Chapter 9 Molecular Geometries and Bonding Theories

9.1 Molecular Shapes Lewis structures do not indicate shape of molecule The shape of a molecule plays an important role in its reactivity. The overall shape is determined by bond angles. By noting the number of bonding and nonbonding electron pairs we can easily predict the shape of the molecule. ABn geometries: (page 347)

9.2 Valence Shell Electron Pair Repulsion Theory (VSEPR) The best arrangement of a given number of electron domains is the one that minimizes the repulsions among them.

What Determines the Shape of a Molecule? Simply put, electron pairs, whether they be bonding or nonbonding, repel each other. By assuming the electron pairs are placed as far as possible from each other, we can predict the shape of the molecule. Each nonbonding pair, single bond, or multiple bond produces an electron domain around the central atom. In the NH3 molecule below, for example, there are four electron domains around the central atom, three bonding and one nonbonding.

Electron-Domain Geometry (ABn molecules) Electron domains are regions of space around the central atom in which electrons are concentrated. The arrangement of electron domains around an ABn molecule or ion is called its electron-domain geometry. All the electrons (to include any multiple bonds) on one side of a central atom constitute an electron domain. This molecule has four electron domains.

These are the electron-domain geometries for two through six electron domains around a central atom.

To determine the electron geometry just count the number of electron domains in the Lewis structure. The geometry will be that which corresponds to that number of electron domains.

Molecular Geometries The electron-domain geometry is often not the shape of the molecule, however. The molecular geometry (i.e., shape of the molecule) is the arrangement of only the atoms in a molecule or ion. The molecular geometry, though influenced by the presence of nonbonding electrons, does not include the nonbonding electron pairs in the shape of the molecule.

Within each electron domain, then, there might be more than one molecular geometry. For example, in the geometries to the right, all three are the tetrahedral electron-domain geometry. There are three molecular geometries based only on the number of atoms present.

Linear Electron Domain In this domain, there is only one molecular geometry: linear. NOTE: If there are only two atoms in the molecule, the molecule will be linear no matter what the electron domain is.

Trigonal Planar Electron Domain There are two molecular geometries: Trigonal planar, if all the electron domains are bonding Bent, if one of the domains is a nonbonding pair.

Nonbonding Pairs and Bond Angle Nonbonding pairs are physically larger than bonding pairs. Therefore, their repulsions are greater; this tends to decrease bond angles in a molecule.

Multiple Bonds and Bond Angles Double and triple bonds place greater electron density on one side of the central atom than do single bonds. Therefore, they also affect bond angles.

Tetrahedral Electron Domain There are three molecular geometries: Tetrahedral, if all are bonding pairs Trigonal pyramidal if one is a nonbonding pair Bent if there are two nonbonding pairs

Trigonal Bipyramidal Electron Domain There are two distinct positions in this geometry: Axial Equatorial

Lower-energy conformations result from having nonbonding electron pairs in equatorial, rather than axial, positions in this geometry.

There are four distinct molecular geometries in this domain: trigonal bipyramidal, seesaw, T-shaped, and linear.

Octahedral Electron Domain All bond angles are 90o. There are three molecular geometries: octahedral, square pyramidal, square planar.

Shapes of Larger Molecules In larger molecules, it makes more sense to talk about the geometry about a particular atom rather than the geometry of the molecule as a whole.

This approach makes sense, especially because larger molecules tend to react at a particular site in the molecule.

9.3 Molecular Shape and Molecular Polarity In Chapter 8 we discussed bond dipoles. But just because a molecule possesses polar bonds does not mean the molecule as a whole will be polar.

By adding the individual bond dipoles, one can determine the overall dipole moment for the molecule.

Polar vs. non-polar molecules. Molecules in which the central atom is symmetrically surrounded by identical atoms are nonpolar.

9.4 Covalent Bonding and Orbital Overlap The sharing of electrons in forming covalent bonds can only occur when orbitals on the two atoms overlap. In the example for H2, below, as the 1s orbitals overlap, electron density is increased between the nuclei. Because the electrons in the overlap region are simultaneously attracted to both nuclei, they hold the atoms together by forming a covalent bond. Orbital overlap applies to other atoms as well, as when the 1s orbital of H overlaps with the 3p orbital of chlorine to form HCl; or when two 3p orbitals on Cl atoms overlap to form the Cl2 molecule.

There is an optimum distance between bonded nuclei in any covalent bond. As shown below, the potential energy of the system changes as two H atoms approach (on the left) to form H2. Increased overlap brings the electrons and nuclei closer together while simultaneously decreasing electron-electron repulsion. However, if atoms get too close, the internuclear repulsion greatly raises the energy. The internuclear distance at the minimum of the PE curve corresponds to the observed bond length of 0.74 Å (the equilibrium bond distance). The energy at this point corresponds to the energy change for the formation of the H-H bond (see Table 8.4).

9.5 Hybrid Orbitals The idea of orbital overlap does not easily extend to polyatomic molecules. Valence-bond theory must explain both the formation of electron-pair bonds and the observed geometries. To explain observed geometries the atomic orbitals are described as mixing to form hybrid orbitals in a process called hybridization. The shapes of the hybrid orbitals are different from the shapes of the original atomic orbitals.

sp Hybrid Orbitals Consider the example of BeF2 which has the Lewis structure This is a linear molecule with two bonds of equal length. But how can valence-bond theory explain this structure and its geometry? The electron configuration of F (1s2 2s2 2p5) shows an unpaired electron in the 2p orbital. This electron can be paired with an unpaired electron from the Be atom to form a covalent bond.

