2-43
Heteronuclear Molecules
• The relative energy of the bonding orbitals determines the
magnitude of the covalent bond energy (∆Ecov):
2-44
Energy Level Diagram of CO
2-45
Hydrogen Fluoride
• In H-F the 1s orbital of H is energetically well above the 1s
and 2s orbitals of F
–> it interacts only with the 2pz orbital (all remaining
electrons are in non-bonding orbitals!)
2-46
Lithium Fluoride
• As the polarity difference between two atoms increases, the
orbital energy difference also increases
–> electrons shift towards the more electronegative atom
• Limiting case: Ionic compounds
Ionic crystal:
Ions are held together in a
3-dimensional lattice by
combination of electrostatic
and covalent interactions
2-47
Homonuclear Bond Energies
Note: Values can vary considerably depending on compounds involved
•
•
•
•
Bond becomes weaker with increasing atom size
But: First row elements of group 15, 16 and 17 form weaker bonds than
2nd row elements (repulsion between lone pairs more pronounced)
Group 1&2: Destabilizing δ+ charges when mutually bonded
Energy of C–C to N–N sharply decreased due to presence of lone pairs
2-48
Heteronuclear Bond Energies
•
•
Heteronuclear bond energies much higher (stronger bonds) than homonuclear
energies (due to electronegativity differences)
Group 2 bonds stronger than group 1 (ionic bond: lattice energies proportional to ion
charges)
•
B–F stronger than Al–F due to π interaction
•
Si–F stronger than C–F: large difference in electronegativity, π interaction with vacant
d orbitals of Si
2-49
Multiple Bond Energies
•
•
N2 triple is very strong (only the CO triple bond is stronger)
N=N is more than twice the bond energy of a N–N single bond
But: P=P is less than twice the bond energy of the P–P bond
–> π bond interaction for 2nd and 3rd row elements weaker (due to larger and more diffuse p
orbitals)
–> P–P single bond considerably stronger than N–N (or O–O) (less repulsion of lone pair
electrons)
2-50
Molecular Orbitals of Polyatomic Molecules
• Concept of linear combination can be also applied to polyatomic
molecules
–> the resulting MOs are delocalized over the entire molecule
• Symmetry analysis by group theory predicts those linear
combinations, which lead to bonding, anti-bonding or nonbonding MOs
• The energy of the resulting MOs is measured via photoelectron
spectroscopy or estimated with quantum chemical calculations
2-51
Beryllium Dihydride (BeH2)
•
VSEPR analysis: linear geometry
•
Set of AOs:
Be:
H:
Note: the 2px and 2py orbitals yield non-bonding interactions
•
Form group orbitals with 1s orbitals of H and H’:
ΨB = Ψ1s ( H ) − Ψ1s ( H' )
ΨA = Ψ1s ( H ) + Ψ1s ( H' )
2-52
Group Orbitals Interact with Be AOs:
ΨA interacts with the 2s orbital of Be to form a bonding (σs) and
anti-bonding (σs*) orbital:
ΨB interacts with the 2pz orbital of Be to form a bonding (σp)
and anti-bonding (σp*) orbital:
2-53
Energy Level Diagram
energy
Group orbitals
ΨB
ΨA
2-54
MOs of Water (H2O)
•
VSEPR analysis: bent geometry
•
•
Set of AOs:
O:
H:
Note: the 2py orbital results a non-bonding interactions
•
Form goup orbitals with 1s orbitals of H and H’:
ΨB = Ψ1s ( H ) − Ψ1s ( H' )
ΨA = Ψ1s ( H ) + Ψ1s ( H' )
2-55
The Two ΨA Group Orbital Interactions:
ΨA interacts with two AOs of Oxygen: The 2s and 2pz orbital:
–> this results in one bonding, one anti-bonding and one
non-bonding (approximately) orbital:
Oxygen AOs
2pz
σs,z*
σs,z nb
ΨA
(Group Orbital)
2s
σs,z
2-56
The ΨB Group Orbital Interaction:
ΨB interacts with the 2px orbital of oxygen to form a bonding (σs)
and anti-bonding (σs*) orbital:
ΨB
2px
2-57
To Give the Final Energy Level Diagram...
Group orbitals
energy
ΨB
ΨA
2-58
Diagram with MO shapes
2-59
Hybridization
•
Molecular Orbital Theory:
–> Electrons are delocalized over entire molecule (including core shell
electrons!)
