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CHAPTER 9: MOLECULAR GEOMETRY AND BONDING THEORIES
Molecular Shapes
Lewis structures, however, do not indicate the shapes of molecules; they simply show the number and types of bonds.
The shape of a molecule is determined by its bond angles, the angles made by the lines joining the nuclei of the atoms in the molecule.
The bond angles of a molecule, together with the bond lengths, define the shape and size of the molecule.
If the A atom lies in the same plane as the B atoms, the shape is called trigonal planar.
If the A atom lies above the plane of the B atoms, the shape is called trigonal pyramidal (a pyramid with an equilateral triangle as its base).
Its symmetric shape (and its name) is derived from the octahedron, with eight faces, all of which are equilateral triangles.
The VSEPR Model
A bonding pair of electrons thus defines a region in which the electrons are most likely to be found. We will refer to such a region as an electron domain. Likewise, a nonbonding pair (or lone pair) of electrons, defines an electron domain that is located principally on one atom.
Each multiple bond in a molecule also constitutes a single electron domain.
In general, each nonbonding pair, single bond, or multiple bond produces a single electron domain around the central atom in a molecule.
The VSEPR modelis based on the idea that electron domains are negatively charged and therefore repel one another.
The best arrangement of a given number of electron domains is the one that minimizes the repulsions among them.
The arrangement of electron domains about the central atom of an ABn molecule or ion is called its electron-domain geometry. In contrast, the molecular geometry is the arrangement of only the atoms in a molecule or ion—any nonbonding pairs in the molecule are not part of the description of the molecular geometry.
How to Predict the Shapes of Molecules and Ions Using the VSEPR Model
Draw the Lewis structure of the molecule or ion, and count the number of electron domains around the central atom. Each nonbonding electron pair, each single bond, each double bond, and each triple bond counts as one electron domain.
Determine the electron-domain geometry by arranging the electron domains about the central atom so that the repulsions among them are minimized.
Use the arrangement of the bonded atoms to determine the molecular geometry.
Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles
A bonding pair of electrons is attracted by both nuclei of the bonded atoms, but a nonbonding pair is attracted primarily by only one nucleus. Because a nonbonding pair experiences less nuclear attraction, its electron domain is spread out more in space than is the electron domain for a bonding pair.
Electron domains for nonbonding electron pairs exert greater repulsive forces on adjacent electron domains and tend to compress bond angles.
Molecules with Expanded Valence Shells
Molecules with five or six electron domains around the central atom have molecular geometries based on either a trigonal-bipyramidal (five domains) or octahedral (six domains) electron-domain geometry.
The most stable electron-domain geometry for five electron domains is the trigonal bipyramid (two trigonal pyramids sharing a base).
The most stable electron-domain geometry for six electron domains is the octahedron. An octahedron is a polyhedron with six vertices and eight faces, each an equilateral triangle.
Molecular Shape and Molecular polarity
For a molecule consisting of more than two atoms, the dipole moment depends on both the polarities of the individual bonds and the geometry of the molecule. For each bond in the molecule, we consider the bond dipole, which is the dipole moment due only to the two atoms in that bond.
Bond dipoles and dipole moments are vector quantities; that is, they have both a magnitude and a direction.The dipole moment of a polyatomic molecule is the vector sum of its bond dipoles. Both the magnitudes and the directions of the bond dipoles must be considered when summing vectors.
The bond dipoles, like the numbers, “cancel” each other.
The geometry of the molecule dictates that the overall dipole moment be zero, making CO2 a nonpolarmolecule.
Covalent Bonding and Orbital Overlap
The VSEPR model provides a simple means for predicting molecular geometries but does not explain why bonds exist between atoms.
The marriage of Lewis’s notion of electron-pair bonds and the idea of atomic orbitals leads to a model of chemical bonding, called valence-bond theory, in which bonding electron pairs are concentrated in the regions between atoms, and nonbonding electron pairs lie in directed regions of space.
In Lewis theory, covalent bonding occurs when atoms share electrons because the sharing concentrates electron density between the nuclei.
