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OC-IV

OC-IV. Orbital Concepts and Their Applications in Organic Chemistry. Klaus Müller. Script ETH Zürich, Spring Semester 2009. Chapter 5. p -systems HMO and extended PMO method. Lecture assistants: Deborah Sophie Mathis HCI G214 – tel. 24489 mathis@org.chem.ethz.ch

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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 2009 Chapter 5 p-systems HMO and extended PMO method Lecture assistants: Deborah Sophie MathisHCI G214 – tel. 24489mathis@org.chem.ethz.ch Alexey FedorovHCI G204 – tel. 34709 fedorov@org.chem.ethz.ch

  2. Sim Sik • For planar unsaturated systems: • the p- and s-orbitals are orthogonal by symmetry • there are no (s,p)-orbital interactions • there are no orbital splitting effects between s- and p-orbitals • hence:the p-orbital system can be treated independently from the s-orbital systemhowever: • the orbital energies of the p-system are affected by the s-electron distribution • and vice-versa Hik interaction energy between adjacent pp orbitals:bCC = b uniform interaction parameter for C-atoms in p-system Hij pp interaction energy involving heteroatoms:in simplest approach bCX = b Him interaction energy between non-adjacent pp orbitals:in simplest approach bC…C = 0 in refined approach: bCX = kCXb ; typically kCX < 1 (prop. SCX/SCC) p p refined approach: bim = kimb ;e.g.kim = typically: b1,3 ~ 0.3 b ; b1,4 = 0 Hjj pp orbital energy for heteroatom :Hjj = a + hjb Hii pp orbital energies Hkk - characteristic for given atom- modulated by local s-electron density- modulated by p-electron density • - specified with reference to aC • modulation in units of b- hi numerical parameterhi > 0 : atom more el.neg. than C • hi < 0 : atom less el.neg. than C in simplest HMO approach:Hii = Hkk = aC=aa : uniform energy parameter for pp-AO of C-atoms in p-systems in refined HMO models:Hii = ai + hi bai: dependent on local topology hi : numerical parameter (small) b : all energy corrections in b units

  3. p S1,2 ~ 0.25 p-overlap integrals are relatively small therefore, they are neglected in the eigenvalue problem p S1,3 ~ 0.08 the typical eigenvalue problem of the LCAO MO approach is: … H11 - e H12 - eS12 H1n - eS1n … H21 – eS21 H22 - e H2n – eS2n = 0 . . . … … … … Hn1 – eSn1 Hn2 – eSn2 Hnn – e this simplifies in the ZOA to … H11 - e H12 H1n … H21 H22 - e H2n = 0 . . . … … … … Hn1 Hnn – e Hn2 with a- and b-parameters of the HMO schemethis transforms into … a- e b 0 … b a- e 0 = 0 . . . … … … … 0 a– e 0 dividing by the universal b parameter andsubstituting –x = (a – e) / b, results in … b b -x 0 1 b e.g., for acrolein (above) in the standard (simple) approximation: … 1 2 1 -x 0 3 4 a aO = 0 . . . a a … … … -x+1 0 0 1 aO = a + b … -x 1 1 0 0 0 -x = 0 giving the x-polynomial: 1 -x 1 0 x4 – x3 – 3x2 + 2x + 1 = 0 the solutions x1, x2, …, xn ofthe polynomial in x provides the eigenvalues (p-CMO energies) viaei = a + xib 0 1 0 -x with the solutions: x1 = 1.88 : e1 = a + 1.88 b x2 = 1.00 : e1 = a + b back-substitution of xi into the above linear equations provides the relative expansion coefficients for CMO yi x3 = -0.35 : e1 = a - 0.35 b x4 = -1.53 : e1 = a - 1.53 b

