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Chapter 9. Molecular Geometry and Bonding Theories
Media Resources
Figures and Tables in Transparency Pack: Section:
Figure 9.2 Shapes of AB2 and AB3 Molecules 9.1 Molecular Shapes
Figure 9.3 Shapes Allowing Maximum Distances 9.1 Molecular Shapes
between Atoms in ABn Molecules
Table 9.1 Electron-Domain Geometries as a 9.2 VSEPR Model
Function of Number of Electron Domains
Figure 9.15 Formation of sp Hybrid Orbitals 9.5 Hybrid Orbitals
Figure 9.17 Formation of sp2 Hybrid Orbitals 9.5 Hybrid Orbitals
Figure 9.18 Formation of sp3 Hybrid Orbitals 9.5 Hybrid Orbitals
Table 9.4 Geometric Arrangements Characteristic 9.5 Hybrid Orbitals
of Hybrid Orbital Sets
Figure 9.23 The Orbital Structure of Ethylene 9.6 Multiple Bonds
Figure 9.24 Formation of Two Bonds in 9.6 Multiple Bonds
Acetylene, C2H2
Activities: Section:
Molecular Polarity 9.3 Molecular Shape and Molecular Polarity
s-p Hybridization 9.5 Hybrid Orbitals
Multiple Bonds 9.6 Multiple Bonds
Animations: Section:
VSEPR 9.2 The VSEPR Model
Chapter 9
118
Hybridization 9.5 Hybrid Orbitals
Molecular Orbital Theory 9.7 Molecular Orbitals
3-D Models: Section:
Diazepam (valium) Introduction
Carbon Tetrachloride 9.1 Molecular Shapes
Carbon Dioxide 9.1 Molecular Shapes
Sulfur Dioxide 9.1 Molecular Shapes
Sulfur Trioxide 9.1 Molecular Shapes
Oxygen 9.8 Period 2 Diatomic Molecules
Other Resources
Further Readings: Section:
Molecular Geometry 9.1 Molecular Shapes
Who Needs Lewis Structures to Get VSEPR 9.2 VSEPR Model
Geometries?
Teaching Molecular Geometry with the VSEPR 9.2 VSEPR Model
Model
Molecular Geometry and Bonding Theories
119
Put the Body to Them! 9.3 Molecular Shape and Molecular Polarity
Demystifying Introductory Chemistry Part 2: 9.4 Covalent Bonding and Orbital Overlap
Bonding and Molecular Geometry without
Orbitals—The Electron-Domain Model
Grade-12 Students’ Misconceptions of Covalent 9.4 Covalent Bonding and Orbital Overlap
Bonding and Structure
Live Demonstrations: Section:
Bending a Stream of Water 9.3 Molecular Shape and Molecular Polarity
Chapter 9
120
Chapter 9. Molecular Geometry and Bonding Theories
Common Student Misconceptions
• Students find it difficult to think in three dimensions. Often, they believe that a square planar
arrangement is the best arrangement for the least repulsion of four electron domains.
• Students often confuse the electron domain geometry and the molecular geometry (shape).
Teaching Tips
• Simple balloon models can be effectively used in classroom presentations of VSEPR.
• Referring to nonbonded electron pairs, single bonds, and multiple bonds as regions of electron density
may help relieve any confusion that might arise from treating the various kinds of electron pairs
differently.
Lecture Outline
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9.1 Molecular Shapes
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• Lewis structures give atomic connectivity: they tell us which atoms are physically connected to which
atoms.
• The shape of a molecule is determined by its bond angles.
• The angles made by the lines joining the nuclei of the atoms in a molecule are the bond angles.
• Consider CCl4:
Molecular Geometry and Bonding Theories
121
• All Cl atoms are located at the vertices of a tetrahedron with the C at its center.
• In order to predict molecular shape, we assume that the valence electrons repel each other.
• Therefore, the molecule adopts the three-dimensional geometry that minimizes this repulsion.
• We call this model the Valence-Shell Electron-Pair Repulsion (VSEPR) model.
FORWARD REFERENCES
• Molecular shapes will affect such physical properties as viscosity (Chapter 11) and boiling
9.2 The VSEPR Model
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• A covalent bond forms between two atoms when a pair of electrons occupies the space between the
atoms.
• This is a bonding pair of electrons.
• Such a region is an electron domain.
• A nonbonding pair or lone pair of electrons defines an electron domain located principally on one
atom.
