General Chemistry
Principles and Modern Applications
Petrucci • Harwood • Herring
8th Edition
Chapter 12: Chemical Bonding II:
Additional Aspects
Contents
12-1
12-2
12-3
12-4
12-5
12-6
12-7
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What a Bonding Theory Should Do
Introduction to the Valence-Bond Method
Hybridization of Atomic Orbitals
Multiple Covalent Bonds
Molecular Orbital Theory
Delocalized Electrons: Bonding in the
Benzene Molecule
Bonding in Metals
Focus on Photoelectron Spectroscopy
General Chemistry: Chapter 12
Slide 2
12-1 What a Bonding Theory Should Do
• Bring atoms together from a distance.
– e- are attracted to both nuclei.
– e- are repelled by each other.
– Nuclei are repelled by each other.
• Plot the total potential energy vs. distance.
– Negative energies correspond to net attractive forces.
– Positive energies correspond to net repulsive forces.
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General Chemistry: Chapter 12
Slide 3
Potential Energy Diagram
• A bonding theory should
help us understand the
nature of molecules
– Bond distance
– Bond dissociation energy
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General Chemistry: Chapter 12
Slide 4
12-2 Introduction to the Valence-Bond Method
• Valence bond theory and molecular orbital theory use the methods
of quantum mechanics to explain chemical bonding.
• Valence bond theory focuses on how atomic orbitals of the isolated
atoms combine on molecular formation to give individual chemical
bonds.
• Basic principles
– Covalent bond is formed between two atoms by the overlap of half-filled
valence atomic orbitals, one from each atom
– Orbitals overlap in-phase (constructive interference)
– Extra stability (bonding) results from increased electron density between the
two bond forming nuclei upon orbital overlap
– Valence bond theory is a localized model of bonding
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General Chemistry: Chapter 12
Slide 5
Bonding in H2S
• H2S is generated by an overlap of 1s orbitals on H with 3p orbitals on S
• Maximum overlap occurs along the lines joining the centers of H and S
• The predicted H-S-H angle (90°) is in good agreement with the experimental
value (92°)
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General Chemistry: Chapter 12
Slide 6
Example 12-1
Using the Valence-Bond Method to Describe a Molecular
Structure.
Describe the phosphine molecule, PH3, by the valence-bond
method..
Identify valence electrons:
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General Chemistry: Chapter 12
Slide 7
Example 12-1
Sketch the orbitals:
Overlap the orbitals:
Describe the shape:
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Trigonal pyramidal
General Chemistry: Chapter 12
Slide 8
12-3 Hybridization of Atomic Orbitals
• Based on valence orbitals, we would expect the H-O-H angle in
water to be 90
• Based on valence orbitals of carbon we would expect a CH2
molecule. This is not the case
• The simplest hydrocarbon observed under normal laboratory
conditions in CH4 whose formation would require 4 orbitals each
containing a single electron which are 109.5° apart
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General Chemistry: Chapter 12
Slide 9
12-3 Hybridization of Atomic Orbitals
• Neither the ground state nor the excites state suggest molecular
geometries in agreement with experiment
• Orbitals of bonded atoms need not necessarily be identical to
orbitals of isolated atoms
• Algebraically combine the wave functions of the 2s and 2p orbitals
to form 4 new orbitals
• Resulting orbitals are called sp3 hybrid orbitals
• sp3 orbitals have equal energies intermediate between 2s (25%) and
2p (75%)
• sp3 orbitals are solutions of the Schrodinger equation of CH4
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General Chemistry: Chapter 12
Slide 10
sp3 Hybridization
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General Chemistry: Chapter 12
Slide 11
sp3 Hybridization
• Number of orbital conserved
• Energy conserved
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Slide 12
Bonding in Methane
• Hybridization is an after-the-fact rationalization of experimentally
observed molecular shapes
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Slide 13
sp3 Hybridization in Nitrogen
• VSEPR for NH3 and H2O described a tetrahedral electron-group
geometry requiring an sp3 hybridization
Lone pair
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Slide 14
Bonding in Nitrogen
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General Chemistry: Chapter 12
Slide 15
sp2 Hybridization: Boron
• For most Boron compounds, the appropriate hybridization
scheme combines a single 2s and two 2p orbitals into three sp2
orbitals leaving a single vacant p orbital.
