Problem 121 - Chemistry: The Central Science

Question

Antibonding molecular orbitals can be used to make bonds to other atoms in a molecule. For example, metal atoms can use appropriate \(d\) orbitals to overlap with the \(\pi_{2 p}^{*}\) orbitals of the carbon monoxide molecule. This is called \(d-\pi\) backbonding. (a) Draw a coordinate axis system in which the \(y\)-axis is vertical in the plane of the paper and the \(x\)-axis horizontal. Write " \(\mathrm{M}^{"}\) at the origin to denote a metal atom. (b) Now, on the \(x\) axis to the right of \(M\), draw the Lewis structure of a CO molecule, with the carbon nearest the \(M\). The CO bond axis should be on the \(x\)-axis. (c) Draw the \(\mathrm{CO} \pi_{2 p}^{*}\) orbital, with phases (see the "Closer Look" box on phases) in the plane of the paper. Two lobes should be pointing toward M. (d) Now draw the \(d_{x y}\) orbital of \(\mathrm{M}\), with phases. Can you see how they will overlap with the \(\pi_{2}^{*}\) orbital of \(\mathrm{CO}\) ? (e) What kind of bond is being made with the orbitals between \(M\) and \(\mathrm{C}_{,} \sigma\) or \(\pi\) ? (f) Predict what will happen to the strength of the CO bond in a metal\(\mathrm{CO}\) complex compared to \(\mathrm{CO}\) alone.

Step-by-Step Solution

Answer

In summary, d-π backbonding occurs between a metal atom (M) and a carbon monoxide molecule (CO) through the overlap of the metal atom's dxy orbital and the CO's π2p* antibonding orbital, forming a π bond. As a result of this backbonding, the strength of the CO bond in the metal-CO complex is weakened compared to an isolated CO molecule.

Step 1: Draw a coordinate axis system and label the metal atom

First, draw a coordinate axis system with the y-axis vertical in the plane of the paper and the x-axis horizontal. Then, label the metal atom M at the origin.

Step 2: Draw the Lewis structure of a CO molecule

Place the CO molecule on the x-axis, with the carbon (C) atom nearest to the metal atom M. The CO bond axis should be along the x-axis. In the Lewis structure, carbon will have a triple bond with oxygen, with one lone pair of electrons on carbon, and two lone pairs on oxygen which will look like: (C≡O)

Step 3: Draw the CO π2p* orbital

Draw the antibonding π2p* orbital of CO in the plane of the paper, with two lobes pointing towards the metal atom M. Remember that antibonding orbitals have a node between the two atoms.

Step 4: Draw the dxy orbital with phases

Draw the dxy orbital of the metal atom M, with phases. This orbital has a butterfly shape, with lobes lying between the x and y axes.

Step 5: Identify the kind of bond being made

Observe the overlap between the metal atom's dxy orbital and the CO π2p* orbital. Since both orbitals have lobes lying parallel to each other, the kind of bond being made between the metal atom and carbon is a π bond.

Step 6: Predict the strength of the CO bond in a metal-CO complex

When the metal atom forms a bond with the CO molecule through d-π backbonding, it donates electron density from the dxy orbital into the antibonding π2p* orbital of CO. This additional electron density weakens the CO bond in the metal-CO complex compared to the bond in CO alone. Therefore, the strength of the CO bond in a metal-CO complex will be weaker than that in an isolated CO molecule.

Key Concepts

Antibonding Orbitals

Antibonding orbitals are quite vital when it comes to molecular interactions, especially in complex formations. These orbitals are characterized by having a node between the two atoms, meaning there is zero electron density across the bond axis. This occurs because the phase of the wave functions of the electrons is reversed between the two atoms, effectively reducing bonding potential.

In chemical terms, antibonding orbitals usually destabilize a molecule when filled because they increase the distance between bonded atoms. However, in certain interactions such as metal-ligand bonding, these orbitals can play an essential role. For example, metals can use their d orbitals to engage with antibonding orbitals of ligands like carbon monoxide, facilitating what we call backbonding.

This interaction showcases the versatility of antibonding orbitals, where they are not merely passenger seats but active participants in molecular bonding under the right conditions.

d-pi Backbonding

d-pi backbonding is a fascinating concept involving the sharing of electrons between a metal and a ligand, primarily using d and \(\pi\) orbitals. This type of bonding happens when a transition metal with available d electrons uses these electrons to enter the \(\pi_{2 p}^{*}\) (antibonding) orbital of a ligand like CO.

This backbonding process strengthens the bond between the metal and the carbon of CO but simultaneously weakens the internal CO bond. Essentially, the metal donates electron density to the antibonding orbital of CO, which enhances the metal-ligand bond while destabilizing the triple bond within CO itself.

Backbonding is not limited to carbon monoxide but is observed in many systems where metal-ligand interactions are crucial. It's a key concept in coordination chemistry, affecting physical properties such as bond length, vibrational frequencies, and even the color of metal complexes.

Metal-Carbonyl Complexes

Metal-carbonyl complexes are significant in coordination chemistry and industrial catalysis. In these complexes, transition metals are bound to carbon monoxide through \(\sigma\) and \(\pi\) interactions.

The \(\sigma\) bond forms when the filled lone pair of CO overlaps with the empty metal orbital, while the \(\pi\) bond forms primarily through d-pi backbonding. The combination of these overlaps results in a very stable metal-carbonyl interaction.

Their versatility and utility make metal-carbonyl complexes a pivotal study area in inorganic chemistry, especially since they play vital roles in various catalytic systems by facilitating transformations of molecules through coordination and electron transfer processes.

• These complexes often show altered reactivity compared to free CO, due to the changes in electron density distribution.
• The study of these complexes aids in understanding electron transfer processes, catalytic cycles, and reaction mechanisms.

Bond Strength Prediction

Predicting bond strength in chemical complexes is crucial for understanding their stability and reactivity. In metal-carbonyl complexes, bond strength predictions play a vital role in assessing the compound's behavior in reactions.

The concept of backbonding is key in predicting how the CO bond will behave when involved with a metal. As the d electrons from the metal populate the \(\pi_{2 p}^{*}\) orbital of CO, it reduces the electron density in the CO bond, leading to elongation and weakening of the CO bond.

The outcome of this interaction can be studied through various methods including spectroscopic techniques which can provide data on bond length and vibrational frequencies, both indicators of bond strength. Understanding these predictions helps chemists tailor and modify complexes for desired reactivity and stability in practical applications.