Ch 5 Lecture 2 Complex MO’s
I.
MO’s from d-orbitals
d z2
Transition metals and other heavy elements use d-orbitals in their bonding interactions
1) d-orbitals may form s, p, or d bonds
a) 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)
II.
Examples
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.
Y = caYa + cbYb
(ca ≠ cb)
b. The AO closest in energy to the MO
contributes most to it
i. In CO the 2s MO is mostly O
ii. The 2s* MO is mostly C
c. The shape and energy of the MO
is similar to the major contributing AO
d.
If DE > 12 eV, there is no interaction
e.
For CO, BO = 3
f.
Mixing is still important
C O
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)
C O
M+
MO Theory helps explain some observations about these orbitals
a) In CO, O is the most electronegative
b)
We would expect the d- 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 = 3s 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 = 1p* is concentrated on C
ii. This orbital can receive e- back from M, strengthening M—C bond
M+
C O
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—F1) Consider separately the central atom and its outer atoms
Linear = D∞h ~ D2h 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 F2, 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 (F2pz): right symmetry and energy
Orbital
Energy
H(1s)
-13.6eV
F(2pz)
-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: F H
b. MO better:
3 center 2 e- bond
F
B.
CO2
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) CO2 is in the D∞h point group, which is hard to work with
c) We will use D2h character table as a simplification
d) O • O group orbitals
with D2h symetry labels:
(Ag + B1u)
(B3u + B2g)
(B2u + B3g)
3)
Carbon AO’s with D2h symmetry labels
4)
Interactions of C AO’s and O GO’s
a.
O GO #1(2s) interacts with C(1s) in Ag symmetry
b.
O GO #2(2s) interacts with C(2pz) in B1u symmetry
c.
d.
O GO#3(2pz) interacts with C(2s) in Ag symmetry
O GO#4(2pz) interacts with C(2pz) in B1u symmetry
5)
Energy of interactions
a. Which of the above 4 interactions are energetically permissible?
b.
c.
d.
e.
f.
g.
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
6)
Additional Favorable Interactions:
a. O GO#5(2py) and C(2py) interact in B2u symmetry
b. O GO#7(2px) and C(2px) interact in B3u symmetry
c. O GO#6 (B3g) and O GO#8 (B2g) have no C orbitals to interact with
7)
Final CO2 MO Diagram
a. 16 valence ei.
2 Bonding s MO
ii. 2 nonbonding s MO
iii. 2 bonding p MO
iv. 2 nonbonding p MO
b.
BO = 4 (2s, 2p)
c. All Bonding MO’s are
3 centered 2 electron bonds