OC-IV

1. OC-IV Orbital Concepts and Their Applications in Organic Chemistry Klaus Müller Script ETH Zürich, Spring Semester 2009 Chapter 4 symmetry-adapted group orbitals Lecture assistants: Deborah Sophie MathisHCI G214 – tel. 24489mathis@org.chem.ethz.ch Alexey FedorovHCI G204 – tel. 34709 fedorov@org.chem.ethz.ch

2. 1 1 √2 √2 Consider the following case of an enol ether p-LMO spn nO-LMO f1 The p-, p*-LMO’s and the two symmetrically equivalent nO-LMO’s would represent a valid starting point for the discussion of the orbital structure of the enol ether. spn nO-LMO f2 However, the two equivalentnO-LMO’s f1 and f2 are not symmetry-adapted to the planar symmetry of the enol ether unit. p-LMO p nOp-type LMO Therefore, it is more convenient to consider the mutual interaction between the two nO-LMO’s firstand, by this, generate symmetry-adapted lone pair orbitals. spm nOs-type LMO Since f1 and f2 are symmetrically related, orthogonal spn hAO’s, they are energetically degenerate; their interaction results a symmetrical split intoan spm-type (s-type) lone pair orbital and an anti-symmetrical (p-type) pure p lone pair orbital: pp (f1 - f2) pp f1 pure pp-type AO ps ps s s f2 -pp (f1 + f2) ps s AO decomposition of the two symmetry equivalent orthonormal spn-type lone pair LMO’s spm-hAO in s-plane

3. n -1 2n 1 2 n 1+n 1+n 1+n 1+n 1+n 1 1 √2 √2 pp (f1 - f2) pp f1 pure pp-type AO ps ps s s f2 (f1 + f2) -pp ps s spm-hAO in s-plane What is the nature of the s-type (spm) hAO by mixing of two symmetry-equivalent spn hAO‘s? s-char = p-char = spn hAO: the s-type spm hAO collects all s-character from the two spn-hAO‘s, while the total p-character is reduced by 1 p-AO that is consumed by the p-type orbital of the minus-linear combination of the 2 spn hAO‘s: s-char = p-char = - 1 = spm hAO: hence: m = (n -1)/2 sp3 p sp sp3 symmetry-equivalent sp3-hAO‘s (equal energy) symmetry-adapted sp-hAO (s-type, lower energy) and p-AO (p-type, higher energy) sp2 sp0.5 p sp2 symmetry-equivalent sp2-hAO‘s (equal energy) symmetry-adapted sp0.5-hAO (lower energy) and p-AO (higher energy)

4. The same principles hold true for symmetry-equivalent s-LMO‘s or s*-LMO‘s sCH1-LMO sp3 sp3 p sp sCH2-LMO symmetry-adapted s-type CH2 group orbital (lower energy) and p-type CH2 group orbital (higher energy) symmetry-equivalent sCH-LMO‘s (equal energy) involving sp3-hAO‘s at central atom * sCX1-LMO sp3 sp3 p sp * sCX2-LMO symmetry-adapted s-type CX2 antibonding group orbital and p-type CH2 antibonding group orbital symmetry-equivalent sCX-LMO‘s (equal energy) involving sp3-hAO‘s at central atom * IPp = - ep (eV) 8 ep calculated byPRDDO SCF MOmethod using STO minimal basis set stabilization of p-orbital by small (1,3)-type interactions betweenp-type CH3 group orbitals by ca 0.1 eV per (1,3)p-interaction IPp -ep(yp) 9 dep=0.6 eV dep=1.2 eV dep=1.2 eV dep=1.1 eV dep=1.7 eV dep=2.2 eV 10 -ep-LMO IPp 11 C slightly more electronegative than H: pulling effect in s-system lowers p-LMOby ca 0.1-0.2 eV per CH3 group hyperconjugative upshift of p-LMO by p-type CH3 group orbitalsby ca 0.6 eV per CH3 group

5. The same principles also hold for the reverse process:generation of symmetry-equivalent LMO‘s from symmetry-adapted LMO‘s: e.g.: t-LMO‘s for a C=C double bond by linear combination of s- and p-LMO‘s: sp5 sp5 sp5 sp5 sp2 sp2 pp pp t1,CC-LMO by +LC t2,CC-LMO by -LC sCC-LMO pCC-LMO rationalization of allylic torsion potential using t-LMO‘s: anticlinal to C=C synclinal to C=C antiplanar to C=C eclipsed to C=C preferred conformation corresponds to torsional transition state torsional energy barrier depends on substitution pattern; DE ~ 1-3 kcal/molfor propene: DE ~ 2.0 kcal/mol t1-LMO Newman projection: in terms of t-LMO description of C=C double bond, the preferred conformation has a staggered arrangement of doubly occupied LMO‘s t2-LMO X-ray structures from the CSD: ZZZDDJ02 ZIZCOA QIMHUP