In valence-bond theory, we visualize the buildup of electron density between two nuclei as occurring when a valence atomic orbital of one atom shares space, or overlaps, with a valence atomic orbital of another atom.
Because the electrons in the overlap region are simultaneously attracted to both nuclei, they hold the atoms together, forming a covalent bond.
There is always an optimum distance between the two nuclei in any covalent bond.
There is always an optimum distance between the two nuclei in any covalent bond.
Because of the resulting increase in electron density between the nuclei, the potential energy of the system decreases
Hybrid Orbitals
To explain molecular geometries, we often assume that the atomic orbitals on an atom (usually the central atom) mix to form new orbitals called hybrid orbitals.
The process of mixing atomic orbitals is a mathematical operation called hybridization.
sp Hybrid Orbitals
Like p orbitals, each new orbital has two lobes. Unlike p orbitals, however, one lobe is much larger than the other. The two new orbitals are identical in shape, but their large lobes point in opposite directions.orbitals. Because we have hybridized one s and one p orbital, we call each hybrid an sp hybrid orbital.
According to the valence-bond model, a linear arrangement of electron domains implies sp hybridization.
The electrons in the sp hybrid orbitals can form bonds with the two fluorine atoms.
sp^2 and sp^3 Hybrid Orbitals
Whenever we mix a certain number of atomic orbitals, we get the same number of hybrid orbitals. Each hybrid orbital is equivalent to the others but points in a different direction.
An s atomic orbital can mix with all three p atomic orbitals in the same subshell.
Each sp^3 hybrid orbital has a large lobe that points toward one vertex of a tetrahedron.
Using valence-bond theory, we can describe the bonding in CH4 as the overlap of four equivalent sp3 hybrid orbitals on C with the 1s orbitals of the four H atoms to form four equivalent bonds.
The idea of hybridization is also used to describe the bonding in molecules containing nonbonding pairs of electrons.
Two of the hybrid orbitals contain non-bonding pairs of electrons, and the other two form bonds with the hydrogen atoms.
Hypervalent Molecules
The elements of period 3 and beyond introduce a new consideration because in many of their compounds these elements are hypervalent— they have more than an octet of electrons around the central atom.
For compounds with more than an octet, we could imagine increasing the number of hybrid orbitals formed by including valence-shell d orbitals.
The hybrid orbital model for period 2 elements has proven very useful and is an essential part of any modern discussion of bonding and molecular geometry in organic chemistry.
Multiple Bonds
The line joining the two nuclei passes through the middle of the overlap region, forming a type of covalent bond called a sigma bond.
The sideways overlap of p orbitals produces what is called a pi bond.
Because carbon has four valence electrons, after sp^2 hybridization one electron in each carbon remains in the unhybridized 2p orbital.
Triple bonds can also be explained using hybrid orbitals.
The bonding electrons are localized.
Delocalization of the electrons in its p bonds gives benzene a special stability. Electron delocalization in p bonds is also responsible for the color of many organic molecules.
Molecular Orbitals
Some aspects of bonding are better explained by a more sophisticated model called molecular orbital theory.
In a similar way, molecular orbital theory describes the electrons in molecules by using specific wave functions, each of which is called a molecular orbital (MO).
Molecular Orbitals of the Hydrogen Molecule
Whenever two atomic orbitals overlap, two molecular orbitals form.
The energy of the resulting MO is lower in energy than the two atomic orbitals from which it was made. It is called the bonding molecular orbital.
The second MO is formed by what is called destructive combination: combining the two atomic orbitals in a way that causes the electron density to be canceled in the central region where the two overlap.
The energy of the resulting MO, referred to as the antibonding molecular orbital, is higher than the energy of the atomic orbitals.
Antibonding orbitals invariably have a plane in the region between the nuclei where the electron density is zero. This plane is called a nodal plane of the MO.
MOs of this type are called sigma molecular orbitals (by analogy to s bonds).
The relative energies of two 1s atomic orbitals and the molecular orbitals formed from them are represented by an energy-level diagram (also called a molecular orbital diagram).
Electrons occupying a bonding molecular orbital are called bonding electrons.
