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OC-IV

OC-IV. Orbital Concepts and Their Applications in Organic Chemistry. Klaus Müller. Script ETH Zürich, Spring Semester 2010. Chapter 6. HMO for relevant p -systems EPMO analysis and its translation to relevant systems in Organic Chemistry. 2 p. 2 p. 2 p. 2 p. e p. n. n. n. n.

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OC-IV

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  1. OC-IV Orbital Concepts and Their Applications in Organic Chemistry Klaus Müller Script ETH Zürich, Spring Semester 2010 Chapter 6 HMO for relevant p-systems EPMO analysis and its translation to relevant systems in Organic Chemistry

  2. 2p 2p 2p 2p ep n n n n a-2b a-b Jm Jm a √ √ √ √ 2 1 2 1 n n n n a+b ep a-2b + a+2b a-b a a+b a+2b p-energy levels for monocyclic peripherally conjugated p systems -x 1 0 0 0 1 -x 1 1 0 0 3 1 -x 1 0 = 0 2 n -2 -x 0 1 0 n -1 1 0 -x 1 m = 0 1 1 0 -x xJ = 2 cos ( J) eJ = a + 2 cos ( J) b for n = even: J = 0, ±1, ±2, n/2 for n = odd: J = 0, ±1, ±2, ± (n-1)/2 J = 3 J = 2 J = -2 J = -2 J = 2 n = 6 n = 5 J = -1 J = 1 J = -1 J = 1 - J = 0 J = 0 n -1 yn/2 = ∑ (-1)mfm for n = even: m = 0 n -1 n -1 y-J = ∑ sin( ) fm yJ = ∑ cos( ) fm p-CMO’s m = 0 m = 0 n -1 y0 = ∑ fm m = 0 + J = 2 J = -3 J = 3 J = 1 J = -1 J = 2 J = -2 J = -1 J = 1 J = 1 J = -1 J = 0 J = 0 J = 0

  3. ep a-2b a-b -1 √12 a 1 1 a+b √6 √6 1 1 1 a+2b √12 2 2 2 2 √12 √12 the benezene p-system there are several approaches to derive the p-orbital structure of benzene: each with specific aspects and chemical associations: y6 y5 y4 y2 y3 y1

  4. p* p* p* - - - p* p* + + ep ep a-2b a-2b a-b a-b -1 √12 p p* NN NN a a 1 1 1 1 a+b a+b √6 √2 √6 √2 1 1 1 1 1 a+2b a+2b √12 2 2 2 2 2 2 √12 √12 this symmetric approach results in two identical 2-orbital interaction schemes with exact level splitting and orbital mixing effects s1 s2 AA SA SA DE =1b de = 1b j- SA : H = √2 b c*= 1/√2 DE =1b de = 1b j+ SS : H = √2 b c*= 1/√2 p- AS p+ SS S/A: symmetric/antisymmetric with respect to first/second symmetry planes (s1 , s2). * - sCN SA * + sCN chemical association: retro-DA to form benzene SS SA levels of same symmetry would not cross if there is residual interaction between them; level mixing is not included here to maintain the clear analogy to the benzene interaction system above; the results are not affected. AA SS SA SA j- SA j+ SS p- AS AS SA p- p+ SS SS SS smooth correlation between electronic ground states of educt and product is indicative for a thermally allowed reaction - sCN SA + sCN SS

  5. p* - p* + ep a-2b a-b a 1 1 a+b √2 √2 1 1 a+2b 2 2 s1 .. DE =2.5b de2= 0.64 b SA H = √2 b c*= 0.45 s2 .. SA a – 1.64 b de2 AA AA a – b antibonding MO doubly occupied; highly prone to oxidation; cyclic 8-electron p-system → ‚anti-aromatic‘ SA SS a – 0.19 b de1 p- AS a + b AS j- p+ SS SA a + 1.5 b de2 SS j+ SA a + 2.14 b de1 DE =0.5b de1= 1.19 b SS H = √2 b SS c*= 0.84 a + 2.69 b in ZOA, the net p-stabilization arises only from the interaction of the N-group orbital of symmetry SA, whereas no stabilization results from the interactionof the other (SS) N-group orbital; in non-ZOA the latter would result in overlap repulsion! X-ray structure of N,N‘-dimethyl-dihydrophenazine: LUBGAQ ‚anti-aromatic‘ diaza-benzene ring with 8 p electrons adopts a nonplanar conformation (dihedral angle between NCCN planes q ~ 39°!) with significantly pyramidalized aniline-type N-atoms (average valence bond angles at N ~117°). q X-ray structure of N,N‘-dimethyl-dihydrophenazinium PF6 salt: Note the complete planarity of the oxidized radical cation of dihydrophenazine. - CIBHIE - PF6

