1Conjugated Organic Molecule• Planar•C– 3 in-plane σ orbitals– 1 out-plane p orbital• π MO– combine out-plane p–|Hij–ESij| Æ best combosHuckel MO Method0 =ƒƒƒƒƒƒƒƒƒƒƒƒƒH11− EH12−ES12H13−ES13H14−ES14H21− ES21H22− EH23− ES23H24− ES24H31− ES31H32− ES32H33− EH34− ES34H41− ES41H42−ES42H43−ES43H44−Eƒƒƒƒƒƒƒƒƒƒƒƒƒ1234Hˆeff= Tˆ+Vˆ1+ Vˆ2+ Vˆ3+ Vˆ4All Vicontainnet attraction btwelectron & Ci2Huckel MO Method0 =ƒƒƒƒƒƒƒƒƒƒƒƒƒH11− EH12−ES12H13−ES13H14−ES14H21− ES21H22− EH23− ES23H24− ES24H31− ES31H32− ES32H33− EH34− ES34H41− ES41H42−ES42H43−ES43H44−Eƒƒƒƒƒƒƒƒƒƒƒƒƒ1234Hˆeff= Tˆ+Vˆ1+ Vˆ2+ Vˆ3+ Vˆ4Hiiall ~same Æ αHijÆ β (if i & j σ-bonded)HijÆ 0 (if i & j not σ-bonded)SijÆ ~0α = E(electron in isolated C p orbital)0 > β > αMath Tricksikjjjjjjjjjα−E β 00βα−E β 00βα−E β00βα−Ey{zzzzzzzzzikjjjjjjjjjjjjjjjjjjjα−Eβ1001α−Eβ1001α−Eβ1001α−Eβy{zzzzzzzzzzzzzzzzzzzikjjjjjjjjjx1001x1001x1001xy{zzzzzzzzz‘x’ that make determinants vanish give EE = α – β x12343More Math Tricksikjjjjjjjjjx1001x1001x1001xy{zzzzzzzzzikjjjjjjjjj0100101001010010y{zzzzzzzzzFind x that make LEFT determinant vanishORFind eigenvalues of RIGHT matrixSpartan MOsethyleneallyl
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