  4. pCO pCC * * a - b a - b 0.707 -0.707 a –0.618b de = 1b de = 0.618b 0.851 -0.526 symmetrical orbital splitting in ZOA DE = 0 a a H = 1b symmetrical orbital splitting in ZOA DE = 1b H = 1b de = 1b pCC a + b a + b de = 0.618b 0.707 0.707 pCO a +1.618b a +2b 0.526 0.851 electron distribution in 2-center LCAO MO in the ZOA: yp = c1f1 + c2f2 2 2 2 2 2 yp = c1f1 + 2c1c2f1f2 + c2f2 2 2 2 2 2 ∫ ∫ ∫ ∫ ypdv = c1f1dv + 2c1c2f1f2dv + c2f2 dv 1 0 (ZOA) 1 2 2 2 yp = c1 + c2 = 1 hence: normalization condition in the ZOA note: there is no overlap population in the ZOA! in its place, one has to resort to ‚bond orders‘ to discuss bonding or antibonding character for example (for C=C and C=O): bond order p12 = 2c1c2 * * p(pCC) = -1 p(pCO) = -0.895 for multi-orbital system: occ p(pCC) = 1 p(pCO) = 0.895 2 Nel = ∑ niyi dv ∫ i occ = ∑ ∑ni qK = ∑ qK i i qK : partial p-AO population in yi at center K i K K qK : total p-electron population at center K occ i pKM =∑ ni pKM i pKM : partial p-bond order in yi between centers K and M pKM : total p-bond order between centers K and M i

  5. 2-center C=X p-system with varying aX = a + hXb 0.707 -0.707 0.788 -0.615 0.851 -0.526 0.894 -0.447 0.924 -0.383 a - b 0.944 -0.331 de = 1.00b de = 0.78b de = 0.62b de = 0.50b de = 0.41b de = 0.35b a DE = 0b DE = 0.5b DE = 1.0b DE = 1.5b DE = 2.0b a + b DE = 2.5b 0.707 0.707 a +2b 0.615 0.788 0.526 0.851 0.447 0.894 a +3b .. 0.383 0.924 .. 0.331 0.944 Note: The electrophilic character of the C=X p-system increases with increasing electronegativity of X, i.e. decreasing energy of the fX AO. The increased electrophilicity manifests itself through - the increased lowering of the p*-orbital of the C=X system - the increased amplitude at the electrophilic C center in the p*-orbital Thus, towards a given nucleophile with a relatively high-lying occupied orbital, e.g., the nN-dominated CMO of an amine or highest occupied MO (HOMO) of an enamine (see below), the possible coupling effect through intermolecular interaction of this HOMO with the p*-orbital of the C=X system increases with decreasing energy gap DEHOMO-p* and increasing p*-orbital amplitude at the C center of the C=X system. Protonation (or complexation by a Lewis acid) of the O-atom in the s-plane of the C=O system results in a marked lowering the fO level and concomitant increase of the p-electrophilicity of the C=O system. The p-MO systems of the C=X units are useful orbital building blocks for the derivation of the p-orbital structures of more complex p-systems using the extended perturbation MO (EPMO) method.

  6. a -2b a -2b a - b a - b * a a 1 1 √2 √2 a + b a + b 1 1 1 1 a +2b a +2b 2 2 2 2 0.71 0.71 cp*p =0.52 cpp* =0.52 2.0 2.0 1 1 1 1 √2 √2 √2 √2 - (fC1 + fC3) (fC1 - fC3) y2 = jC…C - DE = 0 bH = 2·1/√2 ~ 1.41b + - jC…C = jC…C = Two approaches to the allyl system A: formal union of C=C + C * y3 ~ pCC - 0.52 fC + 0.18 pCC fC-induced mixing of p into p*: pCC * DE = 1bH = 0.707b de = 0.37b c* = 0.52 * y2 ~ fC - 0.52 pCC + 0.52 pCC fC note: exact cancellation of orbital amplitude DE = 1bH = 0.707b de = 0.37b pCC c* = 0.52 note: build-up of amplitude of equal absolute size at allylic center fC-induced mixing of p* into p: * * y1 ~ pCC + 0.52 fC + 0.18pCC B: formal union of C1… C3 + Ccentral + a - 1.41 b y3 = ( jC…C - fC2 ) symmetry-adapted group orbitals fC2 note that fC2 interacts exclusively with jC…C de = 1.41b + c* = 1.00 + y1 = ( jC…C + fC2 ) a + 1.41 b