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“Who Needs Lewis Structures To Get VSEPR Geometries?” from Further Readings
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“VSEPR” Animation from Instructor’s Resource CD/DVD
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Table 9.1 from Transparency Pack
Chapter 9
122
Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles
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• We refine VSEPR to predict and explain slight distortions from “ideal” geometries.
• Consider three molecules with tetrahedral electron domain geometries:
• CH4, NH3, and H2O.
• By experiment, the H–X–H bond angle decreases from C (109.5° in CH4) to N (107° in NH3) to
O (104.5° in H2O).
• We will encounter 11 basic molecular shapes:
• Three atoms (AB2)
• Linear
• Bent
• Four atoms (AB3)
• Trigonal planar
• Trigonal pyramidal
• T-shaped
Molecules with Expanded Valence Shells
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• Atoms that have expanded octets have five electron domains (trigonal bipyramidal) or six electron
domains (octahedral) electron-domain geometries.
• Trigonal bipyramidal structures have a plane containing three electron pairs.
• The fourth and fifth electron pairs are located above and below this plane.
• In this structure two trigonal pyramids share a base.
• For octahedral structures, there is a plane containing four electron pairs.
• Similarly, the fifth and sixth electron pairs are located above and below this plane.
• Two square pyramids share a base.
• Consider a trigonal bipyramid.
• The three electron pairs in the plane are called equatorial.
Molecular Geometry and Bonding Theories
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• The two electron pairs above and below this plane are called axial.
• The axial electron pairs are 180° apart and 90° to the equatorial electrons.
• The equatorial electron pairs are 120° apart.
• To minimize electron–electron repulsion, nonbonding pairs are always placed in equatorial
Shapes of Larger Molecules
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• In acetic acid, CH3COOH, there are three interior atoms: two C and one O.
• We assign the molecular (and electron-domain) geometry about each interior (central) atom
separately.
• The geometry around the first C is tetrahedral.
• The geometry around the second C is trigonal planar.
• The geometry around the O is bent (tetrahedral).
FORWARD REFERENCES
• The consequence of water having an sp3 hybridized oxygen atom and bent molecular shape
will be linked to its the ability to form 4 hydrogen bonds in the structure of ice in Chapter 11
(section 11.2).
• Octahedral vs. tetrahedral metal complexes will be discussed in Chapter 23 (section 23.6).
9.3 Molecular Shape and Molecular Polarity
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• Polar molecules interact with electric fields.
• We previously saw that binary compounds are polar if their centers of negative and positive charge do
not coincide.
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“The Use of Molecular Modeling and VSEPR Theory in the Undergraduate Curriculum to Predict the
Three-Dimensional Structure of Molecules” from Further Readings
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“Acetic Acid” 3-D Model from Instructor’s Resource CD/DVD
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Figure 9.12 from Transparency Pack
Chapter 9
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• If two charges, equal in magnitude and opposite in sign, are separated by a distance d, then a
dipole is established.
• The dipole moment,
, is given by:
• Examples:
• In CO2 each +C−O- dipole is canceled because the molecule is linear.
• In H2O, the +H−O- dipoles do not cancel because the molecule is bent.
• It is possible for a molecule with polar bonds to be either polar or nonpolar.
• Example:
• For diatomic molecules:
• polar bonds always result in an overall dipole moment.
• For triatomic molecules:
• if the molecular geometry is bent, there is an overall dipole moment.
FORWARD REFERENCES
• Molecular polarity will affect such physical properties as viscosity, vapor pressure and energy
changes associated with phase changes of compounds (Chapter 11).
• Molecular polarity vs. miscibility will be discussed in Chapter 13 (section 13.3).
• Polar functional groups in otherwise nonpolar organic compounds will be further discussed in
Chapter 24 (section 24.4).
9.4 Covalent Bonding and Orbital Overlap
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• Lewis structures and VSEPR theory give us the shape and location of electrons in a molecule.
• They do not explain why a chemical bond forms.
• How can quantum mechanics be used to account for molecular shape? What are the orbitals that are
involved in bonding?
Molecular Geometry and Bonding Theories
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• As two nuclei approach each other, their atomic orbitals overlap.
• As the amount of overlap increases, the energy of the interaction decreases.
• At some distance the minimum energy is reached.
• The minimum energy corresponds to the bonding distance (or bond length).
• As the two atoms get closer, their nuclei begin to repel and the energy increases.
• At the bonding distance, the attractive forces between nuclei and electrons just balance the
repulsive forces (nucleus-nucleus, electron-electron).
