Chapter 9. Molecular Geometry and Bonding Theories
9.1 Molecular Shapes
• 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: • Experimentally we find all Cl–C–Cl bond angles are 109.5°.
• Therefore, the molecule cannot be planar. • 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.
9.2 The VSEPR Model
• 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. • Example: NH3 has three bonding pairs and one lone pair. • VSEPR predicts that the best arrangement 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 is its electron-domain
geometry.
• There are five different electron-domain geometries: • Linear (two electron domains), trigonal planar (three domains), tetrahedral (four domains), trigonal
bipyramidal (five domains) and octahedral (six domains). • The molecular geometry is the arrangement of the atoms in space. • To determine the shape of a molecule we distinguish between lone pairs and bonding pairs. • We use the electron domain geometry to help us predict the molecular geometry.
• Draw the Lewis structure. • Count the total number of electron domains around the central atom. • Arrange the electron domains in one of the above geometries to minimize electron-electron
repulsion. • Next, determine the three-dimensional structure of the molecule.
• We ignore lone pairs in the molecular geometry.
• Describe the molecular geometry in terms of the angular arrangement of the bonded atoms. • Multiple bonds are counted as one electron domain.
Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles
• 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).
• A bonding pair of electrons is attracted by two nuclei. They do not repel as much as lone pairs which are primarily attracted by only one nucleus.
• Electron domains for nonbonding electron pairs thus exert greater repulsive forces on adjacent electron domains.
• They tend to compress the bond angles. • The bond angle decreases as the number of nonbonding pairs increases.
• Similarly, electrons in multiple bonds repel more than electrons in single bonds. (e.g. in Cl2CO the O–C–Cl angle is 124.3°, and the Cl–C–Cl bond angle is 111.4°).
• We will encounter 11 basic molecular shapes: • Three atoms (AB2) Linear or Bent
• Four atoms (AB3) Trigonal planar, Trigonal pyramidal or T-shaped • Five atoms (AB4) Tetrahedral , Square planar or Seesaw • Six atoms (AB5) Trigonal bipyramidal or Square pyramidal • Seven atoms (AB6) Octahedral
Molecules with Expanded Valence Shells
• 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. • 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 positions and bonding pairs in either axial or equatorial positions.
• Consider an octahedron.
• The four electron pairs in the plane are at 90° to each other. • The two axial electron pairs are 180° apart and at 90° to the electrons in the plane. • Because of the symmetry of the system, each position is equivalent.
• If we have five bonding pairs and one lone pair, it doesn’t matter where the lone pair is placed. • The molecular geometry is square pyramidal. • If two nonbonding pairs are present, the repulsions are minimized by pointing them toward opposite
sides of the octahedron. • The molecular geometry is square planar.
Shapes of Larger Molecules
• 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).
9.3 Molecular Shape and Molecular Polarity
• 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.
• 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: = Qr
• where Q is the magnitude of the charge. • We can extend this to polyatomic molecules. • For each bond in a polyatomic molecule, we can consider the bond dipole. • The dipole moment due only to the two atoms in the bond is the bond dipole.
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• Because bond dipoles and dipole moments are vector quantities, the orientation of these individual dipole moments determines whether the molecule has an overall dipole moment.
• Examples:
• In CO2 each +
CO-
dipole is canceled because the molecule is linear. • In H2O, the
+HO
- 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. • if the molecular geometry is linear, and the B atoms are the same, there is no overall dipole moment. • if the molecular geometry is linear and the B atoms are different, there is an overall dipole moment. • For molecules with four atoms: • if the molecular geometry is trigonal pyramidal, there is an overall dipole moment; • if the molecular geometry is trigonal planar, and the B atoms are identical, there is no overall dipole
moment; • if the molecular geometry is trigonal planar and the B atoms are different, there is an overall dipole
moment.
9.4 Covalent Bonding and Orbital Overlap
• 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?
• We use valence-bond theory: • A covalent bond forms when the orbitals on two atoms overlap.
• The shared region of space between the orbitals is called the orbital overlap. • There are two electrons (usually one from each atom) of opposite spin in the orbital overlap.
