Chem 5 Chapter 12 Chemical Bonding II: Additional Aspects Part 2 November 22, 2002
Summary of the Valence Bond Theory • Hybridized orbitals are linear combinations of atomic orbitals of the central atom, matching the molecular geometry predicted by VSEPR. sp, sp2, sp3, sp3d, sp3d2
• A σ bond results from an end-to-end overlap of two atomic or hybrid orbitals. • A π bond results from a side-to-side overlap of two p orbitals. It is a single bond, with two electrons filling one π orbital. In ethylene, the C=C double bond consists of a σ bond and a π bond. Ethylene
+
+
H2C=CH2
_
_
+ _
In acetelyne, the C≡C triple bond consists of a σ bond and two π bonds.
Sometimes, valence bond theory does not work:
..
Lewis structure of O2
..
: O=O: All electrons are paired. So O2 is expected to be diamagnetic.
Demo
O2 is paramagnetic.
Paramagnetic: There are unpaired electrons. Diamagnetic: No unpaired electrons. N2 is diamagnetic.
Robert S. Mulliken 1896 - 1986 Born in Newburyport, Massachusetts, Mulliken was the son of an artist and a professor of organic chemistry at Massachusetts Institute of Technology. Heavily influenced by his father’s work, Mulliken developed an interest in chemistry as a boy, earning his B.S. at M.I.T. in 1917, and his Ph.D. at the University of Chicago in 1921. Like Linus Pauling, Mulliken was exposed to the papers of G. N. Lewis and Irving Langmuir on chemical bonding during his Ph.D. period. He traveled extensively in Europe, meeting many prominent researchers. During a visit in 1925, he established a relationship with Friedrich Hund who helped him to advance the molecular orbital theory. This work formed the basis of the research that eventually earned him the Nobel Prize in Chemistry in 1966. However, it was overshadowed for some time by the valence-bond method advocated by Pauling. Among the concepts introduced to chemists by Mulliken are molecular orbital, electron donor and acceptor, and electron affinity. He is credited with helping to provide a theoretical foundation for chemistry, which was primarily an empirical science at the time.
MOLECULAR ORBITAL THEORY Basic idea: Electron density between atoms gives a chemical bond • Linear combinations of atomic orbitals (AO) result in molecular orbitals (MO). • The number of MOs is equal to the number of AOs combined. • When two MOs are formed from two AOs, constructive interference gives a bonding MO with a lower energy, and destructive interference gives an antibonding MO with a higher energy than the original AOs. • For MOs formed with equal energy AOs, the more nodes, the higher the energy of the MO. • Electrons fill MOs with the lowest energy first. • Each orbital holds up to two electrons (Pauli exclusion principle) and obeys Hund’s rule, just like atomic orbitals.
MOs Formed from Linear Combination of Two 1s AOs 1sA
1sA + 1sB = MO1
1sB
A
Constructive interference
B
1sA – 1sB = MO2
Destructive interference
B A
B
Electron density builds up between the atoms
A Electron density low in the middle
The two MOs 1sA – 1sB = MO2
-
+ Node
σ anti-bonding orbital Æ
σ1s*
+ 1sA + 1sB = MO1
σ bonding orbital Æ
σ1s
The Energy of the σ1s and σ1s* Orbitals Energy higher than the original orbitals
σ1s* E
1s orbital in a free atom
A
B
σ1s
Energy lower than the original orbitals
1s orbital in a free atom
The bonding in H2
H
H2
H
σ1s* E 1s
1s
σ1s The electrons are placed in the σ1s.
The MO configuration of H2 is (σ1s)2. H
H2
H
σ1s* E 1s
1s
σ1s Two electrons in a bonding orbital results in a stable molecule.
He2 He
He2
σ1s* E 1s
He
Atomic configuration of He is 1s2
1s
σ1s One pair of electrons goes in σ1s and the next pair in
σ1s*
MO configuration He
He2: (σ1s)2(σ1s*)2 He2
He
σ1s* E 1s
1s
σ1s The bonding effect of the (σ1s)2 is cancelled by the antibonding effect of (σ1s*)2. The He2 is not stable.
The MO configurations, such as He2:(σ1s)2(σ1s*)2, tell us four things: • Its shape, σ or π. • The parent AOs. • Its stability (bonding or antibonding): Antibonding is designated with an asterisk (*). • The number of electrons.
BOND ORDER A measure of bond strength and molecular stability. If # of bonding electrons > # of antibonding electrons then the molecule is stable. Bond order = 1/2
{
# of bonding – electrons
For He2 (σ1s)2(σ1s*)2
# of antibonding electrons
}
BOND ORDER = 0
A high bond order indicates high bond energy and short bond length.
Consider H2+,H2,He2+,He2...
