Download Molecular Orbitals Chapter 5 : Molecular Orbitals

Chapter 5 : Molecular Orbitals
N2
NH3
H2O
Why do they make chemical bonds ?
Chapter 5 : Molecular Orbitals
Stabilization
Bond energy
1
Types of Chemical Bonds
Metallic Bond Ionic Bond Covalent Bond
Covalent Bond
Localized electron bonding models
•Lewis dot structure
•VSEPR (Valence shell electron pair repulsion)
•Valence bond theory (hybridization)
Delocalized electron bonding model
•Molecular orbital (MO) theory
2
Molecular Orbital Theory
LE is great to predict bondings and structures and geometries of
molecules.
BUT, there are some short points.
•No concept of resonance.
•No paramagnetic properties.
•No information of bond energy.
Fact: O2 is paramagnetic!
O O
Lewis structure
VSEPR
Valence bond theory
•sp2 hybridized
•lone pairs in sp2 hybrid orbitals
•bonding pairs in σ and π bonds
All show
all electrons
paired.
Molecular Orbital Theory
In contrast to LE, molecular orbitals describe how electrons
spread over all the atoms in a molecule and bind them together,
which can give correct views of
• concept of resonance.
• paramagnetic properties.
• bond energy.
Fact: O2 is paramagnetic!
O O
Lewis structure
VSEPR
Valence bond theory
•sp2 hybridized
•lone pairs in sp2 hybrid orbitals
•bonding pairs in σ and π bonds
All show
all electrons
paired.
3
How to construct
molecular orbitals
H2 – 2 protons and 2 electrons
Schroedinger Eq => Molecular orbitals
But, no way to solve
=> LCAO (linear combination of atomic orbitals)
=> Approximate solutions of Schroedinger Eq
How to make chemical bonds
Overlap of wave functions:
–
–
+
–
destructive
overlap
+
–
φΑ
constructive
overlap
+
+
Α
–
Β
φ+
φΒ
φ+2
Constructive overlap
⇒ enhance e- density between the nuclei
⇒ attract the nuclei
⇒ bonding orbital
φΑ
Α
Β
φ−
φΒ
φ−2
destructive overlap
⇒ node(s) between the nuclei
⇒ repel each other
⇒ antibonding orbital
4
How to make chemical bonds
higher energy
φΑ
Α
Β
φ+
φΒ
φ+2
Constructive overlap
⇒ enhance e- density between the nuclei
⇒ attract the nuclei
⇒ bonding orbital
φΑ
φ−
φΒ
Α
Β
2
lower energy φ−
destructive overlap
⇒ node(s) between the nuclei
⇒ repel each other
⇒ antibonding orbital
Molecular orbitals from s orbitals
H2
σ*1s
antibonding m.o.
(higher energy than
separate atoms)
σ1s
bonding m.o.
(lower energy than
separate atoms)
σ (C2 symmetric about the line connecting the nuclei)
5
Molecular orbitals from p orbitals
π (C2 antisymmetric about the line connecting the nuclei)
Molecular orbitals from p orbitals
6
Molecular orbitals from d orbitals
Molecular orbitals from d orbitals
7
3 things to consider to form MOs
N atomic orbitals => N molecular orbitals
Symmetry match of atomic orbitals
Relative energy of atomic orbitals
3 things to consider to form MOs
N atomic orbitals => N molecular orbitals
Symmetry match of atomic orbitals
Relative energy of atomic orbitals
8
3 things to consider to form MOs
N atomic orbitals => N molecular orbitals
Symmetry match of atomic orbitals
Relative energy of atomic orbitals
Forming nonbonding orbitals
3 things to consider to form MOs
N atomic orbitals => N molecular orbitals
Symmetry match of atomic orbitals
Relative energy of atomic orbitals
dx2-y2 또는 dxy
Forming nonbonding orbitals
9
3 things to consider to form MOs
N atomic orbitals => N molecular orbitals
Symmetry match of atomic orbitals
Relative energy of atomic orbitals
And remember
The more nodes, the higher energy.
