Question

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

The resulting molecular orbital from the in-phase combination of two d_xz atomic orbitals is a σ_d_xz molecular orbital.

Step-by-step solution

Understand the d_xz atomic orbital shape

The d_xz atomic orbital is part of the d-orbital set and has a distinctive shape, with two lobes located on opposite sides of the x-z plane. It is easiest to visualize this as a four-leaf clover pattern on the x-z plane (with the x-axis being the internuclear axis).

Visualize the in-phase combination of two d_xz orbitals

When combining atomic orbitals to form molecular orbitals, we consider both in-phase and out-of-phase combinations. In the in-phase combination, the lobes of the same sign (positive or negative) on both orbitals overlap constructively resulting in a new molecular orbital.

Combine the two d_xz orbitals in-phase

Let's visualize the two d_xz atomic orbitals along the x-axis (the internuclear axis), with one on the left (orbital 1) and one on the right (orbital 2). To combine them in-phase, arrange it so that the positive lobes of orbital 1 overlap with the positive lobes of orbital 2, and the same for negative lobes. This will result in only two lobes along the x-axis, one positive and one negative.

Identify the type of molecular orbital formed

The in-phase combination of two d_xz atomic orbitals has created a new molecular orbital with only two lobes along the x-axis. This type of molecular orbital is called a σ (sigma) orbital. In this case, since it's formed from two d_xz orbitals combination, it will be called a σ_d_xz molecular orbital. In conclusion, the resulting molecular orbital from the in-phase combination of two d_xz atomic orbitals is a σ_d_xz molecular orbital.