Bond Order
A bond order of 1 represents a single bond, a bond order of 2 represents a double bond, and a bond order of 3 represents a triple bond.
Bonding in period 2 Diatomic Molecules
The following rules summarize some of the guiding principles for the formation of MOs and for how they are populated by electrons:
The number of MOs formed equals the number of atomic orbitals combined.
Atomic orbitals combine most effectively with other atomic orbitals of similar energy.
The effectiveness with which two atomic orbitals combine is proportional to their overlap. That is, as the overlap increases, the energy of the bonding MO is lowered and the energy of the antibonding MO is raised.
Each MO can accommodate, at most, two electrons, with their spins paired (Pauli exclusion principle).
When MOs of the same energy are populated, one electron enters each orbital (with the same spin) before spin pairing occurs (Hund’s rule).
The general rule that core electrons usually do not contribute significantly to bonding in molecules.
The rule is equivalent to using only the valence electrons when drawing Lewis structures.
Molecular Orbitals from 2p Atomic Orbitals
MOs of this type are called pi molecular orbitals by analogy to p bonds. The other 2p orbitals overlap sideways and thus concentrate electron density above and below the internuclear axis.
Electron Configurations and Molecular properties
The more unpaired electrons in a species, the stronger the attractive force. This type of magnetic behavior is called paramagnetism.
Substances with no unpaired electrons are weakly repelled by a magnetic field. This property is called diamagnetism.
Heteronuclear Diatomic Molecules
The principles we have used in developing an MO description of homonuclear diatomic molecules can be extended to heteronuclear diatomic molecules—those in which the two atoms in the molecule are not the same.
The NO molecule controls several important human physiological functions.The 1998 Nobel Prize in Physiology or Medicine was awarded to three scientists for their research that uncovered the importance of NO as a “signaling” molecule in the cardiovascular system.
There is one other important difference in the MOs of heteronuclear molecules. The MOs are still a mix of atomic orbitals from both atoms, but in general an MO in a heteronuclear diatomic molecule has a greater contribution from the atomic orbital to which it is closer in energy.
CHAPTER 9: MOLECULAR GEOMETRY AND BONDING THEORIES
Molecular Shapes
Lewis structures, however, do not indicate the shapes of molecules; they simply show the number and types of bonds.
The shape of a molecule is determined by its bond angles, the angles made by the lines joining the nuclei of the atoms in the molecule.
The bond angles of a molecule, together with the bond lengths, define the shape and size of the molecule.
If the A atom lies in the same plane as the B atoms, the shape is called trigonal planar.
If the A atom lies above the plane of the B atoms, the shape is called trigonal pyramidal (a pyramid with an equilateral triangle as its base).
Its symmetric shape (and its name) is derived from the octahedron, with eight faces, all of which are equilateral triangles.
The VSEPR Model
A bonding pair of electrons thus defines a region in which the electrons are most likely to be found. We will refer to such a region as an electron domain. Likewise, a nonbonding pair (or lone pair) of electrons, defines an electron domain that is located principally on one atom.
Each multiple bond in a molecule also constitutes a single electron domain.
In general, each nonbonding pair, single bond, or multiple bond produces a single electron domain around the central atom in a molecule.
The VSEPR modelis based on the idea that electron domains are negatively charged and therefore repel one another.
The best arrangement of a given number of electron domains is the one that minimizes the repulsions among them.
The arrangement of electron domains about the central atom of an ABn molecule or ion is called its electron-domain geometry. In contrast, the molecular geometry is the arrangement of only the atoms in a molecule or ion—any nonbonding pairs in the molecule are not part of the description of the molecular geometry.
How to Predict the Shapes of Molecules and Ions Using the VSEPR Model
Draw the Lewis structure of the molecule or ion, and count the number of electron domains around the central atom. Each nonbonding electron pair, each single bond, each double bond, and each triple bond counts as one electron domain.
Determine the electron-domain geometry by arranging the electron domains about the central atom so that the repulsions among them are minimized.
Use the arrangement of the bonded atoms to determine the molecular geometry.
Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles
A bonding pair of electrons is attracted by both nuclei of the bonded atoms, but a nonbonding pair is attracted primarily by only one nucleus. Because a nonbonding pair experiences less nuclear attraction, its electron domain is spread out more in space than is the electron domain for a bonding pair.
Electron domains for nonbonding electron pairs exert greater repulsive forces on adjacent electron domains and tend to compress bond angles.
Molecules with Expanded Valence Shells
Molecules with five or six electron domains around the central atom have molecular geometries based on either a trigonal-bipyramidal (five domains) or octahedral (six domains) electron-domain geometry.
The most stable electron-domain geometry for five electron domains is the trigonal bipyramid (two trigonal pyramids sharing a base).
The most stable electron-domain geometry for six electron domains is the octahedron. An octahedron is a polyhedron with six vertices and eight faces, each an equilateral triangle.
Molecular Shape and Molecular polarity
For a molecule consisting of more than two atoms, the dipole moment depends on both the polarities of the individual bonds and the geometry of the molecule. For each bond in the molecule, we consider the bond dipole, which is the dipole moment due only to the two atoms in that bond.
Bond dipoles and dipole moments are vector quantities; that is, they have both a magnitude and a direction.The dipole moment of a polyatomic molecule is the vector sum of its bond dipoles. Both the magnitudes and the directions of the bond dipoles must be considered when summing vectors.
The bond dipoles, like the numbers, “cancel” each other.
The geometry of the molecule dictates that the overall dipole moment be zero, making CO2 a nonpolarmolecule.
Covalent Bonding and Orbital Overlap
The VSEPR model provides a simple means for predicting molecular geometries but does not explain why bonds exist between atoms.
The marriage of Lewis’s notion of electron-pair bonds and the idea of atomic orbitals leads to a model of chemical bonding, called valence-bond theory, in which bonding electron pairs are concentrated in the regions between atoms, and nonbonding electron pairs lie in directed regions of space.
In Lewis theory, covalent bonding occurs when atoms share electrons because the sharing concentrates electron density between the nuclei.
In valence-bond theory, we visualize the buildup of electron density between two nuclei as occurring when a valence atomic orbital of one atom shares space, or overlaps, with a valence atomic orbital of another atom.
Because the electrons in the overlap region are simultaneously attracted to both nuclei, they hold the atoms together, forming a covalent bond.
There is always an optimum distance between the two nuclei in any covalent bond.
There is always an optimum distance between the two nuclei in any covalent bond.
Because of the resulting increase in electron density between the nuclei, the potential energy of the system decreases
Hybrid Orbitals
To explain molecular geometries, we often assume that the atomic orbitals on an atom (usually the central atom) mix to form new orbitals called hybrid orbitals.
The process of mixing atomic orbitals is a mathematical operation called hybridization.
sp Hybrid Orbitals
Like p orbitals, each new orbital has two lobes. Unlike p orbitals, however, one lobe is much larger than the other. The two new orbitals are identical in shape, but their large lobes point in opposite directions.orbitals. Because we have hybridized one s and one p orbital, we call each hybrid an sp hybrid orbital.
According to the valence-bond model, a linear arrangement of electron domains implies sp hybridization.
The electrons in the sp hybrid orbitals can form bonds with the two fluorine atoms.
sp^2 and sp^3 Hybrid Orbitals
Whenever we mix a certain number of atomic orbitals, we get the same number of hybrid orbitals. Each hybrid orbital is equivalent to the others but points in a different direction.
An s atomic orbital can mix with all three p atomic orbitals in the same subshell.
Each sp^3 hybrid orbital has a large lobe that points toward one vertex of a tetrahedron.
Using valence-bond theory, we can describe the bonding in CH4 as the overlap of four equivalent sp3 hybrid orbitals on C with the 1s orbitals of the four H atoms to form four equivalent bonds.
The idea of hybridization is also used to describe the bonding in molecules containing nonbonding pairs of electrons.
Two of the hybrid orbitals contain non-bonding pairs of electrons, and the other two form bonds with the hydrogen atoms.