10
H2
bond order =
(no. of e– in bonding m.o.s) - (no. of e– in antibonding m.o.s)
2
σ*1s
H2
E
1s
1s
σ1s
b.o. = 1 (i.e., lower energy than separate atoms)
He2
E
He2
He2+
σ*1s
σ*1s
1s
1s
1s
1s
σ1s
σ1s
b.o. = 0
b.o. = 0.5
11
2nd-row diatomic molecules
2nd-row diatomic molecules
No mixing
O2, F2, Ne2
Mixing
Li2 - N2
Ψ = c1φ(2sa) + c2φ(2sb) + c3φ(2pza) + c4φ(2pzb)
12
2nd-row diatomic molecules
No mixing
O2, F2, Ne2
Mixing
Li2 - N2
Not big
Ψ = c1φ(2sa) + c2φ(2sb) + c3φ(2pza) + c4φ(2pzb)
2nd-row diatomic molecules
No mixing
O2, F2, Ne2
b.o. = 1
Li2
13
2nd-row diatomic molecules
No mixing
O2, F2, Ne2
b.o. = 0
Be2
b.o. = 0
2nd-row diatomic molecules
No mixing
O2, F2, Ne2
b.o. = 1 (π)
paramagnetic
B2
found in gas phase
14
2nd-row diatomic molecules
b.o. = 2 (π)
No mixing
found in gas phase
O2, F2, Ne
2
rare
C2
C22- is more common
C2 d(C-C) 132 pm
CaC2 d(C-C) 119.1 pm
C2H2 d(C-C) 120.5 pm
Bond order ?
2nd-row diatomic molecules
b.o. = 3 (2π+σ)
No mixing
Very high bond energy: 942kJ/mol
O2, F2, Ne2
N2
15
Breaking Nitrogen Bonds
N
N
Bond Enthalphy : 946 kJ/mol
FACTORY
Chemistry: The Study of Change
Nitrogen Cycle
rearrangement of atoms and molecules
16
2nd-row diatomic molecules
O2
b.o. = 2
O
Paramagnetic
O
N2
Other forms of O2n
O2+ b.o ?
O2- b.o ?
O22- b.o ?
2nd-row diatomic molecules
F2
b.o. = 1
N2
17
2nd-row diatomic molecules
b.o. = 0
Ne2
N2
2nd-row diatomic molecules
HOMO (highest occupied molecular orbital)
LUMO (lowest unoccupied molecular orbital)
Big triumph of MO theory
SOMO (singly occupied molecular orbital)
Frontier orbitals
18
Bond lengths in 2nd-row diatomic
molecules
Bond length
Covalent radius
H-X
H-B
H-C
H-N
H-O
H-F
Length (pm)
120
109
101.2
96
91.8
Any trend found?
OK with electronegativity difference
Bond lengths in 2nd-row diatomic
molecules
Bond length
Covalent radius
H-X
H-B
H-C
H-N
H-O
H-F
Length (pm)
120
109
101.2
96
91.8
Any trend found?
19
Bond lengths in 2nd-row diatomic
molecules
Bond length
Covalent radius
H-X
H-B
H-C
H-N
H-O
H-F
Length (pm)
120
109
101.2
96
91.8
Don’t be fooled by the text book.
Covalent radii are defined in X-X single bond (Table 2-8).
How to measure the energy levels of MOs ?
(Photoelectron spectroscopy)
hν = UV Æ UPS : outer electrons
hν = X-ray Æ XPS : inner electrons
photoelectron
v
IE
A + hν Æ A+ + e-
Ionization energy = hν - ½ mv2
20
How to measure the energy levels of MOs ?
(Photoelectron spectroscopy)
N2
Why fine structure?
O2
Ionization energy = hν - ½ mv2
Franck-Condon Principle
Classically, the Franck–Condon principle is the approximation
that an electronic transition is most likely to occur without
changes in the positions of the nuclei in the molecular entity and
its environment. The resulting state is called a Franck–Condon
state, and the transition involved, a vertical transition.
