CHEMISTRY THE CENTRAL SCIENCE
9 MOLECULAR GEOMETRY AND BONDING THEORIES
CHAPTER SUMMARY AND KEY TERMS
INTRODUCTION AND SECTION 9.1 The three-dimensional shapes and sizes of molecules are determined by their bond angles and bond lengths. Molecules with a central atom A surrounded by n atoms B, denoted ABn, adopt a number of different geometric shapes, depending on the value of n and on the particular atoms involved. In the overwhelming majority of cases, these geometries are related to five basic shapes (linear, trigonal pyramidal, tetrahedral, trigonal bipyramidal, and octahedral).
SECTION 9.2 The valence-shell electron-pair repulsion (VSEPR) model rationalizes molecular geometries based on the repulsions between electron domains, which are regions about a central atom in which electrons are likely to be found. Bonding pairs of electrons, which are those involved in making bonds, and nonbonding pairs of electrons, also called lone pairs, both create electron domains around an atom. According to the VSEPR model, electron domains orient themselves to minimize electrostatic repulsions; that is, they remain as far apart as possible. Electron domains from nonbonding pairs exert slightly greater repulsions than those from bonding pairs, which leads to certain preferred positions for nonbonding pairs and to the departure of bond angles from idealized values. Electron domains from multiple bonds exert slightly greater repulsions than those from single bonds. The arrangement of electron domains around a central atom is called the electron-domain geometry; the arrangement of atoms is called the molecular geometry.
SECTION 9.3 The dipole moment of a polyatomic molecule depends on the vector sum of the dipole moments associated with the individual bonds, called the bond dipoles. Certain molecular shapes, such as linear AB2 and trigonal planar AB3, assure that the bond dipoles cancel, producing a nonpolar molecule, which is one whose dipole moment is zero. In other shapes, such as bent AB2 and trigonal pyramidal AB3, the bond dipoles do not cancel and the molecule will be polar (that is, it will have a nonzero dipole moment).
SECTION 9.4 Valence-bond theory is an extension of Lewis's notion of electron-pair bonds. In valence-bond theory, covalent bonds are formed when atomic orbitals on neighboring atoms overlap one another. The overlap region is one of low energy, or greater stability, for the two electrons because of their simultaneous attraction to two nuclei. The greater the overlap between two orbitals, the stronger will be the bond that is formed.
SECTION 9.5 To extend the ideas of valence-bond theory to polyatomic molecules, we must envision mixing s, p, and sometimes d orbitals to form hybrid orbitals. The process of hybridization leads to hybrid atomic orbitals that have a large lobe directed to overlap with orbitals on another atom to make a bond. Hybrid orbitals can also accommodate nonbonding pairs. A particular mode of hybridization can be associated with each of three common electron-domain geometries (linear = sp; trigonal planar = sp2; tetrahedral = sp3).
SECTION 9.6 Covalent bonds in which the electron density lies along the line connecting the atoms (the internuclear axis) are called sigma (σ) bonds. Bonds can also be formed from the sideways overlap of p orbitals. Such a bond is called a pi (π) bond. A double bond, such as that in C2H4, consists of one σ bond and one π bond; a triple bond, such as that in C2H2, consists of one σ and two π bonds. The formation of a π bond requires that molecules adopt a specific orientation; the two CH2 groups in C2H4, for example, must lie in the same plane. As a result, the presence of π bonds introduces rigidity into molecules. In molecules that have multiple bonds and more than one resonance structure, such as C6H6, the π bonds are delocalized; that is, the π bonds are spread among several atoms.
SECTION 9.7 Molecular orbital theory is another model used to describe the bonding in molecules. In this model the electrons exist in allowed energy states called molecular orbitals (MOs). An MO can extend over all the atoms of a molecule. Like an atomic orbital, a molecular orbital has a definite energy and can hold two electrons of opposite spin. We can think of molecular orbitals as built up by combining atomic orbitals on different atomic centers. In the simplest case, the combination of two atomic orbitals leads to the formation of two MOs, one at lower energy and one at higher energy relative to the energy of the atomic orbitals. The lower-energy MO concentrates charge density in the region between the nuclei and is called a bonding molecular orbital. The higher-energy MO excludes electrons from the region between the nuclei and is called anantibonding molecular orbital. Occupation of bonding MOs favors bond formation, whereas occupation of antibonding MOs is unfavorable. The bonding and anti-bonding MOs formed by the combination of s orbitals are sigma (σ) molecular orbitals; they lie on the internuclear axis.
The combination of atomic orbitals and the relative energies of the molecular orbitals are shown by an energy-level (or molecular orbital) diagram. When the appropriate number of electrons are put into the MOs, we can calculate the bond order of a bond, which is half the difference between the number of electrons in bonding MOs and the number of electrons in antibonding MOs. A bond order of 1 corresponds to a single bond, and so forth. Bond orders can be fractional numbers.
SECTION 9.8 Electrons in core orbitals do not contribute to the bonding between atoms, so a molecular orbital description usually needs to consider only electrons in the outermost electron subshells. In order to describe the MOs of period 2 homonuclear diatomic molecules, we need to consider the MOs that can form by the combination of p orbitals. The p orbitals that point directly at one another can form σ bonding and σ* antibonding MOs. The p orbitals that are oriented perpendicular to the internuclear axis combine to form pi (π) molecular orbitals. In diatomic molecules the π molecular orbitals occur as a pair of degenerate (same energy) bonding MOs and a pair of degenerate antibonding MOs. The π2p bonding MO is expected to be lower in energy than the σ2p bonding MOs because of larger orbital overlap of the p orbitals directed along the internuclear axis. However, this ordering is reversed in B2, C2, and N2 because of interaction between the 2s and 2p atomic orbitals of different atoms.
The molecular orbital description of period 2 diatomic molecules leads to bond orders in accord with the Lewis structures of these molecules. Further, the model predicts correctly that O2 should exhibit paramagnetism, which leads to attraction of a molecule into a magnetic field due to the influence of unpaired electrons. Molecules in which all the electrons are paired exhibit diamagnetism, which leads to weak repulsion from a magnetic field.
KEY SKILLS
• Be able to describe the three-dimensional shapes of molecules using the VSEPR model. (Section 9.2)
• Determine whether a molecule is polar or nonpolar based on its geometry and the individual bond dipole moments. (Section 9.3)
• Be able to explain the role of orbital overlap in the formation of covalent bonds. (Section 9.4)
• Be able to specify the hybridization state of atoms in molecules based on observed molecular structures. (Section 9.5)
• Be able to sketch how orbitals overlap to form sigma (σ) and pi (π) bonds. (Section 9.6)
• Be able to explain the existence of delocalized π bonds in molecules such as benzene. (Section 9.6)
• Be able to explain the concept of bonding and antibonding orbitals. (Section 9.7)
• Be able to draw molecular orbital energy-level diagrams and place electrons into them to obtain the bond orders and electron configurations of diatomic molecules using molecular orbital theory. (Sections 9.7 and 9.8)
• Understand the relationships among bond order, bond strength (bond enthalpy), and bond length. (Section 9.8)
KEY EQUATION
