Conjugated Dienes Theory of Linear and Cyclic Conjugation Chemistry 125: Lecture 55 February 23, 2011 Conjugated Dienes Theory of Linear and Cyclic Conjugation (4n+2) Aromaticity This For copyright notice see final page of this file

When does conjugation make a difference? Experimental Evidence Allylic Cation, Anion, Radical stabilized by ~13 kcal/mole. Allylic SN1/SN2 Transition States also stabilized.

Conjugation worth only ~ 4 kcal/mole Diene Stabilization DHhydrogenation (kcal/mole) -30.2 -29.8 -30.0 -60.0 hexadiene 1,4 cis -58.4 1,4 trans -57.6 1,5 -60.3 2,4 -50.5 cHexdiene 1,4 1,3 -54.9 diff 0.4±0.2 1,4 pentadiene 60.22 -60.4 Conjugation worth only ~ 4 kcal/mole -56.5

ps orthogonal at 90° twist anti syn Torsional Angle (°) 90 180 135 45 90 180 135 45 2 4 6 Energy kcal/mole Central “single-bond” twist gives a 6 kcal barrier (vs. ~ 60 kcal for C=C twist) based on Raman spectroscopy - Engeln, Consalvo, Reuss, Chemical Physics, 160, 427 (1992) ps orthogonal at 90°

Why is conjugation worth more in allylic intermediates than in dienes? Because we can draw reasonable resonance structures? good bad

Conjugation & Aromaticity Theory Simple Hückel MOs http://www.chem.ucalgary.ca/SHMO/index.html e.g. J&F Ch. 12-13

Two Ways to Think about Butadiene  System         4 p-orbitals Secondary mixing is minor (because of poor E-match)   : Averagesame as localized To maximize bonding-orbital overlap the central AOs are large in 1 and small in 2. (~3 kcal/mole max) 4 Delocalized  s or Localized /p* picture Very Little Difference! How different in overall stability?

Two Ways to Think about Butadiene  System 4 p-orbitals           : 4 Delocalized   Why ignore this mixing? Despite better E-match, it does not lower energy. Orthogonal (What is gained at two positions is lost at the others)

Two Ways to Think about Butadiene  System How different in overall stability? Very Little! (~3 kcal/mole max) Localized  bond picture 4 Delocalized   : Although total energies are nearly the same with and without conjugation, there are substantial differences in HOMO & LUMO energies (Reactivity) far UV (167 nm) nearer UV (210 nm) and in HOMO-LUMO gap (Color). :

Is There a Limit to 1 Energy for Long Chains? Overlap per  bond (AO product) 1/2 Number of  bonds 1 Total overlap stabilization 1/2 Chain length 2 Normalized AO size 1/2 4 1/4 1/4 3 3/4 8 1/8 1/8 7 7/8 N.B. We are ignoring the smallish influence of overlap on normalization. Also we are using our own “overlap stabilization” units, which are twice as large as the conventional “” units you will see in texts. N 1/N 1/N N-1 (N-1)/N Yes, the limit is 1, i.e. twice the stabilization of the H2C=CH2  bond. Similarly, the UMO destabilization limit is twice that of the H2C=CH2  MO.

Semicircle Mnemonic for  MO Energy in Conjugated Chains. +1 -1 Radius of circle = 2  stabilization of H2C=CH2 [ limit of ±(N-1)/N ] Place points denoting length of chain evenly along circumference between upper and lower limit (+1 and -1). MO Energy (units of 2) etc. All odd chains have a non-bonding MO with nodes on alternant carbons. It is the locus of the “odd” electron in the radical, and of + (-) charge in the cation (anion). p N=2 ethylene N=3 allyl N=1 an isolated 2p AO N=4 1,3-butadiene As the conjugated chain lengthens, more and more levels are crowded between -1 and +1, and the HOMO-LUMO gap decreases.   (difference is resonance stabilization of butadiene vs. 2 isolated ethylenes) allylic stabilization (vs. isolated p and ) same 2-electron stabilization for cation, radical, anion Color shift toward red.