First row diatomic molecules and ions
E
H2
H2+
He2+
He2
Magnetism
Dia-
Para-
Para-
__
Bond order
1
½
½
0
Bond energy (kJ/mol)
436
225
251
—
Bond length (pm)
74
106
108
—
σ1s* σ1s
Now look at second period homonuclear diatomic molecules σ * 2s
2s
2s σ2s σ1s*
E
Li2 Fill the MO’s with electrons, two in each MO from the lowest energy level
1s
1s σ1s
Electron configuration for Li2 σ2s* (σ1s)2(σ1s*)2(σ2s)2 2s
2s
Bond Order = (4 - 2)/2 =1
σ2s
E
σ1s*
A stable single bond. The σ1s and σ1s* orbitals cancel.
1s
1s σ1s
We can omit the inner shell.
DIBERYLLIUM Be
Be2 Be2
Be
σ2s* E
2s
2s σ2s Fill the orbitals
Electron configuration for Be2 is (σ2s)2(σ2s*)2. Be
Be2
Be
σ2s* E
Bond Order =(2 - 2)/2 =0 2s
2s σ2s
No bond
We need to use 2p orbitals to form MOs How about B2? because the Boron atoms have 2p electrons.
σ2px & σ*2px MOs
Two 2px AOs
σ*2px
-
+
-
+
-
+
-
+ -
Anti-bonding
+
σ2px _
-
+
-Bonding
π2pz & π*2pz MOs
Two 2pz AOs
-
+ +
-
+
-
_
π*2pz
-
+ Anti-bonding
+
+ -
π2pz Bonding
π2py & π*2py MOs
Two 2py AOs
_
+ +
-
+
-
π*2py
+
Anti-bonding
+
+
π2py Bonding
ENERGY LEVEL DIAGRAM σ2p*
The π do not split as much because of weaker overlap.
π2p* 2p
π2p
2p
σ2p E
σ2s* 2s
2s σ2s
The π2px and π2py are degenerate We have not considered interactions between s and p orbitals, which pushes the σ2p up and σ∗2s down.
MODIFIED ENERGY LEVEL DIAGRAM σ2p* π2p*
2p E
σ2p π2p
Notice that the σ2p and π2p have switched ! 2p
σ2s* 2s
2s
σ2s
The Order of π2p and σ2p Changes for O, F and Ne
Li2 E
B2
C2 σ2p*
N2
O2
σ2p*
π2p* 2p
σ2p π2p
σ2s* 2s
π2p* 2p
2p
Being away from the axis, π2p is more stable than σ2p , which is repelled by σ2s and σ*2s.
2s σ2s
F2
π2p σ2p σ2s*
2s
2p σ2p is more stable because the larger Zeff compensates for the repulsion by σ2s and σ*2s.
2s σ2s
Electron configuration for B2 σ2p* π2p*
2p E
σ2p π2p σ2s*
2s σ2s
B is [He] 2s22p1
2p Fill electrons from 2s, 2p into σ2s , σ2s* and π2p 2s
Electron configuration for B2: Use HUND’s RULE Unpaired electrons σ2p* Paramagnetic! π2p*
Abbreviated configuration (σ2s)2(σ2s*)2(π2p)2
2p E
σ2p π2p σ2s*
2p Complete configuration (σ1s)2(σ1s*)2(σ2s)2(σ2s*)2(π2p)2
2s
2s σ2s
Bond order = (4 - 2)/2 =1
Second row diatomic molecules NOTE SWITCH OF LABELS
B2
C2
N2
O2
F2
Magnetism
Para-
Dia-
Dia-
Para-
Dia-
Bond order
1
2
3
2
1
Bond E. (kJ/mol)
290
620
942
495
154
Bond length(pm)
159
131
110
121
143
E
σ2p* π2p* σ2p π2p σ2s* σ2s
OXYGEN Lewis Structure
E
σ2p* π2p* π2p σ2p σ2s* σ2s
O
O
Expected to be diamagnetic
Bond Order = (6-2)/2 =2 PARAMAGNETIC Consistent with the DEMO! It was a triumph of MO theory to explain the paramagnetism of O2!
OXYGEN O
O
What does the Lewis structure correspond to in a MO conf.?
E
σ2p* π2p* π2p σ2p σ2s* σ2s
This MO configuration has all electrons paired, but is higher in energy according to Hund’s rule. This excited state of O2 is diamagnetic, whereas the ground state of O2 is paramagnetic.
Demo: Chemiluminascence of Singlet Oxygen Such diamagnetic O2 in the excited state can be generated in the following chemical reaction, and emits light to return to the paramagnetic ground state. Cl2(aq) + H2O2 (aq) + 2OH- → O2*(g) + 2Cl- (aq) + 2H2O Excited state
O2*(g)
→
O2(g) + hν