6. z 1/√6 1/√3 1/√3 1/√2 √3/6 √3/2 s - 1/2 pz = 1/2 s - 1/√2 px - 1/√6 py - √3/6 pz (2√2/√3 py + 1/√6 py + 1/√6 py) = py 1/√6 y = 1/2 s + √2/√3 py - √3/6 pz = 1/2 s + 1/√2 px - 1/√6 py - √3/6 pz x R R sp3 hAO involved in s- and s*-LMO (1) sp3 (4) sp3 (2) sp3 (3) f1 = sp3 (2) symmetry-equivalent orthonormal lone pair hAO‘s(e.g., assuming sp3 hybridization, see slide 1, Chapter 2): sp3 (3) f2 = sp3 (4) f3 = To transform these 3 symmetry-equivalent lone pair orbitals, f1, f2, f3, back into (orthonormal) lone pair orbitals j1, j2, j3, that are adapted to the axial C3-symmetry, we take the following linear combinations: j1 = (f1 + f2 + f3) = (3/2 s - 3 pz) = j2 = ( f2 - f3) = 1/2 px - (1/2 px) = px j3 = (2f1 - f2 - f3) = R Regarding orbital energies and interactions, the symmetry-equivalent sp3 lone pair hAO‘s exhibit strong geminal interactions. R e j3 = py de2=de3 de1 j2 = px j1 This results in a split into the C3-symmetrical (s-type) hAO j1 at low energy (75% s-character!) and the two energetically degenerate j2 and j3 orbitals (identical to the pure px and py orbitals, p-type lone pair orbitals); note that these two pp-orbitals, as a group together, represent the C3-axial symmetry. Note that de1 = 2de2 (= 2de3); since the lone pair orbitals are all doubly occupied, the total energy of the lone pairs remains unaffected. sp1/3 hAO pointing along C3 symmetry axis

7. 3 symmetry-adapted lone pair orbitals; 3 equivalent lone pair spn-hAOs pp spms pp‘ the orthogonal pp(F) pp‘(F) lone pair orbitals interact exclusively with the orthogonal pCC- and p‘CC-LMO‘s, resp., all 3 lone pairs at F interact with both the p- and s-systems of acetylene whereas the spm(F) lone pair orbital interacts exclusively within the axial sCC-system of the acetylene unit. Analogous transformations convert 3 symmetry-equivalent s-LMO‘s (or s*-LMO‘s) into symmetry-adapted (s)3-group orbitals (or (s*)3-group orbitals): p-typeCH3 group orbital by (0):(1):(-1)-mixing orthogonal p-typeCH3 group orbitalby (2):(-1):(-1)-mixing 2 orthogonal equivalent pCN-LMO’s 3 symmetry- equivalent sCH-LMO’s 2 degenerate orthogonal p-typeCH3 group orbitals e de2=de3 e<< 0 s-typeCH3 group orbitalby (1):(1):(1)-mixing de1 sCH-LMO’s s-type CH3 group orbital

8. IPCH p= 13.0 eV 2 a‘ 1 10 11 12 13 14 15 16 17 18 19 20 a‘ a“ 2 2 A particular important application of group orbitals of trigonal symmetry are the generation of group orbitals for the cyclopropane unit (Walsh-orbitals) H sp2 hAO’s are taken here for simplicity; if exact orientation along the bond axes(interorbital angle of 115°) were desired, the hAO‘s would be of type sp2.37;however, the arguments below are not affected by a change in hybridization. 115º sp2 hAO’s H symmetry-equivalent sp5 hAO’s ‘radial’ sp2 hAO peripheral p-AO ≡ cyclopropane CC bond system described by 3 equivalent ‘bent’ sCC-LMO’s (and s*CC-LMO’s) cyclopropane CC bond system described by LC’s of 3 symmetry- adapted radial sp2 hAO’s and 3 peripheral p-AO’s e * WA note: for e‘ IPp= 10.5 eV IPp= 10.85 eV WA WS e‘ e“ Jahn-Teller splitting

9. a‘ 2 * pCC p*CC WA WA similar DE for DE ~ 3 kcal/mol compare to 1,3-butadiene: essentially the same E-profile 5 2 pCC p*CC p*CC pCC * WA p* CO antibonding compare tolmax ~ 160-180 nmfor aliphatic C=O lmax~220-240 nm for C=C-C=O bathochromic shift of p-p* UV band bonding antibonding lmax~190-210 nm WS WA e‘ p CO Nu- : Nu- : compare to Michael addition to a,b-unsaturated carbonyl