  6. - jC+ + jC+ ep jp*CO jp*CO jp*CC jp*CC jpCO jpCO jpCC jpCC + + + + - - - - a-2b - - - - + + + + jp*CO jp*CO jp*CC jp*CC jpCO jpCO jpCC jpCC a-b ep 1 1 1 1 √2 √2 √2 √2 a-2b a a-b a a+b a+b 1 1 a+2b a+2b 2 2 s1 DE =0.38 b de3= 1.03 b SA H = 1.20 b c*= 0.85 s2 DE =2.62b de4= 0.20 b SA SA H = 0.74 b c*= 0.26 de4 de3 SS AA AA de2 SA SA SS de3 SA a + 0.41 b SS AS AS de1 SS de2 SA de4 SA SS de1 SS DE =1.62 b de2= 0.50 b SS H = 1.20 b c*= 0.533 extremely low-lying unoccupied MO (LUMO): p-quinone is highly electrophilic and a strongelectron acceptor (oxidizing agent) DE =0.62 b de1= 0.64 b SS H = 0.74 b c*= 0.667 Note: rather than calculating all coefficients for the group orbitals, it is convenient to relate interactions between group orbitals to the basic p-LMO interactions in acrolein: transition from p-quinone to a system with oxygens of infinite electronegativity would give a benzene dication, a cyclic 4p-electron ‚anti-aromatic‘ system, which would be highly reactive (triplet state). SA AA AA SS unoccupied SA SA H(pCC,pCO) SS AS AS SA SS SA ± jpCO = (pco1 ± pco2) SS ± jpCC = (pcc1 ± pcc2) SS + + H(jCC,jCO) = O- H(pCC,pCO) H(pCC,pCO) 4 = 2 O-

  7. pCC * ep a-2b a-b a a+b a+2b DE =0.62 b de4= 0.30 b A H = 0.53 b c*= 0.57 s DE =1.62b de2= 0.37 b A H = 0.85 b c*= 0.43 a - 2b y4 de4 a - 1.62 b A a - b A a - b 0.71 de2 de3 y3 de4 a - 0.62 b S y2 a + 0.62 b de2 de3 de1 A pCC a + b a + b 0.37 0.60 S 0.71 y1 a + 1.62 b S de1 a+ 2b 0.60 0.37 Note: The HOMO of butadiene (y2) interacts favorably with the pCC orbital of ethylene. DE =0.62 b de1= 0.30 b * S H = 0.53 b c*= 0.57 The pCC orbital of ethylene (HOMO) interacts favorably with the LUMO of butadiene (y3), compensating the interaction between occupied ethylene pCC and butadiene y1 orbitals. The interaction patterns are exactly mirrored in the antibonding orbital domain. DE =1.62b de3= 0.37 b S H = 0.85 b c*= 0.43 genealogy of unnormalized CMO‘s of benzene: induced mixing induced mixing * y3(benzene) ~ y2+ 0.43 pCC + 0.10 y1 y4(benzene) ~ y3 - 0.43 pCC + 0.10 y1 * y2(benzene) ~ pCC - 0.57 y1 + 0.43 y3 y5(benzene) ~ pCC + 0.57 y4 - 0.43 y2 * induced mixing induced mixing y1(benzene) ~ y1 + 0.57 pCC + 0.22 y3 y6(benzene) ~ y6 - 0.57 pCC + 0.22 y3

