Activity 23 Molecular Orbital Model of Electronic Structure

Why? Just as atomic orbitals describe electrons in atoms, molecular orbitals describe electrons in molecules. Molecular orbitals account for the delocalization of electrons in the molecule and provide an alternative description to the Lewis model, which views the electrons as being localized in bonds between pairs of atoms. You can use the molecular orbital model to determine bond order, and consequently predict the strength, energy, length of bonds, and magnetic properties of molecules.

Learning Objectives

• Identify how molecular orbitals can be formed from atomic orbitals • Understand how the electron occupation of molecular orbitals is related to bond order, bond strength, bond energy, bond length, and magnetic properties

Success Criteria

• Construct and identify molecular orbitals • Analyze bond order, bond strength, bond energy, bond length, and magnetic properties in terms of the occupation of molecular orbitals

Prerequisites

• Activity 19: The Description of Electrons in Atoms • Activity 20: Periodic Trends in Atomic Properties • Activity 21: Lewis Model of Electronic Structure

Information

Molecular orbitals can be written as sums of atomic orbitals multiplied by a coefficient, which often is +1 or –1. Some of these orbitals are bonding, some nonbonding, and some antibonding. A bonding orbital has a high electron density between two atomic nuclei. This negative electron charge attracts the positive nuclei and holds them together. A nonbonding orbital positions electrons away from the bonds and does not contribute to bonding, e.g., non-bonded or lone pairs in the Lewis model would be in nonbonding orbitals in the molecular orbital model.

Activity 23 —Molecular Orbital Model of Electronic Structure 153 An antibonding orbital has little electron density between the two atomic nuclei, allowing the nuclei to repel each other. This repulsive effect of electrons which are in antibonding orbitals cancels the attractive effect of electrons in bonding orbitals, so molecules with equal occupations of bonding and antibonding orbitals are not stable. The bond order is given by half the number of bonding electrons minus half the number of antibonding electrons: BO = ½(n bonding – n antibonding) since the bonding electrons attract the atomic nuclei together, and antibonding electrons destabilize this bond. The bond order correlates with bond strength, bond energy, and bond length. The higher the bond order is, the stronger the bond; the higher the bond energy, the shorter the bond length.

odel M 1: Valence Orbitals of Diatomic Molecules Figure 23.1 Notation

atomic orbitals on atom labeled A: 2s(A), 2px(A), 2py(A), 2pz(A)

atomic orbitals on atom labeled B: 2s(B), 2px(B), 2py(B), 2pz(B) σ designates a sigma molecular orbital, which has a maximum electron density along a line connecting the two nuclei. This line is called the internuclear axis. π designates a pi molecular orbital, which has a maximum electron density above and below the internuclear axis * designates an antibonding molecular orbital, which has a region of very low electron density between the two nuclei

Valence Molecular Orbitals Formed from Atomic Orbitals Figure 23.2 + s 2s = 2s (A) + 2s (B) + + B A σ 2s B A s 2s* = 2s (A) – 2s (B) - } A + σ 2 * B s

B A s = 2p (A) + 2p (B) 2pz z z B A - + - σ2p - - z + + B A s * = 2p (A) – 2p (B) 2p 2p 2pz z z z z + - + - } σ2p * z the π orbitals are not shown, p 2p = 2px (A) + 2px (B) 2px x because they look just like the π orbitals but in the x-direction p * = 2p (A) – 2p (B) 2p + 2px x x } y B A π2p + + - y p 2py = 2py (A) + 2py (B) B A - + p 2p * = 2py (A) – 2py (B) y } - - B A * π2py + -

154 Foundations of Chemistry Key Questions

1. How many molecular orbitals are produced by combining two atomic orbitals as illustrated in Model 1?

2. If two s atomic orbitals from different atoms are combined, what are the names of the molecular orbitals that are produced and where are the regions of high and low electron density for these orbitals?

3. If two pz atomic orbitals from different atoms are combined, what are the names of the molecular orbitals that are produced? Where are the regions of high and low electron density for these orbitals?

4. If two py atomic orbitals from different atoms are combined, what are the names of the molecular orbitals that are produced? Where are the regions of high and low electron density for these orbitals?

5. According to Model 1, what are the differences between a bonding and an antibonding molecular orbital that apply to all three pairs of bonding and antibonding orbitals showin in Model 1?

Activity 23 —Molecular Orbital Model of Electronic Structure 155 6. In terms of the relationship to the internuclear axis, what is the difference between a p and a s molecular orbital?

