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.

Step by step solution

01

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″.

02

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.

03

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.

04

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.

05

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.

06

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.

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