sigmatropic and cheletropic shifts

  • Claisen rearrangement of 1-(allyloxy)cyclohex-1-eneDraw the three arrows of the [3,3]-sigmatropic Claisen rearrangement of 1-(allyloxy)cyclohex-1-ene to 2-allylcyclohexanone and identify the six-atom array.
  • Cope rearrangement of cis-1,2-divinylcyclopropaneDraw the [3,3]-sigmatropic rearrangement of cis-1,2-divinylcyclopropane to cyclohepta-1,4-diene and explain why it needs the cis isomer and a boat-like transition state.
  • [1,5]-Hydrogen shift in 5-methylcyclopenta-1,3-dieneDraw the suprafacial [1,5]-hydrogen shift that converts 5-methylcyclopenta-1,3-diene into 1-methylcyclopenta-1,3-diene and state why it is thermally allowed.
  • Mislow–Evans rearrangement of phenyl hex-1-en-3-yl sulfoxideDraw the [2,3]-sigmatropic rearrangement of an allylic sulfoxide to a sulfenate ester, its cleavage by trimethyl phosphite, the protonation that gives (E)-hex-2-en-1-ol and the dealkylation that turns the phosphorus by-product into a neutral phosphorothioate.
  • Cheletropic loss of SO2 from 3-sulfoleneDraw the three arrows of the thermal cheletropic extrusion of SO2 from 3-sulfolene that releases buta-1,3-diene.

Cycloadditions and FMO control

  • 1,3-Dipolar cycloaddition of diazomethane with methyl acrylateDraw the concerted 1,3-dipolar cycloaddition of diazomethane with methyl acrylate and use frontier-orbital coefficients to show why the ester ends up on the ring carbon bonded to nitrogen.
  • Diels–Alder reaction of furan with dimethyl acetylenedicarboxylateDraw the three arrows of the Diels–Alder reaction of furan with dimethyl acetylenedicarboxylate that give the oxygen-bridged bicyclic diester.
  • Diels–Alder reaction of 2-methoxybuta-1,3-diene with methyl vinyl ketoneDraw the three arrows of the Diels–Alder reaction of 2-methoxybuta-1,3-diene with methyl vinyl ketone and use frontier-orbital coefficients to place the acetyl group 1,4 to the methoxy group.
  • Diels–Alder reaction of (E)-penta-1,3-diene with acrylonitrileDraw the Diels–Alder reaction of (E)-penta-1,3-diene with acrylonitrile and explain the 'ortho' regiochemistry of 2-methylcyclohex-3-ene-1-carbonitrile from frontier-orbital coefficients.
  • Diels–Alder reaction of 2-pyrone with DMAD and loss of CO2Draw the Diels–Alder reaction of 2H-pyran-2-one with dimethyl acetylenedicarboxylate and the retro-Diels–Alder extrusion of CO2 that gives dimethyl phthalate.

Electrocyclic reactions

  • Nazarov cyclisation of 2,4-dimethylpenta-1,4-dien-3-oneDraw the acid-promoted Nazarov cyclisation of 2,4-dimethylpenta-1,4-dien-3-one: protonation to the hydroxypentadienyl cation, the 4-electron conrotatory ring closure, elimination and tautomerisation to 2,5-dimethylcyclopent-2-en-1-one.
  • Thermal disrotatory ring closure of (2E,4Z,6E)-octa-2,4,6-trieneDraw the three arrows of the thermal 6-electron electrocyclic ring closure of (2E,4Z,6E)-octa-2,4,6-triene and decide which diastereomer of 5,6-dimethylcyclohexa-1,3-diene the disrotatory motion produces.

Preveja o produto 9

Hückel orbitals and aromaticity

  • Which ring of azulene is negative?Predict the direction of the dipole in a nonalternant hydrocarbon from the aromaticity of its charge-separated contributor.

Sigmatropic and cheletropic shifts

  • [2,3]-Wittig rearrangement of a benzyl crotyl etherPredict the product of a [2,3]-Wittig rearrangement and distinguish it from the [1,2]-Wittig product by its allylic transposition.
  • Alkene geometry from a chair ClaisenPredict the alkene geometry formed in a Claisen rearrangement from the preferred chair transition state.

