12. Molecular Shapes & Valence Bond Theory

Using molecular orbital theory, determine the bond order for Li₂⁺.

Using molecular orbital theory, determine whether F₂, F₂⁻, or F₂²⁻ would have the strongest bond.

Using molecular orbital theory, determine the magnetism of O₂ and O₂⁻.

The following diagrams illustrate p-p orbital overlap or s-p orbital overlap. Which diagram represents a p bond in valence bond theory? (LO 8.3) (a)

(b)

(c)

(d)

The orbital diagram that follows presents the final step in the formation of hybrid orbitals by a silicon atom. (a) Which of the following best describes what took place before the step pictured in the diagram: (i) Two 3p electrons became unpaired, (ii) An electron was promoted from the 2p orbital to the 3s orbital, or (iii) An electron was promoted from the 3s orbital to the 3p orbital?

The following is part of a molecular orbital energy-level diagram for MOs constructed from 1s atomic orbitals.

(a) What labels do we use for the two MOs shown?

For each of these contour representations of molecular orbitals, identify (b) the type of MO (s or p) (iii)

For each of these contour representations of molecular orbitals, identify (b) the type of MO (s or p) (i)

For each of these contour representations of molecular orbitals, identify (a) the atomic orbitals (s or p) used to construct the MO (i)

For each of these contour representations of molecular orbitals, identify (a) the atomic orbitals (s or p) used to construct the MO (iii)

For each of these contour representations of molecular orbitals, identify (c) whether the MO is bonding or antibonding (i)

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (a) How many molecular orbitals are there in the diagram?

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)?

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (c) How many nodes are in the highest-energy molecular orbital?

Repeat Exercise 12.51 for a linear chain of eight lithium atoms. (f) How does the HOMO–LUMO energy gap for this case compare to that of the four-atom case?

Write orbital diagrams (boxes with arrows in them) to represent the electron configurations—without hybridization—for all the atoms in SF2. Circle the electrons involved in bonding. Draw a three-dimensional sketch of the molecule and show orbital overlap. What bond angle do you expect from the unhybridized orbitals? How well does valence bond theory agree with the experimentally measured bond angle of 98.2° ?

(c) Is the p bond in NO2- localized or delocalized?

(c) Would you expect N2O to exhibit delocalized p bonding?

Sketch the bonding molecular orbital that results from the linear combination of two 1s orbitals. Indicate the region where interference occurs and state the kind of interference (constructive or destructive).

Consider the H2+ ion. (f) Which of the following statements about part (e) is correct: (i) The light excites an electron from a bonding orbital to an antibonding orbital, (ii) The light excites an electron from an antibonding orbital to a bonding orbital, or (iii) In the excited state there are more bonding electrons than antibonding electrons?

Draw a picture that shows all three 2p orbitals on one atom and all three 2p orbitals on another atom. (c) How many antibonding orbitals, and of what type can be made from the two sets of 2p orbitals?

Sketch the bonding and antibonding molecular orbitals that result from linear combinations of the 2px atomic orbitals in a homonuclear diatomic molecule. (The 2px orbitals are those whose lobes are oriented along the bonding axis.)

Indicate whether each statement is true or false. (d) Electrons cannot occupy a nonbonding orbital.

Indicate whether each statement is true or false. (c) Molecules containing electrons that occupy antibonding orbitals must be unstable.

Sketch the bonding and antibonding molecular orbitals that result from linear combinations of the 2pz atomic orbitals in a homonuclear diatomic molecule. (The 2pz orbitals are those whose lobes are oriented perpendicular to the bonding axis.) How do these molecular orbitals differ from those obtained from linear combinations of the 2py atomic orbitals? (The 2py orbitals are also oriented perpendicular to the bonding axis, but also perpendicular to the 2pz orbitals.)

What is the difference in spatial distribution between electrons in a bonding MO and electrons in an antibonding MO?

For a given type of MO, use a s2s as an example, is the bonding or antibonding orbital higher in energy? Explain.

In ozone, O3, the two oxygen atoms on the ends of the molecule are equivalent to one another. (d) How many electrons are delocalized in the p system of ozone?

The highest occupied molecular orbital of a molecule is abbreviated as the HOMO. The lowest unoccupied molecular orbital in a molecule is called the LUMO. Experimentally, one can measure the difference in energy between the HOMO and LUMO by taking the electronic absorption (UV-visible) spectrum of the molecule. Peaks in the electronic absorption spectrum can be labeled as p2p9p2p*, s2s9s2s*, and so on, corresponding to electrons being promoted from one orbital to another. The HOMO-LUMO transition corresponds to molecules going from their ground state to their first excited state. (c) The electronic absorption spectrum of the N2 molecule has the lowest energy peak at 170 nm. To what orbital transition does this correspond?

Make a sketch showing the location and geometry of the p orbitals in the nitrite ion, NO2-. Describe the bonding in this ion using a localized valence bond model for s bonding and a delocalized MO model for p bonding.

Molecules that are brightly colored have a small energy gap between filled and empty electronic states (the HOMOLUMO gap; see Exercise 9.104). Suppose you have two samples, one is lycopene which is responsible for the red color in tomato, and the other is curcumin which is responsible for the yellow color in turmeric. Which one has the larger HOMO-LUMO gap?

The energy-level diagram in Figure 9.36 shows that the sideways overlap of a pair of p orbitals produces two molecular orbitals, one bonding and one antibonding. In ethylene there is a pair of electrons in the bonding π orbital between the two carbons. Absorption of a photon of the appropriate wavelength can result in promotion of one of the bonding electrons from the p2p to the p*2p molecular orbital. (b) Assuming this electronic transition corresponds to the HOMO-LUMO transition, what is the LUMO in ethylene?

The energy-level diagram in Figure 9.36 shows that the sideways overlap of a pair of p orbitals produces two molecular orbitals, one bonding and one antibonding. In ethylene there is a pair of electrons in the bonding π orbital between the two carbons. Absorption of a photon of the appropriate wavelength can result in promotion of one of the bonding electrons from the p2p to the p*2p molecular orbital. (a) Assuming this electronic transition corresponds to the HOMO-LUMO transition, what is the HOMO in ethylene?

Cyclooctatetraene dianion, C8H8 2-, is an organic ion with the structure shown. Considering only the p bonds and not the s bonds, cyclooctatetraene dianion can be described by the following energy diagrams of its p molecular orbitals:

(b) Three of the p molecular orbitals are bonding, three are antibonding, and two are nonbonding, meaning that they have the same energy level as isolated p orbitals. Which is which?

The organic molecules shown here are derivatives of benzene in which six-membered rings are 'fused' at the edges of the hexagons.

(e) Benzene, naphthalene, and anthracene are colorless, but tetracene is orange. What does this imply about the relative HOMO–LUMO energy gaps in these molecules? See the 'Chemistry Put to Work' box on orbitals and energy.

The water molecule has similar bond vibrations to carbon dioxide. Decide whether the symmetric, asymmetric, and bending vibrations in water will result in the absorption of IR radiation.

Bond vibrations for the symmetric and asymmetric stretch in methane are illustrated below. Decide whether each vibration will result in the absorption of IR radiation. Arrows indicate the movement of atoms during the vibration.

(b) When xenon absorbs 801 kJ/mol of energy, it is excited into a higher-energy state in which the outermost elec-tron has been promoted to the next available subshell. Write the electron configuration for this excited xenon.