9.5 Hybrid Orbitals
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• We can apply the idea of orbital overlap and valence-bond theory to polyatomic molecules.
sp Hybrid Orbitals
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• Consider the BeF2 molecule.
• Be has a 1s22s2 electron configuration.
• BUT the geometry is still not explained.
• We can solve the problem by allowing the 2s and one 2p orbital on Be to mix or form two new
hybrid orbitals (a process called hybridization).
• The two equivalent hybrid orbitals that result from mixing an s and a p orbital and are called sp
hybrid orbitals.
• The two lobes of an sp hybrid orbital are 180° apart.
sp2 and sp3 Hybrid Orbitals
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• Important: when we mix n atomic orbitals, we must get n hybrid orbitals.
• Three sp2 hybrid orbitals are formed from hybridization of one s and two p orbitals.
• Thus, there is one unhybridized p orbital remaining.
• The large lobes of the sp2 hybrids lie in a trigonal plane.
• Molecules with trigonal planar electron-pair geometries have sp2 orbitals on the central atom.
• Four sp3 hybrid orbitals are formed from hybridization of one s and three p orbitals.
• Therefore, there are four large lobes.
Chapter 9
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• Since there are only three p orbitals, trigonal bipyramidal and octahedral electron-pair geometries
must involve d orbitals.
Hybrid Orbital Summary
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• We need to know the electron-domain geometry before we can assign hybridization.
• To assign hybridization:
• Draw a Lewis structure.
• Assign the electron-domain geometry using VSEPR theory.
• Specify the hybridization required to accommodate the electron pairs based on their geometric
arrangement.
• Name the geometry by the positions of the atoms.
FORWARD REFERENCES
• Hybridization of C atoms in carbon nanotubes and polymers will be mentioned in Chapter 12
9.6 Multiple Bonds
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• In the covalent bonds we have seen so far the electron density has been concentrated symmetrically
about the internuclear axis.
• Sigma () bonds: electron density lies on the axis between the nuclei.
• All single bonds are bonds.
• What about overlap in multiple bonds?
• Pi () bonds: electron density lies above and below the plane of the nuclei.
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Table 9.4 from Transparency Pack
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Figure 9.23 from Transparency Pack
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“Multiple Bonds” Activity from Instructor’s Resource CD/DVD
Molecular Geometry and Bonding Theories
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Resonance Structures, Delocalization, and Bonding
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• So far all the bonds we have encountered are localized between two nuclei.
• In the case of benzene:
• There are six localized C–C bonds and six localized C–H bonds
• Each C atom is sp2 hybridized.
General Conclusions
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• Every pair of bonded atoms shares one or more pairs of electrons.
• Two electrons shared between atoms on the same axis as the nuclei are bonds.
• Bonds are always localized in the region between two bonded atoms.
• If two atoms share more than one pair of electrons, the additional pairs form bonds.
• When resonance structures are possible, delocalization is also possible.
FORWARD REFERENCES
• Delocalized electrons in metallic solids will be mentioned in Chapter 12 (section 12.3).
• Delocalized bonds in graphite will be further discussed in Chapter 12 (section 12.7).
9.7 Molecular Orbitals
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• Some aspects of bonding are not explained by Lewis structures, VSEPR theory and hybridization.
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“The ‘Big Dog-Puppy Dog’ Analogy for Resonance” from Further Readings
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Figure 9.26 from Transparency Pack
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Figure 9.27 from Transparency Pack
Chapter 9
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• For example:
• Why does O2 interact with a magnetic field?
• Why are some molecules colored?
The Hydrogen Molecule
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• When two AOs overlap, two MOs form.
• Therefore, 1s (H) + 1s (H) must result in two MOs for H2:
• One has electron density between the nuclei (bonding MO);
• One has little electron density between the nuclei (antibonding MO).
Bond Order
• Define bond order = ½ (bonding electrons – antibonding electrons).
• Bond order = 1 for single bond.
• Bond order = 2 for double bond.
• Bond order = 3 for triple bond.
• Fractional bond orders are possible.
• For example, consider the molecule H2.
• MO theory correctly predicts that hydrogen forms a diatomic molecule but that helium does not!
FORWARD REFERENCES
• Molecular orbitals in silicon-containing materials will be mentioned in Chapter 12 (section
12.7).
Molecular Geometry and Bonding Theories
129
9.8 Period 2 Diatomic Molecules
• We look at homonuclear diatomic molecules (e.g., Li2, Be2, B2 etc.).
