Ch 5 Lecture 2 Complex MOs

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Ch 5 Lecture 2 Complex MOs

• MOs 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

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• Examples
• Heteronuclear Diatomics
• Polar Bonds
• MO pattern is same as homonuclear
• One set of AOs 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

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• 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 gt 12 eV, there can be no interaction
• For CO, BO 3
• Mixing is still important

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• 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 MOs 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 MOs are generally on the highest
  energy atom
• The LUMO 1p is concentrated on C
• This orbital can receive e- back from M,
  strengthening MC bond

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• 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 gt 12 eV
• The MO picture looks similar to a covalent
  interaction

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• MOs for larger molecules
• FHF-
• Consider separately the central atom and its
  outer atoms
• Group Orbital SALC (symmetry adapted linear
  combination)
• Combine orbitals of outer atoms with same
  symmetry
• New group orbitals are then overlapped with
  central atom AOs
• Same combinations as in F2, but separated by a
  central atom (dot)
• Each combination produces bonding type and
  antibonding type GOs

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• H(1s) orbital on central atom only has 2
  possibilities to combine with F GOs
• Combine for best overlap to give bonding MOs
• Must be correct symmetries to overlap
• Must be correct energies
• H(1s) cant overlap with GO 1(F2s) right
  symmetry, wrong energy
• H(1s) can overlap with GO 3 (F2pz) right
  symmetry and energy

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

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• 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 GOs
• CO2 is in the D8h 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

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• Carbon AOs with D2h symmetry labels
• Interactions of C AOs and O GOs
• O GO 1(2s) interacts with C(1s) in Ag symmetry
• O GO 2(2s) interacts with C(2pz) in B1u symmetry

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• O GO3(2pz) interacts with C(2s) in Ag symmetry

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• Energy of interactions
• Which of the above 4 interactions are
  energetically permissible?
• Interactions are strongest for orbitals of
  similar energies
• Energy match for O GO3(2pz)/C(2s)
  -15.9eV/-19.5eV is good
• Energy match for O GO1(2s)/C(2s)
  -32.4eV/-19.5eV is bad
• Energy match for O GO4(2pz)/C(2pz) -15.9/-10.7
  is good
• Energy match for O GO2(2s)/C(2pz)
  -32.4eV/-10.7eV is bad
• O GOs 1 and 2 will not be involved in MOs

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• Additional Favorable Interactions
• O GO5(2py) and C(2py) interact in B2u symmetry
• O GO7(2px) and C(2px) interact in B3u symmetry
• O GO6 (B3g) and O GO8 (B2g) have no C orbitals
  to interact with

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• 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 MOs are
• 3 centered 2 electron bonds