  7. a -2b a -2b a - b a - b a a a + b a + b a +2b a +2b rel ksolv, (allyl) = 15 rel ksolv, (propyl) = 1 + - - jC…C jC…C jC…C jC…C + + + + chemical associations with allyl orbital interaction schemes pCC pCC pCC * * * symmetricsplitting in 2-center3-el sytem in ZOA repulsion in 2-center-4-el sytem notcounted in ZOA pCC pCC pCC stabilization of anion by allyl resonance stabilization of cation by allyl resonance stabilization of radical by allyl resonance DEp ~ 2 ·0.4 b DEp ~ 2 ·0.4 b DEp ~ 2 ·0.4 b in ZOA: :B C=C-assisted solvolysis (45°C, H2O/EtOH): C=C-assistedhomolytic bond cleavage: C=C-promotedC-H acidity: 94.5 kcal/mol 82.3 kcal/mol C-H acidity (DHº, gas):CH3CH2-H 420.1 CH2=CH-H 407.5 CH2=CH-CH2-H 390.8 (via SN2 not SN1 ?) disrotatory process thermally ‘allowed’; stereochemistry experimentally confirmed at low temperature. sCC sCC * * sCX * + conrotatory process thermally ‘forbidden’; experimentally not observed SbF5, SO2ClF -100ºC, by NMR pC2 pC2 Experimentally, no cyclopropyl cation intermediate can be observed; thus, C-X solvolysis and ring opening may occur in a synchronous fashion; for transparent orbital analysis, the two processes are treated sequentially. ground state correlates with doubly excited state nX nX + solvolysis of C-X sCC sCC + + no inter- action by symmetry sCX disrotatory ring opening conrotatory ring opening

  8. .. a -2b a -2b pCC pCC * * a - b a - b a a a + b a + b a +2b a +2b 0.71 0.71 cp*p = 0.52 cp*p = 0.71 2.0 2.0 .. enamine and enolether p-systems * de2 a - 1.19 b fN-induced p*-mixing into p reduces amplitude at Caand augments amplitude at Cb de2 = 0.19b DE = 2.5 b c* = 0.26 H = 0.707 b y2 = pCC - 0.71 fN - 0.25 pCC * a + 0.5 b de1 pCC DE = 0.5 b de1 = 0.50b fN a + 1.5 b H = 0.707 b c* = 0.71 de1 de2 * y1 = fN + 0.71 pCC + 0.26 pCC a + 2.19 b Note: CMO’s approximated by EPMO method are unnormalized to show mixing effects de2 a - 1.16 b * de2 = 0.16b DE = 3.0 b c* = 0.22 H = 0.707 b fN-induced p*-mixing into p reduces amplitude at Caand augments amplitude at Cb y2 = pCC - 0.52 fO - 0.18 pCC * a + 0.63 b pCC de1 DE = 1.0 b de1 = 0.37b H = 0.707 b c* = 0.52 fO a + 2.0 b de1 de2 a + 2.53 b * y1 = fO + 0.52 pCC + 0.22 pCC