7. What are the similarities between s2s and a s2pz molecular orbitals?

8. What are the differences between s2s* and a s2pz* molecular orbitals?

Exercises

1. Write the p2px and p2px* molecular orbitals in terms of the 2px atomic orbitals.

2. Draw diagrams similar to those in the model to show how the p2px and p2px* molecular orbitals are formed from the 2px atomic orbitals.

156 Foundations of Chemistry Model 2: Relative Energies of Valence Orbitals of Diatomic Molecules Figure 23.3

Relative Energies of the Molecular Orbitals for O2 and F2

------s2pz* p2px* ------p2py*

p2px ------p2py ------s2pz

------s2s* ------s2s

Figure 23.4 Relative Energies of the Molecular Orbitals for Homonuclear Diatomic Molecules with Atomic Number Z < 8 (Li2, Be2, B2, C2, N2)

------s2pz* p2px* ------p2py*

------s2pz p2px ------p2py

------s2s* ------s2s

Key Questions

9. When the atomic number Z < 8, which molecular orbital for homonuclear diatomic molecules is moved up in energy relative to the molecular orbitals for O2 and F2?

Activity 23 —Molecular Orbital Model of Electronic Structure 157 10. In view of the geometry or shape of diatomic molecules, why do you think that the p2px and p2py orbitals have the same energy?

11. What are six insights your team gained about molecular orbitals by examining the two models?

Exercises

3. For the cases of C2 and O2, place the electrons in the energy-level diagrams in Model 2. Represent electrons with up and down arrows, and apply the Aufbau Principle, the Pauli Exclusion Principle, and Hund’s Rule, as discussed in Activity 20 on Periodic Trends in Atomic Properties.

σ2pz* σ2pz*

π2px* π2py* π2px* π2py*

σ2pz π2px π2py

π2px π2py σ2pz

σ2s* σ2s*

σ2s σ2s

Energy Level Diagram for C 2 Energy Level Diagram for O2

158 Foundations of Chemistry 4. Using the insight you have gained from the energy level diagrams that you constructed in Exercise 3, identify which of the following statements are correct for C2 and O2.

a) Both molecules have unpaired electrons.

b) Only oxygen has unpaired electrons.

1 c) Both molecules have a bond order of 2. Bond order = ( nbonding- n antibonding ) 2 1 1 C = (6 - 2) = 2 O = (8 -4 ) = 2 2 2 2 2 d) The bond strength and bond energy are predicted from the occupation of the orbitals to be larger for O2 than for C2.

e) Both are homonuclear diatomic molecules.

f) Oxygen is paramagnetic. (See the Information section which follows.)

5. Some heteronuclear diatomic molecules have energy levels like those in Figure 23.3, while others have energy levels like those in Figure 23.4, e.g, CN, CN–, and CN+ a) Write the molecular orbital electron configurations for these three species. For example, the 2 electron configuration for 2H is (s1s) .

b) Place these species in order of increasing bond order, increasing bond length, increasing bond energy, and increasing vibrational frequency. (The higher the bond order and bond strength, the higher the vibrational frequency.) 1 Bond order = ( nbonding- n antibonding ) 2 1 1 1 CN = (7 - 2) = 2.5 CN- = (8 - 2) = 3 CN+ = (6 - 2) = 2 2 2 2 Bond length: CN – < CN < CN + Bond energy: CN + < CN < CN – Vibrational frequency: CN+ < CN < CN –

Activity 23 —Molecular Orbital Model of Electronic Structure 159 6. Identify the characteristic that determines whether a molecule is paramagnetic or diamagnetic.

7. Label the following species as paramagnetic or diamagnetic.

O2 N2 C2

CN CN – CN +

Information

Electrons behave as tiny bar magnets because they have a magnetic moment. If electrons are paired in molecular orbitals, the magnetic moments of the two electrons cancel each other out because the magnets point in opposite directions. Such a substance is diamagnetic. Unpaired electrons produce a net magnetic moment, and the molecule then is said to be paramagnetic.

Got It!

1. Identify which of the following statements are correct when molecular orbitals (MOs) are formed from two 1s atomic orbitals, each centered on different H-atom nuclei (protons).

a) Two bonding MOs are formed.

b) Two antibonding MOs are formed.

c) One bonding and one antibonding MO are formed with the bonding MO having the lower energy.

d) One bonding and one antibonding MO are formed with the antibonding MO having the lower energy.

e) If the MOs are occupied by electrons with the same value of ms, both electrons will be in the bonding MO as required by the Pauli Exclusion Principle and Hund’s Rule.

160 Foundations of Chemistry