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Ch 5 Lecture 2 Complex MO’s

Ch 5 Lecture 2 Complex MO’s. MO’s from d-orbitals Transition metals and other heavy elements use d-orbitals in their bonding interactions d-orbitals may form s , p , or d bonds A s example is the d z2 /d z2 interaction b) A p example is the d yz /d yz interaction

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Ch 5 Lecture 2 Complex MO’s

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  1. Ch 5 Lecture 2 Complex MO’s • MO’s from d-orbitals Transition metals and other heavy elements use d-orbitals in their bonding interactions • d-orbitals may form s, p, or d bonds • A s example is the dz2/dz2 interaction b) A p example is the dyz/dyz interaction c) A d example is the dxy/dxy interaction d) d bonds change signs upon C4 rotation around the internuclear axis

  2. Examples • Heteronuclear Diatomics • Polar Bonds • MO pattern is same as homonuclear • One set of AO’s will be at a lower energy than the other • Valence Orbital Potential Energy • Negative energies of attraction of e- to the nucleus • Averaged for all e- on the same level (3p) • As Z increases left to right, VOPE becomes larger

  3. The LCAO for heteronuclear diatomics uses different coefficients because the energies of the 2 atoms are no longer identical • Y = caYa + cbYb (ca≠ cb) • The AO closest in energy to the MO contributes most to it • In CO the 2s MO is mostly O • The 2s* MO is mostly C • The shape and energy of the MO is similar to the major contributing AO • If DE > 12 eV, there is no interaction • For CO, BO = 3 • Mixing is still important

  4. HOMO and LUMO • Molecular reactivity occurs at the Frontier Orbitals • HOMO = Highest Occupied Molecular Orbital • LUMO = Lowest Unoccupied Molecular Orbital • MO Theory helps explain some observations about these orbitals • In CO, O is the most electronegative • We would expect the d- oxygen end to bond to M+ • Bonding MO’s are generally concentrated on the lower energy atom, but symmetry considerations put HOMO on C in this case • The HOMO = 3s is concentrated on C • Carbonyls bind metals through the carbon atom • Antibonding MO’s are generally on the highest energy atom • The LUMO = 1p* is concentrated on C • This orbital can receive e- back from M, strengthening M—C bond

  5. Ionic Compounds • This is the limit of polarity • e- completely donated from one atom to another, which becomes –charged • The + ion then has higher energy vacant orbitals • Example LiF • Li 2s donates e- to the F 2pz • In the MO description, these are the 2 orbitals of correct symmetry to interact • The energy difference is > 12 eV • The MO picture looks similar to a covalent interaction

  6. MO’s for larger molecules • F—H—F- • Consider separately the central atom and its outer atoms Linear = D∞h ~ D2h Character Table for symmetries • Group Orbital = SALC (symmetry adapted linear combination) • Combine orbitals of outer atoms with same symmetry • New group orbitals are then overlapped with central atom AO’s • Same combinations as in F2, but separated by a central atom (dot) • Each combination produces bonding type and antibonding type GO’s

  7. H(1s) orbital on central atom only has 2 possibilities to combine with F GO’s Combine for best overlap to give bonding MO’s • Must be correct symmetries to overlap • Must be correct energies • H(1s) can’t overlap with GO #1(F2s): right symmetry, wrong energy • H(1s) can overlap with GO #3 (F2pz): right symmetry and energy

  8. None of the other F GO’s are of appropriate symmetry to interact with H(1s) • Sketching the MO diagram • Central atom on left • 7 F GO’s are nonbonding (lone pairs) • GO #3/ H(1s) give bonding and antibonding MO’s • Bonding Description: • Lewis: • MO better: 3 center 2 e- bond

  9. CO2 • The group orbitals for O • O are the same as for F • F • The central C has filled s and p orbitals to use in bonding • Use symmetry to find out which orbitals will interact with O GO’s • CO2 is in the D∞h point group, which is hard to work with • We will use D2h character table as a simplification • O • O group orbitals with D2h symetry labels:

  10. (Ag + B1u) (B3u + B2g) (B2u + B3g)

  11. Carbon AO’s with D2h symmetry labels • Interactions of C AO’s and O GO’s • O GO #1(2s) interacts with C(1s) in Ag symmetry • O GO #2(2s) interacts with C(2pz) in B1u symmetry

  12. O GO#3(2pz) interacts with C(2s) in Ag symmetry • O GO#4(2pz) interacts with C(2pz) in B1u symmetry

  13. Energy of interactions • Which of the above 4 interactions are energetically permissible? • Interactions are strongest for orbitals of similar energies • Energy match for O GO#3(2pz)/C(2s) = -15.9eV/-19.4eV is good • Energy match for O GO#1(2s)/C(2s) = -32.4eV/-19.4eV is bad • Energy match for O GO#4(2pz)/C(2pz) = -15.9/-10.7 is good • Energy match for O GO#2(2s)/C(2pz) = -32.4eV/-10.7eV is bad • O GO’s #1 and #2 will not be involved in MO’s

  14. Additional Favorable Interactions: • O GO#5(2py) and C(2py) interact in B2u symmetry • O GO#7(2px) and C(2px) interact in B3u symmetry • O GO#6 (B3g) and O GO#8 (B2g) have no C orbitals to interact with

  15. 7) Final CO2 MO Diagram • 16 valence e- • 2 Bonding s MO • 2 nonbonding s MO • 2 bonding p MO • 2 nonbonding p MO • BO = 4 (2s, 2p) • All Bonding MO’s are • 3 centered 2 electron bonds

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