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Chapter 9: Problem 77

What type of molecular orbital would result from the in-phase combination of two \(d_{x z}\) atomic orbitals shown below? Assume the \(x\) -axis is the internuclear axis.

Short Answer

Expert verified
The resulting molecular orbital from the in-phase combination of two \(d_{x z}\) atomic orbitals would be a bonding molecular orbital, represented as \(\sigma_{d_{xz}}\).

Step by step solution

01

Understand the shape of the d_{x z} atomic orbital

A \(d_{x z}\) atomic orbital has a shape where four lobes are arranged in the xz plane, with two lobes on the positive half of the x-axis and the other two lobes on the negative half of the x-axis. The lobes are also symmetric about the z-axis. Keep in mind that the atomic orbital has a nodal plane, which is a plane in which the probability of finding electrons is zero, between the positive and negative lobes, that's the yz plane.
02

Visualize the in-phase combination of two d_{x z} atomic orbitals

In an in-phase combination, the lobes with the same phase (sign of the wave function) are overlapped, which results in a constructive interference, and thus, an increase in the electron probability density. In this case, we have two \(d_{x z}\) atomic orbitals. Since the x-axis is the internuclear axis, the positive lobes will be pointing toward each other, and the negative lobes will be pointing away from each other.
03

Predict the resulting molecular orbital

In the in-phase combination of two \(d_{x z}\) atomic orbitals, the positive lobes merge constructively to form an enlarged lobe along the internuclear axis (x-axis). Similarly, the negative lobes also combine constructively to form enlarged lobes along the x-axis. The resulting molecular orbital is a bonding molecular orbital, as the increased electron density between the two nuclei helps to hold them together. This bonding orbital is often represented as \(\sigma_{d_{xz}}\), where the sigma indicates a symmetric molecular orbital along the internuclear axis.

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Most popular questions from this chapter

Use the localized electron model to describe the bonding in \(\mathrm{C}_{2} \mathrm{H}_{2}\) (exists as \(\mathrm{HCCH}\) ).

The atoms in a single bond can rotate about the internuclear axis without breaking the bond. The atoms in a double and triple bond cannot rotate about the internuclear axis unless the bond is broken. Why?

Consider three molecules: \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\). Molecule A has a hybridization of \(s p^{3}\). Molecule B has two more effective pairs (electron pairs around the central atom) than molecule A. Molecule C consists of two \(\sigma\) bonds and two \(\pi\) bonds. Give the molecular structure, hybridization, bond angles, and an example for each molecule.

Why does the molecular orbital model do a better job in explaining the bonding in \(\mathrm{NO}^{-}\) and NO than the hybrid orbital model?

Use the MO model to explain the bonding in \(\mathrm{BeH}_{2}\). When constructing the MO energy-level diagram, assume that the Be's \(1 s\) electrons are not involved in bond formation.
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