Chapter 3, Problem 3.1P

Interpretation Introduction

(a)

Interpretation:

The MO resulting from the given orbital interaction is to be drawn.

Concept introduction:

When atomic orbitals (AOs) of the same phase interact, they result in a bonding molecular orbital (MO) that is lower in energy than the individual AOs.

Answer to Problem 3.1P

The MO resulting from the given orbital interaction can be drawn as follows:

Explanation of Solution

The orbital interaction shows two orbitals that are lightly shaded. Both have the same negative phase. Since the phases of both are the same, there will be constructive interference, resulting in a bonding MO of negative phase.

The MO resulting from the given orbital interaction can be drawn as follows:

Conclusion

The interaction between orbitals of the same phase results in the formation of a bonding MO.

Interpretation Introduction

(b)

Interpretation:

Whether the resulting MO is unique compared to the one shown on the right of Figure 3-6a is to be determined.

Concept introduction:

When atomic orbitals (AOs) of the same phase interact, the resulting molecular orbital (MO) has a lower energy than the separate AOs. The phases of the interacting orbitals may be both positive or both negative. The resulting stabilization (lowering of energy) is the same for both.

Answer to Problem 3.1P

The MO resulting from the interaction shown will not be unique compared to the one shown in Figure 3-6a.

Explanation of Solution

The interaction in this case is between AOs of negative phases (light shading). Since the phases are the same, the interaction will result in constructive interference, increasing the electron density between the two nuclei. This will lower the energy of the MO compared to the individual AOs. The extent to which the energy is lowered will be the same as in case of the interaction shown in Figure 3-6a. This is because the interacting orbitals are same except for a different phase.

Therefore, the MO resulting from the interaction shown will not be unique compared to the one in Figure 3-6a.

Conclusion

The interaction between AOs of same phase results in a bonding MO with the same stabilization, whether their phases are both positive or both negative.