Ch 5 Lecture 2 Complex MO’s I.MO’s from d-orbitals Transition metals and other heavy elements use d-orbitals in their bonding interactions 1)d-orbitals may form , , or  bonds a)A  example is the d z2 /d z2 interaction b)A  example is the d yz /d yz interaction c)A d example is the d xy/ d xy interaction d)  bonds change signs upon C 4 rotation around the internuclear axis

2)Examples II.Heteronuclear Diatomics A.Polar Bonds 1)MO pattern is same as homonuclear 2)One set of AO’s will be at a lower energy than the other 3)Valence Orbital Potential Energy a)Negative energies of attraction of e- to the nucleus b)Averaged for all e- on the same level (3p) c)As Z increases left to right, VOPE becomes larger

4)The LCAO for heteronuclear diatomics uses different coefficients because the energies of the 2 atoms are no longer identical a.  = c a  a + c b  b (c a ≠ c b ) b.The AO closest in energy to the MO contributes most to it i.In CO the 2  MO is mostly O ii.The 2  * MO is mostly C c.The shape and energy of the MO is similar to the major contributing AO d.If  E > 12 eV, there is no interaction e.For CO, BO = 3 f.Mixing is still important

B.HOMO and LUMO 1)Molecular reactivity occurs at the Frontier Orbitals a)HOMO = Highest Occupied Molecular Orbital b)LUMO = Lowest Unoccupied Molecular Orbital 2)MO Theory helps explain some observations about these orbitals a)In CO, O is the most electronegative b)We would expect the  - oxygen end to bond to M+ c)Bonding MO’s are generally concentrated on the lower energy atom, but symmetry considerations put HOMO on C in this case i.The HOMO = 3  is concentrated on C ii.Carbonyls bind metals through the carbon atom d)Antibonding MO’s are generally on the highest energy atom i.The LUMO = 1  * is concentrated on C ii.This orbital can receive e- back from M, strengthening M—C bond

C.Ionic Compounds 1)This is the limit of polarity a)e- completely donated from one atom to another, which becomes –charged b)The + ion then has higher energy vacant orbitals 2)Example LiF a)Li 2s donates e- to the F 2pz b)In the MO description, these are the 2 orbitals of correct symmetry to interact c)The energy difference is > 12 eV d)The MO picture looks similar to a covalent interaction

III.MO’s for larger molecules A.F—H—F - 1)Consider separately the central atom and its outer atoms Linear = D ∞h ~ D 2h Character Table for symmetries 2)Group Orbital = SALC (symmetry adapted linear combination) a)Combine orbitals of outer atoms with same symmetry b)New group orbitals are then overlapped with central atom AO’s c)Same combinations as in F 2, but separated by a central atom (dot) d)Each combination produces bonding type and antibonding type GO’s

3)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 i.Must be correct symmetries to overlap ii.Must be correct energies iii.H(1s) can’t overlap with GO #1(F2s): right symmetry, wrong energy iv.H(1s) can overlap with GO #3 (F2p z ): right symmetry and energy OrbitalEnergy H(1s)-13.6eV F(2p z )-18.7eV F(2s)-40.2eV

4)None of the other F GO’s are of appropriate symmetry to interact with H(1s) 5)Sketching the MO diagram a.Central atom on left b.7 F GO’s are nonbonding (lone pairs) c.GO #3/ H(1s) give bonding and antibonding MO’s 6)Bonding Description: a.Lewis: b.MO better: 3 center 2 e- bond

B.CO 2 1)The group orbitals for O O are the same as for F F 2)The central C has filled s and p orbitals to use in bonding a)Use symmetry to find out which orbitals will interact with O GO’s b)CO 2 is in the D ∞h point group, which is hard to work with c)We will use D 2h character table as a simplification d)O O group orbitals with D 2h symetry labels:

(A g + B 1u ) (B 2u + B 3g ) (B 3u + B 2g )

3)Carbon AO’s with D 2h symmetry labels 4)Interactions of C AO’s and O GO’s a.O GO #1(2s) interacts with C(1s) in A g symmetry b.O GO #2(2s) interacts with C(2p z ) in B 1u symmetry

c.O GO#3(2p z ) interacts with C(2s) in A g symmetry d.O GO#4(2p z ) interacts with C(2p z ) in B 1u symmetry

5)Energy of interactions a.Which of the above 4 interactions are energetically permissible? b.Interactions are strongest for orbitals of similar energies c.Energy match for O GO#3(2p z )/C(2s) = -15.9eV/-19.4eV is good d.Energy match for O GO#1(2s)/C(2s) = -32.4eV/-19.4eV is bad e.Energy match for O GO#4(2p z )/C(2p z ) = -15.9/-10.7 is good f.Energy match for O GO#2(2s)/C(2p z ) = -32.4eV/-10.7eV is bad g.O GO’s #1 and #2 will not be involved in MO’s

6)Additional Favorable Interactions: a.O GO#5(2p y ) and C(2p y ) interact in B 2u symmetry b.O GO#7(2p x ) and C(2p x ) interact in B 3u symmetry c.O GO#6 (B 3g ) and O GO#8 (B 2g ) have no C orbitals to interact with

7)Final CO 2 MO Diagram a.16 valence e- i.2 Bonding  MO ii.2 nonbonding  MO iii.2 bonding  MO iv.2 nonbonding  MO b.BO = 4 (2 , 2  ) c.All Bonding MO’s are 3 centered 2 electron bonds