Cycloadditions and FMO control

  • Regiochemistry with Danishefsky's dienePredict the regiochemistry of a Diels–Alder reaction of a doubly donor-substituted diene from its largest HOMO coefficient.
  • Butadiene and dimethyl fumaratePredict the ring stereochemistry of a Diels–Alder adduct from the alkene geometry of the dienophile.

Electrocyclic reactions

  • Thermal closure of an 8-electron tetraenePredict the rotational mode and relative stereochemistry of a thermal 8-electron electrocyclisation.
  • Heat (2E,4Z,6Z)-octatrienePredict the relative stereochemistry when a triene with one inward- and one outward-pointing terminal substituent closes thermally.
  • Irradiate (2E,4Z,6E)-octatrienePredict the photochemical 6-electron electrocyclic product of an E,Z,E-triene and its relative stereochemistry.
  • Heat trans-3,4-dimethylcyclobutenePredict the diene geometry from the thermal conrotatory opening of a trans-disubstituted cyclobutene.

Classificar 3

Hückel orbitals and aromaticity

  • Which ring is aromatic?Classify cyclic conjugated ions and neutral rings as aromatic, antiaromatic or nonaromatic from their π-electron count and planarity.

Cycloadditions and FMO control

  • Can two alkenes join thermally?Classify a suprafacial–suprafacial [2 + 2] cycloaddition as thermally forbidden or allowed and justify it with frontier orbitals.

Sigmatropic and cheletropic shifts

  • Classify the previtamin D shiftClassify a thermal hydrogen shift by order, electron count and facial geometry.

Comparar 2

Cycloadditions and FMO control

  • Rank dienophiles by Diels–Alder rateRank dienophiles by Diels–Alder rate with cyclopentadiene and relate the order to LUMO lowering by electron-withdrawing groups.

Hückel orbitals and aromaticity

  • Rank cyclic hydrocarbons by acidityRank cyclic hydrocarbons by C–H acidity using aromaticity of the conjugate base and benzo-fusion effects.

Calcular 5

Hückel orbitals and aromaticity

  • Delocalisation energy of the allyl cationCompute a Hückel delocalisation energy by comparing a conjugated cation with an isolated π bond plus an empty p orbital.
  • HOMO–LUMO gap of butadieneCalculate the Hückel HOMO–LUMO gap of buta-1,3-diene and compare it with that of ethylene.
  • Nodes in the HOMO of hexatrieneCount the nodes in the ground-state HOMO of a linear conjugated triene from its Hückel orbital number.

Sigmatropic and cheletropic shifts

  • Count bullvalene's valence tautomersCount the degenerate Cope valence tautomers of bullvalene using its rotational symmetry.

Cycloadditions and FMO control

  • Energy gap behind a 9:1 endo:exo ratioConvert a kinetically controlled endo:exo product ratio into the difference in activation free energy.

Encontre o erro 1

  • Find the error in a ring-opening predictionDiagnose a misapplied Woodward–Hoffmann rule in a thermal 6-electron electrocyclic ring opening.

Interprete as evidências 1

  • Read the Frost circle of cyclobutadieneInterpret the Frost-circle orbital diagram of square cyclobutadiene to explain its antiaromaticity and distortion.

Planeje uma síntese 1

  • Choose a Claisen variant for an esterChoose the Claisen variant that converts an allylic alcohol directly into a γ,δ-unsaturated ester.

Explique por quê 6

Cycloadditions and FMO control

  • Why is the endo adduct formed faster?Explain the kinetic endo preference of Diels–Alder reactions with carbonyl-activated dienophiles using frontier-orbital overlap.
  • Why do ketenes undergo thermal [2 + 2] reactions?Explain why ketenes undergo thermal [2 + 2] cycloadditions that are forbidden for ordinary alkenes.

Electrocyclic reactions

  • Which way does a formyl group rotate?Explain torquoselectivity: why a π-acceptor substituent rotates inward during a conrotatory cyclobutene opening.
  • Why light reverses the electrocyclic ruleExplain why photochemical electrocyclic reactions follow the opposite rotational mode to thermal ones, using the frontier orbital of the excited state.

Sigmatropic and cheletropic shifts

  • Why [1,5] but not [1,3] hydrogen shifts?Explain why thermal [1,5]-hydrogen shifts occur readily while thermal [1,3]-hydrogen shifts are not observed.

Hückel orbitals and aromaticity

  • Why is [10]annulene not aromatic?Explain why a ring with a 4n + 2 π count can still fail to be aromatic and how bridging restores aromaticity.

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