  8. * * sCC sCC A e A y6 A y4 A y5 S ep a-b S A y3 y4 S A A a - + - + jC…C jC…C jC…C jC…C a-2b S y2 A y3 S A S a+b y2 A a-b y1 S A e y1 S S A a y6 S y4 S S sCC S y5 A a-b y3 y4 A S a+b A A a S S y2 S y3 A a+2b a+b y2 S A y1 A y1 A S sCC S A isodesmic reaction: A A S A + + de2 de3 S ° ° ° ° DHf = 25.4 DHf = -1.1 DHf = 19.8 DHf = -29.5 de3 de2 A S A S DHreact = - 34.0 kcal/mol S S net p-energy stabilization relative to butadiene and ethylene: DEp = 2·de2 + 2·de3 = 4·0.38 b ~ 1.5 b with a conservative thermodynamic b parameter of -25 kcal/mol : dEp ~ -37 kcal/mol Diels-Alder cycloaddition At an intermediate stage of the cycloaddition the p-p s-type overlap (and interaction) will be comparable to the p-p p-type overlap (and interaction) between adjacent p-AO‘s in the reactants. Hence, at this intermediate stage the reaction system experiences a significant resonance stabilization of a pericyclic 6-electron system (→ ‚aromatic‘ character). As this resonance stabilization arises from a proper symmetry match between highest occupied and lowest unoccupied MO‘s of the reactants in their thermodynamic ground states, the Diels-Alder cycloaddition reaction is a thermally ‚symmetry-allowed‘ reaction. electrocyclic ring opening Cs a-2b disrotatory ring opening(reaction trajectory of Cs symmetry) thermally favored - observed s In the disrotatory, but not in the conrotatory, mode the MO-level diagram shows a smooth correlation of the electronic ground states of the reactant and product, passing through an intermediate state of significant resonance stabiization (→ pericyclic 6-electron configuration). a+2b C2 conrotatory ring opening(reaction trajectory of C2 symmetry) thermally disfavored – not observed C2 By orbital symmetry, only orbitals of the same symmetry can interact: thus, upon conrotatory ring opening, the electronic ground state of the reactant would correlate with an excited state of the product!

  9. A e A a-2b A y6 A y4 A y5 S S a-b * sCC S A y3 y4 S A A A a S y2 A y3 S S A S ep a+b y2 A y1 A S y1 S a+2b S + - + - jC…C jC…C jC…C jC…C a-2b S sCC S a-b A e A a-2b S a y6 S y4 S S y5 A A a-b y3 y4 A S a+b S A A a S S y2 S y3 A A a+2b a+b y2 S A y1 S A y1 A a+2b S A sCC S A isodesmic reaction: A A S A + + de2 de3 S ° ° ° ° DHf = 25.4 DHf = -1.1 DHf = 19.8 DHf = -29.5 de3 de2 A S A S DHreact = - 34.0 kcal/mol S S net p-energy stabilization relative to butadiene and ethylene: DEp = 2·de2 + 2·de3 = 4·0.38 b ~ 1.5 b with a conservative thermodynamic b parameter of -25 kcal/mol : dEp ~ -37 kcal/mol Diels-Alder cycloaddition At an intermediate stage of the cycloaddition the p-p s-type overlap (and interaction) will be comparable to the p-p p-type overlap (and interaction) between adjacent p-AO‘s in the reactants. Hence, at this intermediate stage the reaction system experiences a significant resonance stabilization of a cyclic 6 electron system (→ ‚aromatic‘ character). As this resonance stabilization arises from a proper symmetry match between highest occupied and lowest unoccupied MO‘s of the reactants in their thermodynamic ground states, the Diels-Alder cycloaddition reaction is a thermally ‚symmetry-allowed‘ reaction. electrocyclic ring opening Cs disrotatory ring opening(reaction trajectory of Cs symmetry) thermally favored - observed s In the disrotatory, but not in the conrotatory, mode the MO-level diagram shows a smooth correlation of the electronic ground states of the reactant and product, passing through an intermediate state of significant resonance stabiization (→ cyclic 6-electron configuration). C2 conrotatory ring opening(reaction trajectory of C2 symmetry) thermally disfavored – not observed C2 By orbital symmetry, only orbitals of the same symmetry can interact: thus, upon conrotatory ring opening, the electronic ground state of the reactant would correlate with an excited state of the product!

  10. 1 1 1 1 1 1 1 1 √2 √2 √2 √2 √2 √2 √2 √2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 ep a-2b 2 √2 a-b - - - - a a+b a+2b s1 de4 a - 1.41 b a - 1.41 b de3 = 0.5b y3 y3 DE = 0 b H = 0.5 b S S de3 = 0.5b y5(benzene) de4 de2 = 1b y2 y2 DE = 0 b H = 1.0 b A A major resonance stabilization arises from y2…y2 interaction DEp = 2·de2 = 2b de2 = 1b de4 y2(benzene) de1 = 0.5b y1 y1 DE = 0 b H = 0.5 b S S de1 = 0.5b a + 1.41 b a + 1.41 b de4 interactions between y1…y3 de4 ~ 0.09 b DE = b H = 0.5 b c* ~ 0.17 y3…y1 contribute a minor stabilization of DEp ~ 4·0.09 b ~ 0.35 b chemical association: p-type interactions [3,3]-sigmatropic rearrangement thermally favored – suprafacial mode s-type interactions evolving sp3 hAO‘s on transition from p→ sp3 evolving p-AO‘s on transition from sp3→ p cyclic transition state in which partial s-type and p-type interactions are of comparable size: this correspondsto a p-type 6-electron ‚aromatic‘ configuration with high conjugative stabilization relative to two separated allyl fragments:thus, a [3,3]-sigmatropic rearrangement can favorably proceed in a synchronous fashion

