Theories of Covalent Bonding
Theories of Covalent Bonding
• Valence Bond (VB) Theory and Orbital Hybridization
• The Mode of Orbital Overlap and the Types of Covalent Bonds
• Molecular Orbital (MO) Theory and Electron Delocalization
The Central Themes of VB Theory
• A covalent bond forms when the orbitals of two atoms overlap and the overlap
region, which is between the nuclei, is occupied by a pair of electrons
• The two wave functions are in phase so the amplitude increases between the
nuclei
The Central Themes of VB Theory
• A set of overlapping orbitals has a maximum of two electrons that must have
opposite spins
• The greater the orbital overlap, the stronger (more stable) the bond
• The valence atomic orbitals in a molecule are different from those in isolated
atoms
• There is a hybridization of atomic orbitals to form molecular orbitals
Orbital overlap and spin pairing in three diatomic molecules
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The sp hybrid orbitals in gaseous BeCl2
2
The sp2 hybrid orbitals in BF3
The sp3 hybrid orbitals in CH4
3
The sp3 hybrid orbitals in NH3
The sp3d hybrid orbitals in PCl5
4
The sp3d2 hybrid orbitals in SF6
Hybrid Orbitals: An Overview
Hybridization = mixing of orbitals – Linus Pauling “The Nature of the Chenical Bond”
• The number of hybrid orbitals obtained equals the number of atomic orbitals
mixed
• The type of hybrid orbitals obtained varies with the types of atomic orbitals
mixed
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The conceptual steps from molecular formula to the hybrid orbitals used in
bonding
Bond = overlap of orbitals on adjacent atoms
When necessary hybridize orbitals
Procedure:
i.
Draw Lewis structures
ii.
use VSEPR to determine geometry
iii. assign bonds based upon electron configuration of each ato
iv.
if unable ⇒ hybridize valence atomic orbitals,
SN
2
3
4
5
6
v.
vi.
Hybrid orbitals
sp
sp2
sp3
sp3d
sp3d2
put electrons in hybrid orbitals following Hund’s rules
overlap atomic orbitals to form bonds
Postulating Hybrid Orbitals in a Molecule
Use partial orbital diagrams to describe how mixing of the
atomic orbitals of the central atom leads to hybrid orbitals in
each of the following:
PROBLEM:
(a) Methanol, CH3OH
PLAN:
(b) Sulfur tetrafluoride, SF4
Use the Lewis structures to ascertain the arrangement of
groups and shape of each molecule. Postulate the hybrid
orbitals. Use partial orbital box diagrams to indicate the hybrid
for the central atoms.
SOLUTION:
H
(a) CH3OH
H
C O
H H
The groups around C are
arranged as a tetrahedron.
O also has a tetrahedral
arrangement with 2 nonbonding
e- pairs.
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Postulating Hybrid Orbitals in a Molecule (con’d)
(b) SF4 has a seesaw shape with 4 bonding and 1 nonbonding e- pairs.
The σ bonds in ethane(C2H6)
Both C’s are sp3 hybridized
sp3-sp3 overlap to form a σ bond
s-sp3 overlaps to σ bonds
↑
relatively even distribution of electron
density over all σ bonds
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The σ and π bonds in ethylene (C2H4)
The σ and π bonds in acetylene (C2H2)
Electron density and bond order
Describing the Types of Bonds in Molecules
Describe the types of bonds and orbitals in acetone, (CH3)2CO
Use the Lewis structures to ascertain the arrangement of groups and shape at each
central atom. Postulate the hybrid orbitals taking note of the multiple bonds and their
orbital overlaps
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The Central Themes of Molecular Orbital Theory
• A molecule is viewed on a quantum mechanical level as a collection of nuclei
surrounded by delocalized molecular orbitals
• Atomic wave functions are summed to obtain molecular wave functions
• If wave functions reinforce each other, a bonding MO is formed (region of high
electron density exists between the nuclei)
• If wave functions cancel each other, an antibonding MO is formed (a node of zero
electron density occurs between the nuclei)
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Contours and energies of the bonding and antibonding molecular orbitals (MOs) in
H2
The bonding MO is lower in energy and the antibonding MO is higher in energy than
the AOs that combined to form them
The MO diagram for H2
Filling molecular orbitals with electrons follows the same concept as filling atomic
orbitals
Bond Order = ½ (no. of electrons in bonding MOs – no. of electrons in antibonding
MOs)
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MO diagram for He2+ and He2
Predicting Stability of Species Using MO
Diagrams
Use MO diagrams to predict whether H2+ and H2- exist.
For any species that exists, write the electron
configuration
Plan: accommodate the number of electrons in bonding
and antibonding orbitals. Find the bond order.
B.O. = ½ (1-0) = ½
H2+ does exist
σ 1s
B.O. = ½ (2-1) = ½
H2- does exist
(σ 1s ) 2 σ 1*s
Bonding in s-block homonuclear diatomic molecules
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Contours and energies of σ and π MOs through combinations of 2p atomic orbitals
Relative MO energy levels for Period 2 homonuclear diatomic molecules
Z ≥ 8
Z ≤7
12
MO occupancy and molecular properties for B2 through Ne2
The paramagnetic properties of O2
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Using MO Theory to Explain Bond Properties
Example
As the following data show, removing an electron from N2 forms an ion with a weaker,
longer bond than in the parent molecule, whereas the ion formed from O2 has a stronger,
shorter bond
N2
N2+
O2
O2+
Bond energy (kJ/mol)
945
841
498
623
Bond length (pm)
110
112
121
112
Explain these facts with diagrams that show the sequence and occupancy of MOs.
N2 has 10 valence electrons, so N 2+ has 9 valence electrons
O2 has 12 valence electrons, so O 2+ has 11 valence electrons
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Heteronuclear Diatomics
• How do we expect the MO diagram to change when we have two different atoms
in a bond, ie CO?
• The MO diagram will distort, due to the different starting energy levels of each
atom, C and O
• The starting energy level of each atom depends on its electronegativity- let’s take
a look at the MO diagram for CO
C and O are fairly similar in terms of electronegativity, with O more electronegative
than C, so we saw some distortion but not a lot.
What happens when the electronegativities are extremely different? HF
15
Energies of 1s and 2p orbitals are very different
Putting our bonding models together
The VSEPR / hybridization approach is good at explaining shapes around a central atom
in a molecule
BUT, since it depends on keeping electrons in pairs at all times, it is not so good at
predicting electron distributions (like in oxygen!) Is there a way to bring them together?
Let’s go back to RESONANCE
Combining our two bonding models
• σ bonds can be described as being localized.
• π bonding must be treated as being delocalized.
The Resonance Structures for O3 and NO 3−
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Double bonds involve interacting p orbitals, outside of the bonding line
p-π bonding
spread over
whole molecule
p-π antibonding
p-π non-bonding
We can make a similar π molecular orbital for the nitrate ion too!
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Delocalized Electrons
Benzene - aromatic molecules
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The π System for Benzene
Benzene
HOMO-LUMO transitions
• HOMO=Highest occupied molecular orbital
• LUMO=Lowest occupied molecular orbital
• Electron transferred from HOMO to LUMO
Example π-π* transition
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