  9. * pcc the enol ether p-system orbital interactions and mixing effects 0.707 c*pp* = 0.224 2.0 pCC mixes from belowinto pCC, thus enhancingthe antibonding characterwith fO a – 1.16 b * y3 ≈ p* – 0.22 fO+ 0.08 p a – b a - b Hfp* = 0.707 b de2 = 0.16 b c* = 0.22 DEfp* = 3.0 b 0.707 a c*p*p = 0.518 2.0 DEpp* = 2 b * pCC mixes from above into pCC, thus enhancingthe bonding characterwith fO a + 0.63 b y2 ≈ p – 0.52 fO– 0.18 p* pcc a + b Hfp= 0.707 b de1 = 0.37 b a + b c* = 0.52 DEfp= 1.0 b a + 2.0 b fO a + 2b a + 2.53 b y1 ≈ fO+ 0.52 p + 0.22 p* polarization of y2 by admixture of p* in a bonding mode to fO as p* admixes from above polarization of y2 0.51 0.45 0.73 normalized amplitudes in y2 prior to polarization: 0.63 0.46 0.63 normalized amplitudes in y2 after to polarization HOMO-controlled electrophilic attack (by soft electrophile) occurs at Cbof enol ether. Note that the large amplitude at Cb in the HOMO of the enol ether p-system arises from polarization of the C=C double bond by the O-p lonepair, not from p-el.transfer! (see next 2 slides)

  10. * pcc .. the enol ether p-system how much p-charge transfer from X into CC p-system? generalized orbital interactions and mixing effects assuming fX to lie below pCC-level induced mixing effects y3 ≈ p* – d* fX+ b* p a - b a – b direct mixing effects a induced mixing effects y2 ≈ p – c* fX– a* p* pcc a + b direct mixing effects a + b fX a + 2b y1 ≈ fX+ c* p + d* p* direct mixing effects Net p-charge transfer arises only from the interaction of the doubly occupied fX with the unoccupied p*CC orbital; hence, net p-charge transfer can be estimated to be ≤ 2d*2 . For a more quantitative estimate, the atomic p-charges from the normalized p-orbitals y1 and y2 have to be considered:

  11. a - b * pcc a + b a + hXb p p p p qCC qCC qX qX 2 2 2 2 2 2 2 2 N2 N1 N1 N2 induced mixing effects y3 ≈ p* – d* fX+ b* p direct mixing effects a – b induced mixing effects a 2 y2 ≈ p – c* fX– a* p* N2 = 1 + c*2 + a*2 pcc a + b direct mixing effects fX 2 y1 ≈ fX+ c* p + d* p* N1 = 1 + c*2 + d*2 direct mixing effects (1) + (c*2) total p-charge in fX unit: = ≈ 2 2 (1 + 2c*2 + a*2) (1 + c*2 + a*2 + c*2 + …) ≈ 2 2 2 2 N1 N2 N1 N2 2 2 (1 + 2c*2 + a*2) - N1 N2 p 2 dqX= - 2 ≈ net charge transfer from fX: ≈ 2 2 N1 N2 - 2d*2 (1 + 2c*2 + a*2) - (1 + 2c*2 + a*2 + d*2) 2 ≥ (1 + 2c*2) (1 + 2c*2 + a*2 + d*2) (c*2 + d*2) + (1 + a*2) = total p-charge in CC-p-unit: ≈ 2 2 (1 + 2c*2 + a*2 + 2d*2) (c*2 + d*2 + 1 + a*2 + c*2 + d*2 + …) ≈ 2 2 2 2 N1 N2 N1 N2 2 2 (1 + 2c*2 + a*2 + 2d*2) - N1 N2 p 2 dqCC = - 2 ≈ ≈ net charge transfer into CCp: 2 2 N1 N2 + 2d*2 (1 + 2c*2 + a*2 + 2d*2) - (1 + 2c*2 + a*2 + d*2) 2 ≤ (1 + 2c*2) (1 + 2c*2 + a*2 + d*2) for the specific example of the enol ether, net p-charge transfer is estimated to be . . p dq (X→CC)≤ 2 0.2182 / (1 + 2 0.5182) = 0.062; hence, not more than ca. 3%