Mnucleus >> Melectron
e-: faster motion
21
Franck-Condon Principle
N2+
N2
Ionization energy = hν - ½ mv2 – Evib+
How to measure the energy levels of MOs ?
(Photoelectron spectroscopy)
N2
O2
stronger bonding involved
less bonding involved
22
Correlation Diagram
No mixing
O2, F2, Ne2
Mixing
Li2 - N2
Not big
Correlation Diagram
23
Correlation Diagram
non-crossing rule
r(X-X)=0
r(X-X)=∞
MOs of Heteronuclear Diatomic Molecules
3 things to consider to form MOs
N atomic orbitals => N molecular orbitals
Symmetry match of atomic orbitals
Relative energy of atomic orbitals
|cA| = |cΒ|
|cA| = |cΒ|
|cA| > |cΒ|
|cA| < |cΒ|
|cA| >> |cΒ|
|cA| << |cΒ|
Ψ = cAφA + cΒφB
24
MOs of Heteronuclear Diatomic Molecules
Average potential energy
of all terms
MOs of Heteronuclear Diatomic Molecules
25
MOs of Heteronuclear Diatomic Molecules
z
C
O
p orbital w/o
considering signs
C2v
MOs of Heteronuclear Diatomic Molecules
C∞v
26
MOs of Heteronuclear Diatomic Molecules
M – C≡O
M – O≡C ?
MOs of Heteronuclear Diatomic Molecules
M – C≡O
M – O≡C ?
27
Ionic Compounds
LiF
View of ionic interaction
Li: 1s22s1 Æ Li+: 1s2
F: 1s22s2sp5 Æ F-: 1s22s22p6
Electrostatic interaction
View of MO
transfer of Li2s e- to F2p orbital which is lowered
F2p character
Don’t forget
that ionic interaction is
omnidirectional and more
accurate MO description requires
bands.
Ionic Compounds
LiF
View of ionic interaction
Li: 1s22s1 Æ Li+: 1s2
F: 1s22s2sp5 Æ F-: 1s22s22p6
Is this process really helpful?
28
Ionic Compounds
LiF
thermodynamically unfavorable!!
Ionic Compounds
LiF
Lattice enthalpy is the deriving force.
29
MOs of Polyatomic Molecules
1.
2.
3.
4.
5.
6.
Determine the point group of molecules. (D∞h Æ D2h, C∞v Æ C2v)
Assign x, y, z coordinates.
Find reducible representations for ns orbitals on the outer atoms. Repeat for np
orbitals in the same symmetry. (valence orbitals)
Reduce the reducible representations of step 3 to derive group orbitals or
symmetry adapted linear combinations (SALCs)
Find the atomic orbitals of the central atoms with the same symmetries as those
found in step 4.
Combine the atomic orbitals of the central atom and the SALCs of the outer atoms
with the same symmetry and similar energy to form MOs.
MOs of Polyatomic Molecules
FHF-
D∞h Æ D2h
F(2px)+F(2px)
2
-2
0
0
0
0
2
-2
Æ B3u + B2g
F(2py)+F(2py)
2
-2
0
0
0
0
-2
2
Æ B2u + B3g
F(2pz)+F(2pz)
2
2
0
0
0
0
2
2
Æ Ag + B1u
F(2s)+F(2s)
2
2
0
0
0
0
2
2
Æ Ag + B1u
30
MOs of Polyatomic Molecules
FHF-
Ag
can combine to form MOs
F---F: SALCs
H: 1s orbital
MOs of Polyatomic Molecules
FHF(-13.6 eV)
H 1s
(-18.7 eV)
(-40.2 eV)
H 1s will strongly interact with F2Pzs (Ag).
Don't forget if F2s contributes, 3 MOs are formed.