• AOs combine according to the following rules:
• The number of MOs = number of AOs.
Molecular Orbitals for Li2 and Be2
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• Each 1s orbital combines with another 1s orbital to give one 1s and one *1s orbital, both of which
are occupied (since Li and Be have 1s2 electron configurations).
• Each 2s orbital combines with another 2s orbital to give one 2s and one
s orbital.
• The energies of the 1s and 2s orbitals are sufficiently different so that there is no cross mixing of
orbitals (i.e., we do not get 1s + 2s).
• Consider the bonding in Li2.
• There are a total of six electrons in Li2.
• 2 electrons in 1s.
• 2 electrons in 1s.
Molecular Orbitals from 2p Atomic Orbitals
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• There are two ways in which two p orbitals can overlap:
• End on so that the resulting MO has electron density on the axis between nuclei (i.e., type
orbital).
• Sideways, so that the resulting MO has electron density above and below the axis between nuclei.
• These are called pi () molecular orbitals.
Chapter 9
130
Electron Configurations for B2 through Ne2
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• Features of the energy-level diagrams for these elements:
• 2s orbitals are lower in energy than 2p orbitals so both s orbitals (2s and *2s) are lower in
energy than the lowest energy MO derived from the 2p AOs.
• There is greater overlap between 2pz orbitals.
• They point directly towards one another, so the 2p MO is lower in energy than the 2p
orbitals.
Electron Configurations and Molecular Properties
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• Two types of magnetic behavior:
• paramagnetism (unpaired electrons in molecule)
• strong attraction between magnetic field and molecule
• diamagnetism (no unpaired electrons in molecule)
• weak repulsion between magnetic field and molecule
Heteronuclear Diatomic Molecules
• Heteronuclear diatomic molecules contain 2 different elements.
• If both atoms do not differ greatly in electronegativity, the description of their MOs will be similar to
those for homonuclear diatomic molecules.
FORWARD REFERENCES
• The HOMO and LUMO gap will be mentioned in Chapter 12 (section 12.7).
• Magnetism in coordination chemistry will be discussed in Chapter 23 (section 23.5).
Molecular Geometry and Bonding Theories
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Further Readings:
1. H. O. Desseyn, M. A. Herman, and J. Mullens, “Molecular Geometry,” J. Chem. Educ., Vol. 62, 1985,
220–222.
6. Brian W. Pfennig and Richard L. Frock, “The Use of Molecular Modeling and VSEPR Theory in the
Undergraduate Curriculum to Predict the Three-Dimensional Structure of Molecules,” J. Chem. Educ.,
Vol. 76, 1999, 1018–1022.
7. Gordon H. Purser, “Lewis Structures Are Models for Predicting Molecular Structure, Not Electronic
Structure,” J. Chem. Educ., Vol. 76, 1999, 1013–1017.
8. Carlos Furio and Ma. Luisa Calatayud, “Difficulties with the Geometry and Polarity of Molecules:
Beyond Misconceptions,” J. Chem. Educ., Vol. 73, 1996, 36–41.
12. Robert R. Perkins, “Put the Body to Them!” J. Chem. Educ., Vol. 72, 1995, 151–152. This reference
includes an analogical demonstration of the concept of molecular polarity.
13. Ronald J. Gillespie, James N. Spencer and Richard S. Moog, “Demystifying Introductory Chemistry
Part 2: Bonding and Molecular Geometry without Orbitals—The Electron-Domain Model,” J. Chem.
Educ., Vol. 73, 1996, 622–627.
Chapter 9
132
19. A. B. Sannigrahi and Tapas Kar, “Molecular Orbital Theory of Bond Order and Valency,” J. Chem.
Educ., Vol. 65, 1988, 674–676.
20. John Barbaro, “Orbital Bartending,” J. Chem. Educ., Vol. 71, 1994, 1012. An analogy for orbital
hybridization is suggested in this short article.
21. Albert Haim, “The Relative Energies of Molecular Orbitals for Second-Row Homonuclear Diatomic
Molecules: The Effect of s-p Mixing,” J. Chem. Educ., Vol. 68, 1991, 737–738.
Live Demonstrations:
1. Lee. R. Summerlin, Christie L. Borgford, and Julie B. Ealy, “Bending a Stream of Water,” Chemical
Demonstrations, A Sourcebook for Teachers, Volume 2 (Washington: American Chemical Society, 1988),
p. 91. The polarity of water and cyclohexane are compared in this demonstration.