  11. s1 a + b a - b √3 √3 - 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 √3 √3 √3 √3 √3 2 2 2 2 √3 √3 √3 √3 - - - - ep a-2b a-b * * sCH sCH ep a-2b a y5 j4 j4 a-b y4 * sCX j3 j3 a sH fC→y3 a+b a+b j2 j2 y2 a+2b j1 j1 y1 a+2b sCH sCH y5 a - 1.9 b de5 = de1 ~ 0.18b S y4 a - 1.1 b a - b a - b A de3 ~ 1.1b fC y3 a S S de3 ~ 1.1b y4 de1 de5 a + b a + b a + 1.1 b A y1 de1 ~ 0.18b S a + 1.9 b Note that this unsymmetrical approach by the extended perturbation MO method does not produce the exact energy levels and the full symmetry of the benzene p-MO’s. genealogy of unnormalized CMO‘s of benzene · · induced mixing Neverless, the approach is quite useful to visualize the p-localization energy upon a p-disrupting reaction at a single center of the aromatic (benzene) system, e.g., by an attack of an electrophile (bottom right), or the resonance stabilization of a pericyclic 6e-arrangement in the transition state of a suprafacial [1,5]-sigmatropic shift (bottom). y6(benzene) ~ y5 - 0.30 fC + 0.20 y3 + 0.05 y5 induced mixing y4(benzene) ~ y3 - fC + 0.17 y1 - 0.17 y5 ep y6 j5 y4 y3(benzene) ~ fC + y3 - 0.30 y1 + 0.30 y5 j4 y5 X+ j3 · induced mixing · fC y3 y1(benzene) ~ y1 + 0.30 fC + 0.20 y3 + 0.05 y5 j2 y2 j1 y1 sCX X+ suprafacial [1,5]-sigmatropic shift electrophilic addition

  12. - - - 1 1 1 1 1 1 1 1 1 √2 √2 √2 √2 √2 √2 √2 √3 √2 √3 √3 2 2 b b b b DE(je,je) = 1b * -1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 ep -1 1 -1 1 1 √12 √12 √12 √12 √12 - 2 a-2b √12 je je * * a-b a a+b a+2b C3 symmetry H(p*,p*) = b = b p* H(je,je) = b de = b * c* = H(p,p) = b = b p b b 2 je b je H( , ) = 3 b = b synchronous suprafacial (2p + 2p + 2p) cycloaddition reaction is a thermally allowed process it can proceed through an intermediate stage with significant resonance stabilization in a cyclic 6-electron (‚aromatic‘) arrangement with partial s- and p-interactions There are numerous examples of transition metal-catalyzed [2+2+2] cycloadditions of arynes, alkynes, alkenes, imines, isocyanates, etc, in ‚atom-economical‘ syntheses of a variety of highly substituted benzene, pyridine, cyclohexadiene, cyclohexene, and cyclohexane derivatives. see e.g., P R Chopade & J Louie, Adv Synth Catal (2006), 348, 2307-2327 TM-cat + regioisomers

  13. pCC pCC * * ep a-2b a-b a a+b a+2b What is the difference between the p-systems of aromatic benzene and non-aromatic fulvene? the difference can be traced to a different topological connection of an ethylene unit relative to a butadiene unit DE =2.62 b de~ 0.10 b H = 0.53 b de4 a - 1.62 b y4 A de5 de3 de3 de2 A S a - 0.62 b DE =0.38 b y3 de5~ 0.68 b H = 0.85 b de5 S e ~ a – 0.31 b a + 0.62 b y2 de3 A de2 de3 de1 de1 pCC pCC S S a + 1.62 b y1 de1 de1 S de4 p-resonance stabilization DEp = 4·0.38 b ~ 1.5 b(see slides 7 & 8) p-resonance stabilization DEp = 2·0.38 b + 2·0.10 b ~ 0.95 b The different connection topology allows only one major occupied-unoccupied interaction(between pCC and y3 butadiene) to come into play; hence the p-resonance stabilization is almost half that obtained for the benzene connectivity; a minor contribution (de4) comes from pCC and y1 butadiene, but the large energy gap mitigates the additional resonance stabilization. genealogy of fulvene LUMO: º º * highest amplitude in low-lying LUMO of fulvene; site for nuclephilic attack e ~ a – 0.31 b * On the other hand, the interaction between pCC and y3 butadiene, absent in the benzene connectivity,results in a relatively low-lying empty CMO for fulvene, rendering it a rather reactive system! * y4 (fulvene) ~ y3 + 0.80 pCC – 0.43 pCC – 0.09 y1 unnormalized induced mixing by pCC and pCC partially compensated *

