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.
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.
Hydrogen (H2)
The overlap of two atomic
orbitals produces two MOs.
(antibonding MO)
s*1s
1s
+
1s
H atomic orbitals
s1s
(bonding MO)
H2 molecular 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.
Energy-level diagram (molecular orbital diagram)
s*1s
1s
1s
H atom s1s
H atom
H2 m’cule
(antibonding MO)
s*1s
1s
+
1s
H atomic orbitals
s1s
(bonding MO)
H2 molecular orbitals
Consider the energy-level diagram for the
hypothetical He2 molecule…
s*1s
1s
1s
He atom s1s
He atom
He2 m’cule
2 bonding e–, 2 antibonding e–
No energy benefit to bonding.
He2 molecule won’t form.
bond order = ½ (# of bonding e– – # of antibonding e–)
-- the higher the bond order,
the greater the bond stability
-- a bond order of...
0=
1=
2=
3=
no bond
single bond
double bond
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
Second-Row Diatomic Molecules
3
4
Li Be
6.941
9.012
B
5
10.811
C
6
12.011
7
8
N
O
14.007
15.999
F
9
18.998
10
Ne
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.
Use MO theory to
predict whether Li2
and/or Be2 could
possibly form.
s*2s
2s
2s
s2s
s*1s
1s
1s
Li
BO = ½ (4–2) = 1
s1s
Li
Li2
“YEP.”
s*2s
2s
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
BO = ½ (4–4) = 0 Be2
“NOPE.”
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
y
x
z
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)
Rule 3 above suggests that, from low energy to
high, the 2p MOs SHOULD follow the order:
LOW
HIGH
s2p < p2p < p*2p < s*2p
ENERGY
ENERGY
General energy-level diagrams for MOs
of second-row homonuclear diatomic molecules...
For B2, C2, and N2...
s*2p
“Mr. B”
(or Mr. C)
(or Mr. N)
same for
both
p*2p
s2p
p2p
For O2, F2, and “Ne2”...
s*2p
p*2p
p2p
s2p
s*2s
s*2s
s2s
s2s
(1s MOs are down here)
Here, the interaction is weak.
Here, the interaction between
the 2s of one atom and the 2p The energy distribution is
as expected.
of the other is strong. The
orbital energy distribution is
altered.
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
Paramagnetic or diamagnetic?
B2
(10)
P
C2
(12)
D
N2
(14)
D
s*2p
p*2p
s2p
p2p
s*2p
p*2p
p2p
s2p
s*2s
s*2s
s2s
s2s
O2
(16)
P
F2
(18)
D
s*1s
s*1s
O2+ (15)
P
s1s
s1s
O22– (18)
D
C22– (14)
D