  12. a -2b a -2b - - a - b a - b - a a 1 1 1 1 √2 √2 √2 √2 a + b a + b exact solution: a - √2 b exact solution: a +√2 b 1 1 1 1 a +2b a +2b 2 2 2 2 pCO * comparison: allyl anion – carbanion a to C=O p-system y3 = pCC - 0.52 fC + 0.18 pCC * 0.71 c*pp* = 0.52 2.0 fC-induced mixing of p into p* pCC * DE = 1bH = 0.707b de = 0.37b c* = 0.52 .. 0 fC * y2 = fC - 0.52 pCC + 0.52 pCC DE = 1bH = 0.707b de = 0.37b fC-induced mixing of p* into p pCC c* = 0.52 0.71 c*pp* = 0.52 2.0 * y1 = pCO + 0.52 fC + 0.18 pCO from exact HMO-solution of allyl system: net p energy stabilization: ~ 2 · 0.4 b = 0.8 bnet p charge shift from fC to C=C: ~ - 0.5 Note: CMO’s approximated by EPMO method are unnormalized to show mixing effects net p energy stabilization: ~ 2 · 0.6 b = 1.2 b net p chargeshift from fC to C=O: ~- 0.57 y3 = pCO - 0.70 fC + 0.17 pCO * 0.53 0.85 a - 1.22 b c*pp* = 0.70 2.24 fC-induced mixing of pCO into pCO -0.53 DE = 0.62bH = 0.85b de = 0.60b * a – 0.62 b c* = 0.70 .. fC a + 0.44 b * y2 = fC - 0.30 pCO + 0.70 pCO DE = 1.62bH = 0.53b de = 0.16b c* = 0.30 fC-induced mixing of pCO into pCO pCO * a + 1.62 b 0.85 c*pp* = 0.30 a + 1.78 b 2.24 0.53 0.85 * y1 = pCO + 0.30 fC + 0.11 pCO * * Note: the pCO orbital lies at a lower energy and has a larger amplitude at C than the pCC; likewise, the energy pCO is lower and its amplitude at C is smaller compared to the pCC; these combined factors result in a net downshift of the fCa to C=O to produce the CMO y2 with net bonding amplitudes (positive partial p bond order) between the two C atoms.

  13. a -2b a -2b a - b a - b a a a + b a + b a +2b a +2b comparison: amide and ester p-systems net p energy stabilization: ~ 2 · 0.3 b = 0.6 b net p chargeshift from fN to CO:~- 0.13 the C-N torsion barrier disrupting N…C=O p conjugationis typically 18-20 kcal/mol .. 0.85 -0.53 y3 = pCO - 0.35 fN + 0.08 pCO a – 0.92 b * de2 a - 0.62 b 0.53 pCo * c*pp* = 0.35 2.24 DE = 2.12 b de = 0.30 b fN-induced mixing of pCO into pCO H = 0.85 b c* = 0.35 * DE = 0.12 b de = 0.47 b H = 0.53 b c* = 0.89 * y2 = fN - 0.89 pCO + 0.35 pCO de2 fN-induced mixing of pCO into pCO a + 1.33 b de1 * a + 1.5 b pCO 0.85 fN a + 1.62 b c*pp* = 0.89 de1 2.24 a + 2.09 b 0.53 * y1 = pCO + 0.89 fN + 0.34 pCO 0.85 Note: CMO’s approximated by EPMO method are unnormalized to show mixing effects .. fN-induced mixing of pCO into pCO net p energy stabilization: ~ 2 · 0.25 b = 0.5 b net p chargeshift from fO to C=O:~- 0.11 * 0.53 c*pp* = 0.30 2.24 y3 = pCO - 0.30 fO + 0.07 pCO * 0.85 -0.53 de2 a – 0.87 b fN-induced mixing of pCO into pCO a - 0.62 b pCo * * de = 0.25 b DE = 2.62 b 0.85 c* = 0.30 H = 0.85 b c*pp* = 0.70 2.24 * y2 = pCO - 0.70 fO - 0.27 pCO DE = 0.38 b de = 0.37 b H = 0.53 b c* = 0.70 a + 1.25 b de1 pCO a + 1.62 b a + 2.0 b fO 0.53 de1 0.85 de2 a + 2.62 b * y1 = fO + 0.70 pCO + 0.30 pCO