AROMATICITY Cyclic Conjugation worth ~30 kcal ! ~78 predicted ~22-24 54 26 observed 49 Conjugation worth ~2 kcal 28 Heats of Hydrogenation (kcal/mole) Cf. J&F 13.5a pp. 580-581

Bringing the ends of a conjugated chain together to form a ring gives a lowest  MO with an additional bond. (much more effective than adjusting AO sizes) Lowest MO will have energy = -N/N = -1 In a conjugated ring peripheral nodes must come in even numbers. e.g. cyclopropenyl E = -1 E = +1/2 E = +1/2 0 nodes 2 nodes 2 nodes

Energy Shifts on “Ring Formation” Shifts Alternate (because of node parity). +1 -1 MO Energy (units of 2) unfavorable favorable unfavorable End to End Interaction favorable

On bringing the ends of a chain together, odd-numbered  MOs (1, 3, 5, etc.) decrease in energy (favorable terminal overlap for 0,2,4… nodes), while even-numbered  MOs (2, 4, 6, etc.) increase in energy (unfavorable terminal overlap for 1,3,5… nodes). Thus having an odd number of occupied  MOs (more odd-numbered than even-numbered) insures overall  stabilization of ring (compared to chain). [though there may be strain in the  bonds] Hückel’s Rule: 4n+2  electrons is unusually favorable in a conjugated ring. an odd number of e-pairs (where n in an integer)

Circle Mnemonic for  MO Energy in Conjugated Rings. +1 -1 MO Energy (units of 2) open-chain  energies from semicircle mnemonic Same radius as for open chain Stabilized (vs. hexatriene) : : 4n “Antiaromatic”! slightly destabilized (vs. butadiene) Inscribe regular polygon with point down. Cation strongly stabilized (vs. allyl+) : Radical less stabilized (vs. allyl•) . Read MO energies on vertical scale. : . . Anion de stabilized • - reactive SOMOs ! 3 cyclopropenyl 4 cyclobutadiene 6 benzene : : There is always an MO at -1.

Generalization of Aromaticity: 4n+2 Stability Transition State “Aromaticity” Cycloadditions & Electrocyclic Reactions e.g. J&F Sec. 13.6 pp. 582-595

Heteroaromatic Compounds Pyridine H O Furan Y- H X H X- Y H N Pyrrole H H N Imidazole (occurs in amino acid histidine) Relay for long-range proton transfer by enzymes N.B. Single denotes contribution of 1 e to  system (redundant with double bond). e.g. J&F Sec. 13.9 pp. 598-601

Furan 4 ABNs 2 ABNs 0 anti-bonding nodes

SHMo2 (Simple Hückel Molecular Orbital Program) (N.B. must click “Show Orbitals” to update energies after changing structure) SHMo2 (Simple Hückel Molecular Orbital Program) Crude  calculation shows heterocycle analogy. N N identical shape energy lower energy node on N high N density N Benzene Pyridine larger on N lower energy

Cyclodecapentaene  Naphthalene (SHMo2) same as ethylene same as cyclodecapentaene & butadiene same as butadiene

Another Criterion of Aromaticity is the PMR Chemical Shift (coming soon, Chapter 15)

Generalized Aromaticity H H OH- We’ll cover this frame on Friday. I’ve left it in because it is fair game for Monday’s exam. pKa 15 vs. 16 for H2O 6  electrons (4n+2) cyclo-C7H8 cyclo-C7H7- pKa 39 (despite more resonance structures) 8  electrons (4n, antiaromatic) e.g. J&F Sec. 13.6 p. 591 R H + Ph3C+ + Ph3CH R + even more stable unusually stable cation (triply benzylic) 2  electrons (4n+2) Same for cyclo-C7H8 cyclo-C7H7+ (cycloheptatrienyl “tropylium”) e.g. J&F Sec. 13.6pp. 587, 592 6  electrons (4n+2)

End of Lecture 55 February 23, 2011 Copyright © J. M. McBride 2011. Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0). Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol . Third party materials may be subject to additional intellectual property notices, information, or restrictions.   The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0