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Slide 16
Orbitals in Boron
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General Chemistry: Chapter 12
Slide 17
sp Hybridization: Beryllium
• For most Beryllium compounds, the appropriate hybridization
scheme combines a single 2s and a single 2p orbital into two sp
orbitals leaving two vacant p orbitals.
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General Chemistry: Chapter 12
Slide 18
Orbitals in Beryllium
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General Chemistry: Chapter 12
Slide 19
How Are Atomic Orbitals Mix to Form a
Hybrid Orbital
• A hybrid orbital is a mathematic combination of wave functions
• Phases are important!
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General Chemistry: Chapter 12
Slide 20
sp3d and sp3d2 Hybridization
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General Chemistry: Chapter 12
Slide 21
Hybrid Orbitals and VSEPR
• The valence bond method could be combined with
VSEPR as follows:
– Write a plausible Lewis structure.
– Use VSEPR to predict electron geometry.
– Select hybridization scheme consistent with this geometry.
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General Chemistry: Chapter 12
Slide 22
12-4 Multiple Covalent Bonds
• Ethylene has a double bond in
its Lewis structure
• VSEPR predicts trigonal planar
geometry at carbons
• How are the two CH2 groups
situated one relative to the
other?
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General Chemistry: Chapter 12
Slide 23
Ethylene
•
•
•
•
Molecular shape determined by the s framework
Rotation around the central C=C bond is limited
CH2=CH2 is planar
A double bond (s + p) is stronger that a s bond but not twice as strong
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Slide 24
Acetylene
• Acetylene, C2H2, has a triple bond.
• VSEPR predicts linearity at carbons.
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Slide 25
Acetylene
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General Chemistry: Chapter 12
Slide 26
CO2
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Slide 27
12-5 Molecular Orbital Theory
• Molecular Orbital (MO) theory improves upon several aspects of
previously discussed theories
– Paramagnetizm
– Bond energies/order/lengths
– Predictive (as opposed to rationalizing)
• Atomic orbitals are localized on atoms.
• Molecular orbitals are spread over the entire molecule.
– Each MO can accommodate maximum 2 electrons with opposite spins
• Molecular orbitals are generated via the LCAO procedure
– Linear combination of atomic orbitals.
• When two atoms approach each other to form a bond, their
respective wave functions combine either constructively or
destructively
Ψ1 = φ1 + φ2
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Ψ2 = φ1 - φ2
General Chemistry: Chapter 12
Slide 28
Combining Atomic Orbitals
Increased electron density between nuclei => bond
(1sa  1sb ) 2  (1sa2  1sb2  2 1sa1sb )  s 1s  bonding orbital
(1sa  1sb ) 2  (1sa2  1sb2  2 1sa1sb )  s 1*s  anti - bonding orbital
Decreased electron density between nuclei => “anti-bond”
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Slide 29
Molecular Orbitals of Hydrogen
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Slide 30
Basic Ideas Concerning MOs
•
•
•
•
•
Number of MOs = Number of AOs.
Bonding and antibonding MOs formed from AOs.
e- fill the lowest energy MO first.
Pauli exclusion principle is followed.
Hund’s rule is followed
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General Chemistry: Chapter 12
Slide 31
Bond Order
• Stable species have more electrons in bonding
orbitals than antibonding orbitals.
No. e- in bonding MOs - No. e- in antibonding MOs
Bond Order =
2
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General Chemistry: Chapter 12
Slide 32
Diatomic Molecules of the First-Period
BO = (e-bond - e-antibond )/2
BOH += (1-0)/2 = ½
2
BOH = (2-0)/2 = 1
2
BOHe + = (2-1)/2 = ½
2
BOHe = (2-2)/2 = 0
2
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General Chemistry: Chapter 12
Slide 33
Molecular Orbitals of the Second Period
• First period use only 1s orbitals.
• Second period have 2s and 2p orbitals available.
• 2s orbitals overlap as do 1s orbitals
• 2p orbital overlap:
– End-on overlap is best – sigma bond (σ).
– Side-on overlap is good – pi bond (π).