  14. - - ep a-2b ep ep a-b a-2b a-2b y4 y4 A A a-b a-b a y3 y3 S S a a a+b y2 y2 A A a+b a+b y1 a+2b y1 S S a+2b a+2b DHr DHr ° ~ -14.6 ° ~ -23.6 . y4 a - 1.618 b a - 1.618 b a – 1.55 b A de3 DE =0.62 b de3= 0.93 b H(y3,fC) : H = 1.20 b y3 c*= 0.78 a - 0.618 b S de1 fC S de3 a + 0.618 b y2 a + 0.618 b a + 0.64 b A DE =1.62 b de1= 0.29 b H(y1,fC) : H = 0.74 b c*= 0.39 y1 a + 1.618 b The results by the approximate EPMO method should be compared to the exact solutions given on slide 2: lowest MO level at a + 2b; 2 degenerate MO‘s at a + 0.618b; 2 degenerate MO‘s at a – 1.618b. de1 S a + 1.91 b The net p-resonance stabilization relative to a carbanion and butadiene results from the interaction of the (occupied) fC and y3 (LUMO) of butadiene: DEp = 2·de3 ~ 1.9 b pKa ~ 15.5 The net p-resonance stabilization compared to butadiene and amine DEp ~ 2·de3 ~ 1.1 b The net p-resonance stabilization compared to butadiene and ether DEp ~ 2·de3 ~ 0.9 b de3 de3 DE =2.12 b DE =2.62 b de3= 0.54 b de3= 0.47 b H(y3,fN) : H(y3,fN) : H = 1.20 b H = 1.20 b c*= 0.45 c*= 0.39 de3 de1 de1 fN de1 S fO de1 S de3 +31.9 -0.80 +25.9 -18.4 +31.9 -44.0 -8.3 -18.4 DHf °(kcal/mol) DHf °(kcal/mol) compare to benzene case (slide 9)

  15. 1 √6 1 1 2 2 1 √6 ep -1 1 a-2b √12 √12 2 2 √12 √12 a-b a DE =1. 0 b DE =1.0 b DE =2.0 b DE =2.0 b de4= 0.26 b de1= 0.08 b de3= 0.08 b de3= 0.26 b H(y4,fC) : H(y6,fC) : H(y1,fC) : H(y3,fC) : H = 0.41 b H = 0.58 b H = 0.41 b H = 0.58 b c*= 0.20 c*= 0.46 c*= 0.20 c*= 0.46 a+b a+2b 2 -1 0 -1 0 0 1 y7(bn) de6 y6 y6(bn) y4 de4 y5 de6 de1 de4 de3 fC y4 (bn) de3 y2 y2(bn) y3 de1 y1 y1(bn) genealogy of nonbonding MO of the benzyl system: y4 (bn) ~ fC – 0.46 y3 + 0.46 y4 – 0.20 y1 + 0.20 y6 fC –y3 +y4 –y1 +y6 y4(bn) The symmetrical mixing pattern of bonding and antibonding benzene MO‘s into fC to generate y4 of the benzyl system results in exact cancellation of amplitudes at the ipso and meta position, and the build-up of amplitudes at the ortho- and para-positions. Thus, if fC is vacant (carbenium ion), singly occupied (radical), or doubly occupied (carbanion), p-conjugation with the benzene unit results in a build-up of carbenium, radical, or carbanion character at the ortho- and para-positions, respectively. The benzyl system is an example of a so-called alternating p-system: * in an alternating p-system, C-centers can be flagged in an alternating fashion so that any flagged center is connected only to non-flagged center(s), and vice versa. * * • For alternating p-systems, there are a number of simple rules: • their MO level diagram is symmetrical with respect to e = a (see, e.g., allyl, butadiene, pentadienyl, benzene, etc);- symmetrically related MO‘s have an identical pattern of absolute amplitudes, the antibonding MO‘s being generated • from the corresponding bonding MO‘s simply by changing the signs at the labeled centers;- if the number of centers is odd, a nonbonding MO at e = a results; its orbital can be generated by assigning an • amplitude 1 at a labeled center, then propagating along the p-topology, assigning integer amplitudes at labeled • centers in such a way that the sum of amplitudes around an unlabeled center is zero (see example on the left). *

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