Hypervalent Molecules
The elements of period 3 and beyond introduce a new consideration because in many of their compounds these elements are hypervalent— they have more than an octet of electrons around the central atom.
For compounds with more than an octet, we could imagine increasing the number of hybrid orbitals formed by including valence-shell d orbitals.
The hybrid orbital model for period 2 elements has proven very useful and is an essential part of any modern discussion of bonding and molecular geometry in organic chemistry.
Multiple Bonds
The line joining the two nuclei passes through the middle of the overlap region, forming a type of covalent bond called a sigma bond.
The sideways overlap of p orbitals produces what is called a pi bond.
Because carbon has four valence electrons, after sp^2 hybridization one electron in each carbon remains in the unhybridized 2p orbital.
Triple bonds can also be explained using hybrid orbitals.
The bonding electrons are localized.
Delocalization of the electrons in its p bonds gives benzene a special stability. Electron delocalization in p bonds is also responsible for the color of many organic molecules.
Molecular Orbitals
Some aspects of bonding are better explained by a more sophisticated model called molecular orbital theory.
In a similar way, molecular orbital theory describes the electrons in molecules by using specific wave functions, each of which is called a molecular orbital (MO).
Molecular Orbitals of the Hydrogen Molecule
Whenever two atomic orbitals overlap, two molecular orbitals form.
The energy of the resulting MO is lower in energy than the two atomic orbitals from which it was made. It is called the bonding molecular orbital.
The second MO is formed by what is called destructive combination: combining the two atomic orbitals in a way that causes the electron density to be canceled in the central region where the two overlap.
The energy of the resulting MO, referred to as the antibonding molecular orbital, is higher than the energy of the atomic orbitals.
Antibonding orbitals invariably have a plane in the region between the nuclei where the electron density is zero. This plane is called a nodal plane of the MO.
MOs of this type are called sigma molecular orbitals (by analogy to s bonds).
The relative energies of two 1s atomic orbitals and the molecular orbitals formed from them are represented by an energy-level diagram (also called a molecular orbital diagram).
Electrons occupying a bonding molecular orbital are called bonding electrons.
Bond Order
A bond order of 1 represents a single bond, a bond order of 2 represents a double bond, and a bond order of 3 represents a triple bond.
Bonding in period 2 Diatomic Molecules
The following rules summarize some of the guiding principles for the formation of MOs and for how they are populated by electrons:
The number of MOs formed equals the number of atomic orbitals combined.
Atomic orbitals combine most effectively with other atomic orbitals of similar energy.
The effectiveness with which two atomic orbitals combine is proportional to their overlap. That is, as the overlap increases, the energy of the bonding MO is lowered and the energy of the antibonding MO is raised.
Each MO can accommodate, at most, two electrons, with their spins paired (Pauli exclusion principle).
When MOs of the same energy are populated, one electron enters each orbital (with the same spin) before spin pairing occurs (Hund’s rule).
The general rule that core electrons usually do not contribute significantly to bonding in molecules.
The rule is equivalent to using only the valence electrons when drawing Lewis structures.
Molecular Orbitals from 2p Atomic Orbitals
MOs of this type are called pi molecular orbitals by analogy to p bonds. The other 2p orbitals overlap sideways and thus concentrate electron density above and below the internuclear axis.
Electron Configurations and Molecular properties
The more unpaired electrons in a species, the stronger the attractive force. This type of magnetic behavior is called paramagnetism.
Substances with no unpaired electrons are weakly repelled by a magnetic field. This property is called diamagnetism.
Heteronuclear Diatomic Molecules
The principles we have used in developing an MO description of homonuclear diatomic molecules can be extended to heteronuclear diatomic molecules—those in which the two atoms in the molecule are not the same.
The NO molecule controls several important human physiological functions.The 1998 Nobel Prize in Physiology or Medicine was awarded to three scientists for their research that uncovered the importance of NO as a “signaling” molecule in the cardiovascular system.
There is one other important difference in the MOs of heteronuclear molecules. The MOs are still a mix of atomic orbitals from both atoms, but in general an MO in a heteronuclear diatomic molecule has a greater contribution from the atomic orbital to which it is closer in energy.
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