A tutorial on Molecular Orbitals

Molecular Orbitals of BenzeneM. Samiullah,Nov 18, 2009Suchi’s OLED groupUMC-PhysicsOverview• Absorption spectrum of benzene film• Molecular Orbitals– Quantum Problem– Approximations• Linear Combination of Atomic Orbitals (LCAO)– Assignment of absorption bandsTakashi Inagaki J. Chem. Phys. 1972UV Absorption Spectrum (thin film of Benzene between quartz plates) -3Y-scale = x 10 Extremely 1900 Å weakStrongestY-scale = x 12100 Å 2550 Å4SWhat are the origins of these bands? (known since 1880s).3SThree transitions from ground state to low lying states.2S1SElectronic problem of benzene• Full electronic Hamiltonian for 54 particles ( 42 e and 12 nuclei) 1. H = T + T + V + V + Ve n nn en ee2T = KE =1⁄2 m v ; V = PE=(1/4πε ) q q / r ; 0 1 2 12(e = electrons; n = nuclei).2. Solve for stationary states : HΨ(r,R)=EΨ(r,R) Assumptions1. Divide the electrons into valence (e’) and core electrons (e ).02. Born-Oppenheimer adiabatic approximation.– Expand around equilibrium positions of the nuclei.→ H ≈ T + V + V (no vibrations) (6+24 = 30 e problem!) +e’ e’n0 e’e’3. Chemical properties linked to pπ electrons (e”) of C only. -→ H = T + V + V (6 e + 12 nuclei).e’’ e’’n0 e’’e’’4. Mean Field Approximation . Assume each of the six electrons moves in some effective potential called mean field. → (1 e + 12 nuclei)5. Ignore H-nuclei. → (1 e moving in potential of 6 nuclei)Electronic problem of benzene (Summary)1. Solve H Ψ =E Ψ with ...