•
Hybrid Orbital Description:
–> Valence bond approach
–> Bonds described as localized interactions of TWO electrons
Bonding between two atoms can be also described as overlap of two
hybrid orbitals, which represent the correct valence geometries
– A hybrid orbital is a linear combination of AOs of a SINGLE atom
– Different linear combinations will result different geometries
2-60
Hybrid Orbitals
2-61
Linear Geometry
• Beryllium Hydride
Linear combination of one 2s and one 2p orbitals results two sp
hybrid orbitals:
sp(1) =
1
(2 s + 2 pz )
2
sp(2) =
1
(2 s − 2 pz )
2
promotion
2-62
Linear Geometry
• Ethyne (HCCH)
• The two remaining p orbitals contain one electron each
–> Delocalization of these two electrons results two orbitals
with π symmetry (with 90° angle between each other):
2-63
Trigonal Geometry
• Boron Trihydride:
• The remaining 2pz orbital is perpendicular to the the three
hybrid orbitals and is not occupied
2-64
Trigonal Geometry
• Ethene (H2CCH2):
• The remaining two 2px orbitals is perpendicular to the the three
hybrid orbitals and contain one electron each
–> Delocalization results one additional orbital with π symmetry
2-65
Tetrahedral Geometry
• Methane (CH4)
• The 2s and three 2p orbitals of carbon result four sp3 hybrid
orbitals
2-66
How useful are hybrid orbitals?
• Provides a qualitative picture of the bonding around an atom
• Purely mathematical concept
• Hybridization arguments are not predictive, just descriptive!
• MO theory is predictive, but complicated to use
2-67
Frontier Orbitals
• Many properties of molecules can be interpreted through the
use of the molecular orbital model, and in particular by
looking at the frontier orbitals:
– the HOMO (highest occupied molecular orbital)
–> Donor orbital
– the LUMO (lowest unoccupied molecular orbital)
–> Acceptor orbital
• The energy difference between the HOMO and LUMO
corresponds to the lowest excitation energy
2-68
Conjugated Systems
•
When two or more double (or triple) bonds are close to one another, the
valence π electrons tend to “mingle together”
–> the MO model with its emphasis on delocalization explains this effect
better than the localized valence bond approach:
• Ethene:
π*
π
H
H
H
H
2-69
Conjugated Sytems
• Butadiene:
H
π*
3 nodes
π*
2 nodes
π
1 node
π
no node
H
H
H
H
H
Carbon: sp2 hybridized
2-70
Energy Levels
• With increasing number of orbitals, the energy levels get
closer and closer
–> the energy difference between HOMO and LUMO is
decreasing
–> excitation by a small electric potential or by light will move
electrons into the LUMO orbitals, ready to convey a current
(if a potential difference is imposed)
–> semiconducting properties
2-71
Cyclic Structures
2-72
August Kekulé had a dream...
• Benzene was isolated 1823 from distillation of whale oil by
Michael Faraday (named ‘bicarburet of hydrogen’)
• The structure was an unsolved puzzle
until 1865, when Kekulé dreamed of
“carbon-chain snakes” and finally
proposed the correct structure
Some older “versions” of benzene:
2-73
Resonance Structures of Benzene
•
There are two possible resonance structure for benzene:
–> each carbon has sp2 hybridization, the remaining 6
p-orbitals combine to give 6 delocalized MO π orbitals
2-74
MO Energy Diagram
π*
3 nodes
Energy
2 nodes
1 node
no node
π*
π*
π
π
π
2-75
Large Conjugated Sytems
•
Graphite consists of layers of fused 6-membered carbon rings (sp 2 hybridized) with an
interlayer spacing of 335 pm (sum of carbon radii)
•
The remaining unhybridized p-orbitals participate in extensive π bonding, with electron density
delocalized over the layers
Bond distance: 142 pm = bond order of 1.333
•
•
•
At very high pressure graphite can
be converted to diamonds, another
allotrope of carbon
All carbon atoms are sp3 hybridized,
there are no delocalized electrons
–> diamond is an insulator
2-76
Buckminster Fullerene
•
•
•
In 1985 another allotrope of carbon (C60) was discovered via pulsed laser
vaporization of graphite
It was named after the architect Buckminster Fuller
All 60 carbons are sp2 hybridized, leaving 60 p-orbitals to give 60 MOs
(spread over both sides of the surface)
2-77
Natural Products
•
Many colored compounds in nature consist of large, delocalized π-systems
•
The HOMO-LUMO energy difference in these molecules is small enough to
absorb light in the visible region
N
N
Mg
H3 C
N
beta-carotene (orange)
N
H
O
H3CO
O
O
O
Note: The color of a material is complementary
to the absorbed light
–> beta carotene is orange, and therefore it
absorbs strongly in the blue and violet region of
the spectrum
Chlorophyll (green)
2-78
Photosynthesis
• The green color of plants is due to absorption of light by
chlorophyll pigments
–> the absorbed energy is used to convert CO2 to carbohydrates
(sugars), oxygen is produced as a “side product”