南京大学结构化学双语课件CH6LEC2.ppt

6.2 More about Energy Levels and Molecular Orbitals•The BOUND and SUM of energy levels（能级的 “和” 与 “界”）•Alternant Hydrocarbons（交替烃）Bound of the Energy LevelsTheoremThe  energy levels of the conjugated hydrocarbons are bounded, satisfying |x|3 |x| FbFg> Fa>FbAnthraceneNaphthalene4. Molecular Graph0.840.890.450.390.520.550.730.800.100.450.406.4 Aromaticity• Aromaticity, Anti-aromaticity, 4n+2 rule• Resonance Energy （共振能）• The Eight-parameter Scheme• The Five-parameter Scheme1. Aromaticity, anti-aromaticity and 4n+2 ruleCyclic conjugated hydrocarbons are, either,Aromatic – Having 4n+2 pi electrons, extra stabilities is originated from the -electron delocalizationAnti-aromatic – Having 4n pi electrons, destabled due to the -electron delocalization2. Resonance Energy, a Criteria of AromaticityRE = E – ERER?> 0 Aromatic, benzene, etc. = 0 non-aromatic, acyclic hydrocarbons= (13.128+2*13.1135)/3= 13.124 E = 13.68 RE = 13.68-13.124 = 0.56 (b)The Eight-parameter schemeDefine: REPE = RE/NResonance Energies per ElectronFor Benzene REPE = 0.39/6 =0.065For Naphthalene REPE = 0.55/10 = 0.055The Eight-parameter schemeMoleculeRE(b)REPE(H-S) benzene2.000.065naphthalene3.680.056anthracene3.360.020biphenylene4.510.027pentalene2.46*-0.018haptalene3.62*-0.0044. Five-parameter SchemeJ-T-H five-parameter SchemeYuansheng Jiang (江元生） Au-Chin Tang （唐敖庆） Roald HoffmannProblem Set:7，8，10，14Charge DensitiesFor neutral A.H’s, the  electron charges on all of the carbon atoms are equal to 1.TheoremProofFor A.H.’s, the energy levels occurs in pairs (x). The molecular orbitals of each pair should have the property:Charge DensitiesProofThe probability of finding the rth AO in all of the MOs is equal to 1m: the MO index for bonding MOs m′: the MO index for anti-bonding MOs 。