31
MOs of Polyatomic Molecules
FHF-
antibonding
non-bonding
* there are slight
long-range
interactions.
bonding
MOs of Polyatomic Molecules
FHF-
MO
3-center 2-electron bond
F H F
Lewis structure
32
MOs of Polyatomic Molecules
CO2
D∞h Æ D2h
O(2px)+O(2px)
2
-2
0
0
0
0
2
-2
Æ B3u + B2g
O(2py)+O(2py)
2
-2
0
0
0
0
-2
2
Æ B2u + B3g
O(2pz)+O(2pz)
2
2
0
0
0
0
2
2
Æ Ag + B1u
O(2s)+O(2s)
2
2
0
0
0
0
2
2
Æ Ag + B1u
MOs of Polyatomic Molecules
CO2
O C O
O C O
O---O: SALCs
combine to form MOs
C: valence orbitals
33
MOs of Polyatomic Molecules
CO2
Ag
stronger interaction
MOs of Polyatomic Molecules
CO2
O C O
O C O
O---O: SALCs
combine to form MOs
C: valence orbitals
34
MOs of Polyatomic Molecules
CO2
B1u
stronger interaction
MOs of Polyatomic Molecules
CO2
O C O
O C O
O---O: SALCs
C: valence orbitals
35
MOs of Polyatomic Molecules
CO2
B2u
MOs of Polyatomic Molecules
CO2
O C O
O C O
O---O: SALCs
C: valence orbitals
36
MOs of Polyatomic Molecules
CO2
B3u
MOs of Polyatomic Molecules
forming non bonding orbitals
CO2
O C O
O C O
O---O: SALCs
C: valence orbitals
37
MOs of Polyatomic Molecules
CO2
O=C=O
Lewis structure
2-center 2 electron bond
16 valence e-'s
non-bonding π
bonding π
3-center 2 electron bond
bonding σ
non-bonding σ
MOs of Polyatomic Molecules
H2O
C2v
H(1s)+H(1s)
2
0
2
0
Æ A1 + B1
Α1
H
Β1
H
H
H
Ψa1= (1/√2){φa(H1s)+φb(H1s)}
Ψb1= (1/√2){φa(H1s)-φb(H1s)}
H------H: SALCs
38
MOs of Polyatomic Molecules
H2O
C2v
2py B2
Α1
Β1
2pz A1
H
2px B1
2s
A1
H
H
H
Ψa1= (1/√2){φa(H1s)+φb(H1s)}
Ψb1= (1/√2){φa(H1s)-φb(H1s)}
H------H: SALCs
O: valence orbitals
MOs of Polyatomic Molecules
H2O
C2v
1b1 bonding
2b1 antibonding
2py B2
Α1
Β1
2pz A1
H
2px B1
2s
A1
O: valence orbitals
H
H
H
Ψa1= (1/√2){φa(H1s)+φb(H1s)}
Ψb1= (1/√2){φa(H1s)-φb(H1s)}
H------H: SALCs
39
MOs of Polyatomic Molecules
H2O
C2v
2a1 nearly
non-bonding
3a1 bonding
4a1 antibonding
2py B2
Α1
Β1
2pz A1
H
2px B1
2s
H
H
H
Ψa1= (1/√2){φa(H1s)+φb(H1s)}
Ψb1= (1/√2){φa(H1s)-φb(H1s)}
A1
H------H: SALCs
O: valence orbitals
MOs of Polyatomic Molecules
H2O
C2v
O
H
2py B2
1b2 non-bonding
Α1
Β1
2pz A1
H
2px B1
2s
A1
O: valence orbitals
H
H
H
Ψa1= (1/√2){φa(H1s)+φb(H1s)}
Ψb1= (1/√2){φa(H1s)-φb(H1s)}
H------H: SALCs
40
MOs of Polyatomic Molecules
H2O
C2v
MOs of Polyatomic Molecules
H2O
C2v
bonding
41
MOs of Polyatomic Molecules
H2O
C2v
bonding
nearly non-bonding
(c2<<c1)
MOs of Polyatomic Molecules
5.269 eV
H2O
4.219
E
-12.35
-14.69
-17.51
-37.03
42
MOs of Polyatomic Molecules
H2O
O
Other approach
A1
2s
2pz
sp
sp
b1
b2
H----H SALCs
A1
B1
b1
O
B2
B1
MOs of Polyatomic Molecules
H2O
104.5°
Why 104.5o in MO theory?