• 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
• We can apply the idea of orbital overlap and valence-bond theory to polyatomic molecules.
sp Hybrid Orbitals
• Consider the BeF2 molecule.
• Be has a 1s22s
2 electron configuration.
• There is no unpaired electron available for bonding. • We conclude that the atomic orbitals are not adequate to describe orbitals in molecules. • We know that the F–Be–F bond angle is 180° (VSEPR theory). • We also know that one electron from Be is shared with each one of the unpaired electrons from F. • We assume that the Be orbitals in the Be–F bond are 180° apart. • We could promote an electron from the 2s orbital on Be to the 2p orbital to get two unpaired electrons for
bonding. • 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. • According to the valence-bond model, a linear arrangement of electron domains implies sp
hybridization. • Since only one of 2p orbitals of Be has been used in hybridization, there are two unhybridized p orbitals
remaining on Be. • The electrons in the sp hybrid orbitals form shared electron bonds with the two fluorine atoms.
sp2 and sp
3 Hybrid Orbitals
• 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 sp
2 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.
• Each lobe points towards the vertex of a tetrahedron. • The angle between the large lobes is 109.5°. • Molecules with tetrahedral electron pair geometries are sp
3 hybridized.
• Since there are only three p orbitals, trigonal bipyramidal and octahedral electron-pair geometries must involve d orbitals.
• Trigonal bipyramidal electron pair geometries require sp3d hybridization.
• Octahedral electron pair geometries require sp3d
2 hybridization.
• Note that the electron pair VSEPR geometry corresponds well with the hybridization.
• Use of d orbitals in making hybrid orbitals corresponds well with the idea of an expanded octet.
Hybrid Orbital Summary
• 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.
9.6 Multiple Bonds
• 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.
• A double bond consists of one bond and one bond. • A triple bond has one bond and two bonds. • Often, the p orbitals involved in bonding come from unhybridized orbitals. • For example: ethylene, C2H4, has a C=C double bond:
• One and one bond. • Both C atoms sp
2 hybridized.
• Both C atoms with trigonal planar electron-pair and molecular geometries. • For example: acetylene, C2H2, has a CC triple bond
• The electron-domain geometry of each C is linear. • Therefore, the C atoms are sp hybridized.
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• The sp hybrid orbitals form the C–C and C–H bonds. • There are two unhybridized p orbitals on each C atom. • Both unhybridized p orbitals form the two bonds;
• One bond is above and below the plane of the nuclei; • One bond is in front and behind the plane of the nuclei. • When triple bonds form (e.g., N2), one bond is always above and below and the other is in
front and behind the plane of the nuclei.
Resonance Structures, Delocalization, and Bonding
• 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 sp
2 hybridized.
• There is one unhybridized p orbital on each carbon atom, resulting in six unhybridized carbon p orbitals in a ring.
• In benzene the three bonds are delocalized over the entire ring (i.e., the electrons are shared by all
six carbon atoms). • Experimentally, all C–C bonds are the same length in benzene. • Therefore, all C–C bonds are of the same type (recall single bonds are longer than double bonds).
General Conclusions
• 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. • bonds in alkenes and alkynes will be discussed in Chapter 24 (section 24.3). • Delocalized bonds in aromatic compounds will be mentioned in Chapter 24 (section 24.3).
9.7 Molecular Orbitals
• Some aspects of bonding are not explained by Lewis structures, VSEPR theory and hybridization. • For example: • Why does O2 interact with a magnetic field? • Why are some molecules colored? • For these molecules, we use molecular orbital theory. • Just as electrons in atoms are found in atomic orbitals, electrons in molecules are found in molecular
orbitals (MO). • Molecular orbitals: • Some characteristics are similar to those of atomic orbitals. • Each contains a maximum of two electrons with opposite spins. • Each has a definite energy. • Electron density distribution can be visualized with contour diagrams.
• However, unlike atomic orbitals, molecular orbitals are associated with an entire molecule.
The Hydrogen Molecule
• 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).
