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 \(\pi_{2 p}^{\star}\) 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 \(^{4} \mathrm{M}^{\prime \prime}\) 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 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 \(\pi_{2 p}^{\star}\) orbital of CO? (e) What kind of bond is being made with the orbitals between \(\mathrm{M}\) and \(\mathrm{C}, \sigma\) or \(\pi ?(\mathrm{f})\) Predict what will happen to the strength of the CO bond in a metal-CO complex compared to CO alone.

Short answer

In summary, d-π backbonding occurs between a metal atom (4M″) and a CO molecule. The CO molecule has a π2p* orbital with two lobes pointing towards the metal atom. The metal atom possesses a dxy orbital that overlaps with the π2p* orbital of CO, forming a π bond between the metal and carbon atoms. This interaction effectively donates electron density from the metal atom to the π* (anti-bonding) orbital of CO, resulting in a weakened CO bond strength in the metal-CO complex compared to CO alone.

Step-by-step solution

Draw the coordinate axis system and metal atom

Begin by drawing a coordinate axis system, with the y-axis being vertical and the x-axis being horizontal. Denote the metal atom at the origin as 4M″.

Draw the Lewis structure of the CO molecule

On the x-axis to the right of the metal atom, draw the Lewis structure of the CO molecule, with the carbon atom closest to the metal atom. The CO bond axis should lie on the x-axis.

Draw the π2p* orbital of the CO molecule

Draw the π2p* orbital of the CO molecule in the plane of the paper, with two lobes pointing towards the metal atom at the origin. Make sure to include phase labeling on the lobes of the orbital.

Draw the dxy orbital of the metal atom

Now, draw the dxy orbital of the metal atom in the same plane as the coordinate axis system and the π2p* orbital of the CO molecule. Make sure to include phase labeling on the lobes of the dxy orbital.

Determine the type of bond being formed between the metal and carbon atoms

Observe the overlap between the dxy orbital of the metal atom and the π2p* orbital of the CO molecule. You should see that the orbitals overlap above and below the x-axis, perpendicular to the σ-bond axis between the carbon and oxygen atoms. This means that the bond formed between the metal and carbon atoms is a π bond.

Predict the change in CO bond strength in a metal-CO complex compared to CO alone

When the metal atom forms a π bond with the CO molecule through d-π backbonding, it effectively donates electron density to the π* (anti-bonding) orbital of the CO molecule. This donation of electron density weakens the CO bond strength in the metal-CO complex compared to the CO bond strength when the CO molecule is not bonded to the metal atom.

Key concepts

Antibonding Molecular Orbitals

Antibonding molecular orbitals are an interesting aspect of molecular chemistry. Unlike bonding orbitals, which stabilize a molecule, antibonding orbitals do the opposite. They have higher energy and their presence can actually weaken the bonds.
Antibonding orbitals are formed when atomic orbitals overlap out of phase, which means their wave functions cancel each other out. These orbitals are often marked with an asterisk (*). For example, in a scenario involving carbon monoxide (CO), the antibonding \(\pi_{2p}^*\) orbital is one that can participate in interactions, such as d-π backbonding with metal atoms. This interaction occurs when a metal donates electron density into the antibonding orbital, thus modifying the bonding properties of CO.
This can lead to changes in bond lengths and strengths, which are frequently observed in metal-carbon monoxide complexes.

Molecular Orbital Theory

Molecular Orbital Theory is fundamental in understanding the electronic structure of molecules. This theory describes how atomic orbitals combine to form molecular orbitals, which are spread over the entire molecule rather than localized between individual atoms.
Molecular orbitals can be classified into bonding, antibonding, and non-bonding orbitals based on how they influence a molecule’s stability.

• Bonding molecular orbitals stabilize the molecule by having lower energy than the original atomic orbitals.
• Antibonding orbitals, as previously discussed, are higher in energy and can destabilize bonds.
• Non-bonding orbitals have energy similar to their respective atomic orbitals and often do not contribute to bonding.

In the context of metal-CO complexes, molecular orbital theory helps explain how orbitals from metal atoms and CO molecules interact and overlap, particularly focusing on how metal d orbitals can engage in backbonding with CO antibonding orbitals.

Metal-Carbon Monoxide Complex

Metal-carbon monoxide complexes are an essential part of organometallic chemistry. In these complexes, carbon monoxide acts not only as a ligand but also plays a role in altering metal properties and reactivity.
The bonding in these complexes typically involves two key components:

• σ-donation: Carbon monoxide donates electrons from its lone pair into empty metal orbitals, forming a sigma bond.
• π-backbonding: Metals with filled d orbitals can donate electron density back into the antibonding π* orbitals of CO.

This dual interaction of σ-donation and π-backbonding is pivotal in shaping the properties of metal-CO complexes. The π-backbonding aspect is particularly important because it can weaken the CO bond, decrease its vibrational frequency, and ultimately enhance the overall stability of the metal complex.

Chemical Bonding

Chemical bonding is a fundamental concept that holds matter together. Understanding the types of bonds in molecules is critical to predicting molecular behavior and reactivity.
Bonds are primarily formed due to the attractive forces between electrons and nuclei. There are several types of chemical bonds:

• Covalent Bonds: Atoms share electrons to achieve stability, common in organic molecules.
• Ionic Bonds: Transfer of electrons between atoms, usually seen in compounds formed between metals and non-metals.
• Metallic Bonds: Atoms in a metal share a "sea" of electrons, allowing for conductivity and malleability.

In advanced chemistry, hybrid forms of bonding, such as those seen in metal-CO complexes, challenge the simple classifications. The combination of σ-bonds and π-backbonding exemplifies how variable and complex chemical bonding can be in certain contexts, particularly affecting properties such as bonding energy and molecular structures.