However, the ground-state orbital diagram for Be shows no singly-occupied orbitals. It would be unable to form a bond with fluorine. But if Be absorbs a small amount of energy it can promote an electron from the 2s to the 2p orbital and form two bonds. The two bonds, however, would not be identical since one would be formed from the Be 2s orbital and one from the Be 2p orbital. The promotion of an electron allows two Be—F bonds to form but doesn’t explain the structure.

The problem is solved by “mixing” the 2s orbital and one 2p orbital to generate two new orbitals, as shown. The sp orbitals are higher in energy than the 1s orbital but lower than the 2p. The electrons in the sp hybrid orbitals can now form two-electron bonds with the two fluorine atoms. (Note that no extra orbitals have been created.) Original Be orbitals Hybrid Be sp orbitals

These two equivalent sp hybrid orbitals have two lobes like a p orbital, but one of the lobes is larger. The larger lobes can be better directed at other atoms better than unhybridized atomic orbitals. Hence, they can overlap more strongly with the orbitals of other atoms

The two degenerate (i.e., they have the same amount of energy) orbitals would align themselves 180 from each other. This is consistent with the observed geometry of beryllium compounds: linear. The observed bonds of equal length would not be possible if Be were unhybridized.

sp2 and sp3 Hybrid Orbitals Other orbital combinations can be mixed to produce hybrid orbitals to support other geometries. An sp2 geometry is seen in BF3, for example, which produces three equivalent hybrid orbits that point in different directions. Hybridization in boron: The three sp2 hybrid orbitals lie in the same plane 120o apart from one another, leading to the trigonal-planar geometry of BF3.

One s orbital and two p orbitals hybridize to form three equivalent (degenerate) sp2 hybrid orbitals. The large lobes point to the corners of an equilateral triangle.

Carbon can form up to four bonds with other elements. Its electron configuration is 1s2 2s2 2p2. It hybridizes four orbitals to produce four equivalent sp3 hybridized orbitals.

sp3 hybridization supports tetrahedral molecular geometry. Each lobe points to a different corner of a tetrahedron. The bonding in CH4 is described as the overlap of four equivalent sp3 hybrid orbitals on C with the 1s orbitals of four H atoms to form four equivalent bonds.

Hybridization and nonbonding electrons sp3 hybridization can describe bonding in atoms containing nonbonding pairs of electrons. In water, for example, the electron-domain around the central O atom is approximately tetrahedral. Two of the hybrid orbitals contain nonbonding pairs of electrons, while the other two forms bonds with H atoms.

Hybridization Involving d Orbitals For geometries involving expanded octets on the central atom, we must use d orbitals in our hybrids. Mixing one s orbital, three p orbitals, and one d orbital leads to five sp3d hybrid orbitals. The formation of five sp3d hybrid orbitals is seen in P in PF5:

The five equivalent sp3d orbitals support the trigonal bipyramidal molecular geometry. The six equivalent sp3d2 orbitals support the octahedral molecular geometry.

Summary Once you know the electron-domain geometry, you know the hybridization state of the atom.

9.6 Multiple Bonds In covalent bonds as discussed so far, the electron density is concentrated symmetrically along a line connecting the nuclei (the internuclear axis). These head-to-head overlap bonds between two s bonds, an s and a p bond, or two p bonds are called sigma (σ) bonds.

 

Single bonds are always  bonds, because  overlap is greater, resulting in a stronger bond and more energy lowering. In a multiple bond one of the bonds is a  bond and the rest are  bonds.

Examples of Multiple Bond Hybridization 1. Ethylene Ethylene (C2H4) contains a C=C double bond. After hybridization, one electron remains in an unhybridized 2p orbital.

 

The unhybridized 2p orbitals on each C atom overlap to form a  bond. The electron density is above and below the bond axis, whereas in the σ bonds the electron density lies along the bond axis.

2. Formaldehyde In a molecule like formaldehyde (shown at left) an sp2 orbital on carbon overlaps in  fashion with the corresponding orbital on the oxygen. The unhybridized p orbitals overlap in  fashion.

3. Acetylene Acetylene (C2H2) contains a C≡C triple bond. In triple bonds two sp orbitals form a  bond between the carbons, and two pairs of p orbitals overlap in  fashion to form the two  bonds.

Delocalized Electrons: Resonance When writing Lewis structures for species like the nitrate ion, we draw resonance structures to more accurately reflect the structure of the molecule or ion.

In reality, each of the four atoms in the nitrate ion has a p orbital. The p orbitals on all three oxygens overlap with the p orbital on the central nitrogen. This means the  electrons are not localized between the nitrogen and one of the oxygens, but rather are delocalized throughout the ion.

Delocalized Electrons: Resonance This means the  electrons are not localized between the nitrogen and one of the oxygens, but rather are delocalized throughout the ion.

The organic molecule benzene has six  bonds and a p orbital on each carbon atom.

In reality the  electrons in benzene are not localized, but delocalized. The even distribution of the  electrons in benzene makes the molecule unusually stable.

9.7 Molecular Orbital (MO) Theory Though valence-bond theory allows us to view the molecular geometry of molecules in terms of atomic orbitals, it does not explain all aspects of bonding. For example, it is not able to describe the excited states of molecules. Some aspects of bonding are better explained by an alternative model called molecular orbital theory. This course does not include an examination of MO theory.