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General Chemistry: Chapter 12
Slide 34
Molecular Orbitals of the Second Period
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General Chemistry: Chapter 12
Slide 35
Combining p Orbitals
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Slide 36
Expected MO Diagram for Homonuclear
Diatomic Molecules of the Second Period
mixing
C2
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Slide 37
Modified MO Diagram for Homonuclear
Diatomic Molecules of the Second Period
C2
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Slide 38
MO Diagrams of 2nd Period Diatomics
s
p
s
p
s
s
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General Chemistry: Chapter 12
Slide 39
MO Diagrams of 2nd Period Diatomics
s
p
p
s
s
s
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General Chemistry: Chapter 12
Slide 40
MO Diagrams of Heteronuclear Diatomics
• Atomic orbitals have different energies
• Mixing “weighted” by elecronegativity.
C≡O
s  cO 2sO  cC 2sC
s  c 2sO  c 2sC
*
*
O
*
C
• Greater probability of finding an electron in an orbital
associated with the more electronegative atom
• s2s resembles 2so more than 2sc
• s*2s resembles 2sc more than 2so
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General Chemistry: Chapter 12
Slide 41
MO Diagrams of Heteronuclear Diatomics
Unmodified scheme
Bond order = 3
Bond order = 2.5
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General Chemistry: Chapter 12
Slide 42
12-6 Delocalized Electrons
Kekulé forms (resonance)
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General Chemistry: Chapter 12
Slide 43
Benzene: VB View
• Partition the benzene molecule into a s framework (VB) and a p
framework (MO)
sp2 hybridization
Delocalized p
electrons
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General Chemistry: Chapter 12
Slide 44
Benzene: MO View
• Six 2p orbitals combine to form 3 bonding and 3 non-bonding p-type MOs
• Bond order = [(6-0)/2]/6 + 1 = 1.5 (similar to Kekulé).
• MOs are delocalized orbitals
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General Chemistry: Chapter 12
Slide 45
Ozone
••+ •• -
••
O
O O
••
••
- ••
••+ ••
O
O O
••
••
••
••
• 18 valence electrons
• 14 e- in sp2 hybrid orbitals
• 4 bonding electrons
• 10 lone pairs
• 4 in 3 MO formed from p orbitals
Bond order 1.5
Anti-bonding (0 e-)
Non-bonding (2 e-)
(same energy as original orbital)
Bonding (2 e-)
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General Chemistry: Chapter 12
Slide 46
12-7 Bonding in Metals
• Metallic crystals: Few valance electrons but a lot of binding
• Electron sea model
– Nuclei in a sea of e-.
– Metallic luster.
– Malleability.
• Applied force leads to readjustment of the sea of
electrons
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General Chemistry: Chapter 12
Slide 47
Bonding in Metals: Band Theory
• Extension of MO theory
– N atoms contribute N valence
electrons and N AO which give rise
to N MO that are closely spaced
energy wise (energy band)
– N/2 orbitals are filled forming the
valence band
– N/2 orbitals are empty forming the
conductions band
– Conduction results from movement
of electrons from the valence band to
the conduction band
Electrical conductivity requires an energy band that is
partially filled with electrons
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General Chemistry: Chapter 12
Slide 48
Band Theory
• Filled valence shell
• Overlapping empty conduction shell
• Half-filled valence shell
•
•
•
•
Filled valence shell
Empty conduction shell
Small energy gap
Thermal energy suffices to cross gap
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•
•
•
•
General Chemistry: Chapter 12
Filled valence shell
Empty conduction shell
Large energy gap
Thermal energy not sufficient
to cross gap
Slide 49
Semiconductors
• Intrinsic semiconductors
– Fixed energy gap between valence band and conduction band
– Conductance proportional to temperature (higher temperature allows
more electron to cross the gap
• Extrinsic semiconductors
– Size of gap controlled by impurities (doping)
• n-type
– Conductance by electrons
promoted to the conduction
level of the impurity (e.g. P)
• p-type
– Conductance by “positive”
holes formed by electrons
promoted to the acceptor level
of the impurity (e.g. Al)
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General Chemistry: Chapter 12
Slide 50
Photovoltaic Cells
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General Chemistry: Chapter 12
Slide 51
Focus on Photoelectron Spectroscopy
• Photoelectron spectroscopy can be used to measure orbital energies
electron
Eorbital  h radiation  Ekinetic
• Fine structure results from excitation of
vibrational energy levels
• More vibrational peaks correspond to a
stronger bonding orbital
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General Chemistry: Chapter 12
Slide 52