43
MOs of Polyatomic Molecules
Walsh Diagram
- a diagram showing the variation of orbital energy
with molecular geometry
a1g σg
a1
b1u σu
b1
b2
e1u πu
a1
b1
b1u σu
a1g σg
a1
D∞h
C2v
MOs of Polyatomic Molecules
Walsh Diagram
- a diagram showing the variation of orbital energy
with molecular geometry
a1g σg
a1
b1u σu
b1
b2
e1u πu
a1
b1
b1u σu
a1g σg
a1
D∞h
C2v
44
MOs of Polyatomic Molecules
Walsh Diagram
- a diagram showing the variation of orbital energy
with molecular geometry
MOs of Polyatomic Molecules
Walsh Diagram
- a diagram showing the variation of orbital energy
with molecular geometry
45
MOs of Polyatomic Molecules
NH3
C3v
3H(1s)
3
0
1 Æ A1 + E
O
3H SALCs
MOs of Polyatomic Molecules
NH3
N
C3v
3H(1s)
3
0
1 Æ A1 + E
3H SALCs
46
MOs of Polyatomic Molecules
C3v
NH3
pz character
non-bonding
2s
MOs of Polyatomic Molecules
D3h
BF3
F
B
F
F
3F(2s)
3
0
A1'
1
3
0
1 Æ A1' + E'
E'
47
MOs of Polyatomic Molecules
D3h
BF3
F
B
F
F
3F(2px)
3
0
-1
3
0
-1 Æ A2' + E'
E'
A2'
MOs of Polyatomic Molecules
D3h
BF3
F
B
F
F
3F(2py)
3
0
A1'
1
3
0
1 Æ A1' + E'
E'
48
MOs of Polyatomic Molecules
D3h
BF3
F
B
F
F
3
3F(2pz)
0
-1
-3
0
1 Æ A2'' + E''
E''
A2''
MOs of Polyatomic Molecules
D3h
BF3
F
B
F
F
B
2s
A1'
2px
2py
E'
2pz
A2''
49
MOs of Polyatomic Molecules
BF3
D3h
A2''
2py
SALCs
3F(2pxz
E''
2pz A2''
A2'
2px
E'
3F(2px)
E'
2s A1'
A1'
3F(2py)
E'
B
A1'
MOs of Polyatomic Molecules
BF3
2px
SALCs
D3h
A2''
2py
3F(2s)
E'
3F(2pxz
E''
2pz A2''
A2'
E'
3F(2px)
E'
2s A1'
A1'
E'
3F(2py)
B
A1'
E'
3F(2s)
50
MOs of Polyatomic Molecules
BF3
D3h
Lewis ?
VBT?
antibonding
? σ and ? π
non-bonding
almost non-bonding
bonding
same for SO3, NO3-, CO32-
Symmetry Adapted Orbitals
(SALCs, Group Orbitals)
CO2
FHF-
H2O
2px B1
2py B2
2pz A1
2s
A1
51
Symmetry Adapted Orbitals
(SALCs, Group Orbitals)
NH3
Symmetry Adapted Orbitals
BF3
D3h
A2''
2py
2px
SALCs
E''
3F(2pxz
2pz A2''
A2'
E'
3F(2px)
E'
2s A1'
B
A1'
A1'
E'
E'
3F(2py)
3F(2s)
52
Symmetry Adapted Orbitals
Symmetry Adapted Orbitals
53
Symmetry Adapted Orbitals
Molecular Shapes in MO
Semiempirical or Estimated shape
Æ Determination of overall energy and molecular orbitals
Æ Different shape
Æ Determination of overall energy and molecular orbitals
Æ Different shape
Æ .....
Æ until minimum energy is found
calculated minimum energy ≥ true energy
54
Hybrides
Which atomic orbitals form hybrides?
4 1
0
0
2 Æ A1+ T2
s
px, py, pz
sp3
why not d ?
55
Which atomic orbitals form hybrides?
F
B
F
F
3
0
1
3
0
1 Æ A1' + E'
s
px, py
sp2
pz is left over.
Expanded Shells and MO
from MO
56