  14. a -2b a -2b a - b a - b a a 1 1 1 1 1 1 √2 √2 √2 √2 √2 √2 a + b a + b a +2b a +2b 1,3-butadiene: from 2 conjugated ethylene p-systems y4 induced mixing de2 a - 1.62 b de1 y3 p1,CC p2,CC * * de1 a - 0.62 b de2 * pCC - pCC DE = 2.0 b de2= 0.12 b induced mixing H = 0.5 b c* = 0.24 DE = 0.0 b de1= 0.50 b induced mixing pCC - pCC H = 0.5 b c* = 1.00 de2 a + 0.62 b de1 p2,CC p1,CC de1 de2 y2 a + 1.62 b net p-energy stabilization: ~ 2 · 2 de2 = 0.47 b induced mixing Note that the closed-shell (overlap) repulsion effect due to the pCC – pCC interaction is neglected in the ZOA; hence the net p energy stabilization is overestimated: the trans → cis torsional barrier is ca. 5 kcal/mol. y1 PE spectrum of 1,3-butadiene: IP1 = 9.03 eV, IP2 = 11. 46 eV; hence b ~ 2.4 eV Note that b parameter cannot be transferred from spectroscopy to thermodynamic properties Note the build-up of a large LUMO amplitude at the Cb position to the O=C group in acrolein (Michael addition) de3 a - 1.49 b de4 0.851 0.65 -0.58 p2,CC * DE = 0.38 b de4= 0.44 b * * pOC - pCC H = 0.60 b c* = 0.73 p1,OC * de4 a - 0.37 b DE = 2.62 b de3= 0.05 b * pOC - pCC de2 H = 0.37 b c* = 0.14 * * y3 = pOC + 0.73 pCC - 0.33 pCC - 0.03 pOC DE = 1.62 b de2= 0.19 b * pOC - pCC H = 0.60 b c* = 0.33 * * y2 = pCC - 0.47 pOC + 0.33 pOC - 0.00 pCC DE = 0.62 b de1= 0.18 b de1 pOC - pCC p2,CC de2 H = 0.37 b c* = 0.47 a + 0.99 b 0.526 The EPMO-estimated p-energy levels may be compared to the exact HMO- energies given on slide 2 of this Chapter de1 p1,OC de3 a + 1.85 b net p-energy stabilization: ~ 2 · (de2 + de3) = 0.48 b thus, essentially the same as for 1,3-butadiene;indeed, the trans → cis torsional barrier for acrolein is essentially the same as for 1,3-butadiene.

  15. a -2b a -2b a - b a - b a a 1 1 1 1 √2 √2 √2 √2 a + b a + b a +2b a +2b * sCC 1,3-butadiene: from symmetry-adapted group orbitals 0.372 0.602 - - y4 = jin - 0.62 jout A a - 1.62 b -0.372 + + y3 = jout - 0.62 jin A 0.602 j- = (f2 - f3) j- = (f1 – f4) a - 0.62 b in S out A DE = 1.0 b de2= 0.62 b H = 1.0 b c* = 0.62 S A j+ = (f2 + f3) j+ = (f1 + f4) a + 0.62 b in out 0.602 S - - y2 = jout + 0.62 jin -0.372 a + 1.62 b S + + y1 = jin + 0.62 jout 0.372 0.602 chemical association: thermal ring opening of cyclobutene occurs in conrotatory mode * sCC A S y4 S * pCC A 175 ºC y3 pCC j- S out j+ A out 175 ºC S y2 C2 pCC A y1 A * pCC C2 sCC sCC S conrotatory ring opening

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