1. -- The VSEPR and valence-bond theories don’t
Molecular Orbitals
-- The VSEPR and valence-bond theories don’t
explain the excited states of molecules, which
come into play when molecules absorb and
emit light.
-- This is one thing that the molecular orbital (MO)
theory attempts to explain.
Molecules respond to the
many wavelengths of light.
The wavelengths that are
absorbed and then re-emitted
determine an object’s color,
while the wavelengths that are
NOT re-emitted raise the
temperature of the object.

2. molecular orbitals: wave functions that describe the
locations of electrons in molecules
-- these are analogous to atomic orbitals in atoms
(e.g., 2s, 2p, 3s, 3d, etc.), but MOs are possible
locations of electrons in molecules (not atoms)
-- MOs, like atomic orbitals,
can hold a maximum of
two e– with opposite spins
-- but MOs are for
entire molecules
MO theory is more powerful than valence-bond theory;
its main drawback is that it isn’t easy to visualize.

3. The overlap of two atomic orbitals produces two MOs. Hydrogen (H2)
(antibonding MO)
s*1s 1s 1s +
s1s
(bonding MO)
H2 molecular orbitals
H atomic orbitals
-- The lower-energy bonding molecular orbital
concentrates e– density between nuclei.
-- For the higher-energy antibonding molecular orbital,
the e– density is concentrated outside the nuclei.
-- Both of these are s molecular orbitals.

4. Energy-level diagram (molecular orbital diagram)
s*1s 1s 1s
s1s
H atom
H atom
H2 m’cule 1s
H atomic orbitals +
H2 molecular orbitals
s1s
(bonding MO)
(antibonding MO)
s*1s

5. Consider the energy-level diagram for the hypothetical He2 molecule…
s*1s 1s 1s
s1s
He atom
He atom
He2 m’cule
2 bonding e–, 2 antibonding e–
No energy benefit to bonding.
He2 molecule won’t form.

6. bond order = ½ (# of bonding e– – # of antibonding e–)
-- the higher the bond order,
the greater the bond stability
-- a bond order of =
no bond
1 =
single bond
2 =
double bond
3 =
triple bond
-- MO theory allows for fractional bond orders as well.
What is the bond order of H2+?
1 e–
total
1 bonding e–,
zero antibonding e–
BO = ½ (1–0)
= ½

7. Second-Row Diatomic MoleculesLi 3
6.941 Be 4
9.012 B 5
10.811 C 6
12.011 N 7
14.007 O 8
15.999 F 9
18.998 Ne 10
20.180
1. # of MOs = # of combined atomic orbitals
2. Atomic orbitals combine most effectively
with other atomic orbitals of similar energy.
3. As atomic orbital overlap increases, bonding
MO is lowered in energy, and the antibonding
MO is raised in energy.
4. Both the Pauli exclusion principle and
Hund’s rule apply to MOs.

8. Use MO theory to
predict whether Li2
and/or Be2 could
possibly form.
s1s
s*1s 1s 2s
s*2s
s2s Li Li
BO = ½ (4–2)
= 1
Li2
“YEP.”

9. Bonding and antibonding e– cancel each 2s
s*2s
s2s
Bonding and antibonding e– cancel each
other out in core energy levels, so any
bonding is due to e– in bonding orbitals of
outermost shell. Be Be
Be2
BO = ½ (4–4)
= 0
“NOPE.”

10. Molecular Orbitals from 2p Atomic Orbitals
The 2pz orbitals overlap in head-to-head fashion,
so these bonds are...
s bonds.
-- the corresponding MOs are:
s2p and s*2p z x y
The other 2p orbitals (i.e., 2px and 2py) overlap in
sideways fashion, so the bonds are...
p bonds.
-- the corresponding MOs are:
p2p (two of these) and p*2p (two of these)

11. Rule 3 above suggests that, from low energy to
high, the 2p MOs SHOULD follow the order:
LOW
ENERGY
HIGH
ENERGY
s2p < p2p < p*2p < s*2p
General energy-level diagrams for MOs
of second-row homonuclear diatomic molecules...

12. s*2p s*2p “Mr. B” p*2p p*2p s2p p2p p2p s2p same for both s*2s s*2s
For B2, C2, and N2...
For O2, F2, and “Ne2”...
s*2p
s*2p
“Mr. B”
p*2p
p*2p
(or Mr. C)
s2p
p2p
(or Mr. N)
p2p
s2p
same for
both
s*2s
s*2s
s2s
s2s
(1s MOs are down here)
Here, the interaction between
the 2s of one atom and the 2p
of the other is strong. The
orbital energy distribution is
altered.
Here, the interaction is weak.
The energy distribution is
as expected.

13. paramagnetism of liquid oxygen
paramagnetism: describes the
attraction of molecules with
unpaired e– to a magnetic field
diamagnetism: describes substances
with no unpaired e–
(“di-” = two; diamagnetic = “dielectron”) ~
-- such substances are VERY weakly (almost
unnoticeably) repelled
by a magnetic field
Use the energy diagrams
above to tell if diatomic
species are paramagnetic
or diamagnetic.
paramagnetism of liquid oxygen

14. Paramagnetic or diamagnetic?
s2s
s*2s
p2p
p*2p
s2p
s*2p
s1s
s*1s B2 C2 N2 O2 F2
O2+
O22–
C22–
(10)
(12)
(14)
(16)
(18)
(15) P D