• Sigma () MOs have electron density in both molecular orbitals centered about the internuclear axis. • The bonding MO is lower in energy than the
(antibonding) MO.
• The energy-level diagram or MO diagram shows the energies of the orbitals in a molecule.
• The total number of electrons in all atoms are placed in the MOs starting from lowest energy (1s) and ending when all electrons have been accommodated.
• Note that electrons in MOs have opposite spins.
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.
• H2 has two bonding electrons. • Bond order for H2 is:
½ (bonding electrons - antibonding electrons) = ½ (2 – 0) = 1. • Therefore, H2 has a single bond. • For example, consider the species He2. • He2 has two bonding electrons and two antibonding electrons.
• Bond order for He2 is: ½ (bonding electrons - antibonding electrons) = ½ (2 – 2) = 0.
• Therefore He2 is not a stable molecule. • MO theory correctly predicts that hydrogen forms a diatomic molecule but that helium does not!
9.8 Period 2 Diatomic Molecules • We look at hom*onuclear diatomic molecules (e.g., Li2, Be2, B2 etc.).
• AOs combine according to the following rules: • The number of MOs = number of AOs. • AOs of similar energy combine (e.g., 1s + 1s rather than 1s + 2s). • As overlap increases, the energy of the bonding MO decreases and the energy of the antibonding MO
increases. • Pauli: each MO has at most two electrons, with spins paired.
• Hund: for degenerate orbitals, each MO is first occupied singly before spin pairing occurs.
Molecular Orbitals for Li2 and Be2
• 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.
• 2 electrons in 2s.
• 0 electrons in *2s.
• Therefore the bond order is ½ (4 – 2) = 1. • Since the 1s AOs are completely filled, the 1s and
*1s are filled.
• We generally ignore core electrons in MO diagrams. • Core electrons usually don’t contribute significantly to bonding in molecule formation. • Consider bonding in Be2.
• There are a total of eight electrons in Be2. • 2 electrons in 1s. • 2 electrons in
*1s.
• 2 electrons in 2s.
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• 2 electrons in *2s.
• Therefore the bond order is ½ (4 – 4) = 0. • Be2 does not exist.
Molecular Orbitals from 2p Atomic Orbitals
• 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. • The six p-orbitals (two sets of three) must give rise to six MOs:
• 2p, 2p, 2p, 2p
, 2p and 2p
.
• Therefore, there are a maximum of two bonds which can come from p orbitals. • The relative energies of these six orbitals can change.
Electron Configurations for B2 through Ne2
• 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. • The
p MO is higher in energy than the
2p orbitals.
• The 2p and *2p orbitals are doubly degenerate.
• As the atomic number decreases, it becomes more likely that a 2s orbital on one atom can interact with
the 2p orbital on the other.
• As the 2s–2p interaction increases, the 2s MO lowers and the 2p MO increases in energy. • For B2, C2 and N2 the 2p orbital is higher in energy than the 2p. • For O2, F2 and Ne2 the 2p orbital is lower in energy than the 2p. • Once we know the relative orbital energies, we add the required number of electrons to the MOs, taking
into account Pauli’s exclusion principle and Hund’s rule.
• As bond order increases, bond length decreases and bond energy increases.
Electron Configurations and Molecular Properties
• 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 • Magnetic behavior is detected by determining the mass of a sample in the presence and absence of a
magnetic field:
• A large increase in mass indicates paramagnetism. A small decrease in mass indicates diamagnetism. • Experimentally, O2 is paramagnetic, has a short bond length (1.21 Å) and high bond dissociation energy
(495 kJ/mol). • The Lewis structure for O2 shows no unpaired electrons. • The MO diagram for O2 shows 2 unpaired electrons in the
*2p orbital.
• This suggests a double bond. • The MO diagram for O2 predicts both paramagnetism and the double bond (bond order = 2).
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 hom*onuclear diatomic molecules.
xane are compared in this demonstration. Selected Problems: 19, 20, 21, 27, 28, 31, 33, 35, 36, 43, 44, 46, 51, 55, 56, 61, 66, 69, 70, 74, 78, 81, 83.
