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 \(^{\prime} \mathrm{M}^{\prime \prime}\) 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 \(\mathrm{M}\). The \(\mathrm{CO}\) 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 \(\mathrm{M}\). (d) Now draw the \(\mathrm{d}_{x y}\) orbital of \(\mathrm{M}\), with phases. Can you see how they will overlap with the \(\pi_{2 p}^{*}\) orbital of CO? (e) What kind of bond is being made with the orbitals between \(\mathrm{M}\) and \(\mathrm{C}, \sigma\) or \(\pi ?\) (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 back bonding occurs between a metal atom and carbon monoxide as the metal's d(xy) orbital overlaps side-by-side with CO's π2p* orbital, forming a π bond. This electron transfer weakens the carbon-oxygen bond in the metal-CO complex compared to CO alone, making it longer and weaker.

Step-by-step solution

Draw the coordinate axis system

Begin by drawing a coordinate axis system in the plane of the paper. Label the horizontal axis as the x-axis and the vertical axis as the y-axis. Place the metal atom (M) at the origin of the coordinate system.

Draw the Lewis structure of CO

Draw the Lewis structure of a carbon monoxide (CO) molecule on the x-axis to the right of the metal atom M. The carbon atom should be nearest to the metal atom, and the CO bond axis should be on the x-axis.

Draw the CO π2p* orbital

Draw the π2p* antibonding molecular orbital of CO in the plane of the paper. The orbital should have two lobes pointing towards the metal atom M. Indicate the opposite phases in the lobes using different shading (positive phase is shaded, and negative phase is empty).

Draw the d(xy) orbital of M

Draw the d(xy) orbital of the metal atom M in the plane of the paper. The orbital will have four lobes and sit between the x and y axes, with alternating phases (positive phase is shaded, and negative phase is empty).

Determine the type of bond formed between M and C

Observe the overlap between the d(xy) orbital of M and the π2p* orbital of CO. Since the orbitals are overlapping side by side, the bond formed between the metal atom M and the carbon atom C is a π bond.

Predict the effect on the CO bond strength

The d-π back bonding in the metal-CO complex results in some electron density being transferred from the metal atom to the CO molecule's π2p* orbital. This transfer of electron density weakens the CO bond, leading to a longer and weaker carbon-oxygen bond in the metal-CO complex compared to CO alone.

Key concepts

Understanding Molecular Orbitals

Molecular orbitals are formed when atomic orbitals combine and overlap in a molecule. They can either stabilize or destabilize the molecule, depending on their type. In the context of d-π backbonding, where metal atoms interact with a ligand like carbon monoxide (CO), the molecular orbitals play a crucial role. Typically, these interactions are between the d orbitals of the metal and the antibonding π orbitals of CO. These interactions can strengthen bonds between different atoms and affect the overall stability and properties of the complex.

• Bonding orbitals - lower energy, stable
• Antibonding orbitals - higher energy, less stable
• d-π backbonding - overlapping of d orbitals with π* orbitals

Interpreting the Lewis Structure

The Lewis structure is a vital tool for visualizing the arrangement of electrons around atoms in a molecule. It helps in predicting the types of bonds and the possible interactions in a molecule. In a CO molecule, the Lewis structure shows a triple bond between carbon and oxygen: one sigma bond and two pi bonds. In the exercise, the carbon atom is closest to the metal atom, enabling effective orbital overlap. This structure sets the stage for d-π backbonding by arranging the CO in a way that promotes interaction with the metal's d orbitals. Representing the CO molecule and positioning it correctly aids in visualizing how these interactions might occur.

• Triple bond - includes one σ and two π bonds
• CO bond orientation - essential for backbonding
• Carbon facing metal - allows for orbital overlap

Analyzing Bond Strength in Metal-CO Complexes

The bond strength between atoms is a measure of how much energy is required to break the bond. When CO forms a complex with a metal through d-π backbonding, the electron density of the π* orbitals of CO increases. This electron donation from the metal weakens the internal CO bond. Consequently, the CO bond becomes longer and weaker compared to its original state. This is a direct result of the electron density rearrangement caused by the metal-ligand interaction.

• Backbonding - increases electron density in π* orbitals
• CO bond becomes weaker and longer
• Influence on bond energy and length

The Role of Antibonding Orbitals

Antibonding orbitals are characterized by nodes between nuclei, making them higher in energy and less stable than bonding orbitals. In the context of d-π backbonding, the \(\pi_{2p}^{*}\) orbital of CO, an antibonding orbital, interacts with the metal's d orbitals. Despite being higher in energy, when electrons are transferred from the metal to the antibonding orbitals, new stable interactions are formed. This overlap is crucial for forming the \(\pi\) bond between the metal and CO, illustrating how antibonding orbitals can paradoxically foster bond formation under specific conditions.

• Antibonding orbitals - higher energy, include nodes
• Interaction with metal - forms stable complexes
• Key in d-π backbonding - allows electron transfer and bond formation