Many compounds of the transition-metal elements contain...

Many compounds of the transition-metal elements contain direct bonds between metal atoms. We will assume that the $z$-axis is defined as the metal-metal bond axis. (a) Which of the $3 d$ orbitals (Figure $6.23$ ) can be used to make a $\sigma$ bond between metal atoms? (b) Sketch the $\sigma_{3 d}$ bonding and $\sigma_{3}^{*} d$ antibonding MOs. (c) With reference to the "Closer Look" box on the phases of orbitals, explain why a node is generated in the $\sigma_{3 d}^{*} \mathrm{MO}$. (d) Sketch the energy-level diagram for the $\mathrm{Sc}_{2}$ molecule, assuming that only the $3 d$ orbital from part (a) is important. (e) What is the bond order in $\mathrm{Sc}_{2}$ ?

Many compounds of the transition-metal elements contain direct bonds between metal atoms. We will assume that the $z$-axis is defined as the metal-metal bond axis. (a) Which of the $3 d$ orbitals (Figure $6.23$ ) can be used to make a $\sigma$ bond between metal atoms? (b) Sketch the $\sigma_{3 d}$ bonding and $\sigma_{3}^{*} d$ antibonding MOs. (c) With reference to the "Closer Look"
box on the phases of orbitals, explain why a node is generated in the $\sigma_{3 d}^{*} \mathrm{MO}$. (d) Sketch the energy-level diagram for the $\mathrm{Sc}_{2}$ molecule, assuming that only the $3 d$ orbital from part (a) is important. (e) What is the bond order in $\mathrm{Sc}_{2}$ ?

Key Concepts

d Orbital Symmetry and Orientation

Transition metal d orbitals have specific shapes and orientations that determine how they can overlap and form bonds. For instance, when forming a sigma bond along a designated bond axis (like the z-axis), only d orbitals with lobes aligned along that axis (typically the dz² orbital) can provide effective head-on overlap, which is essential for sigma bonding.

Molecular Orbital Theory in Metal–Metal Bonding

Molecular orbital (MO) theory explains how atomic orbitals combine to form new bonding and antibonding molecular orbitals in diatomic and polyatomic molecules. In the context of metal–metal bonds, the sigma bonding MO results from the constructive interference of orbitals (such as the dz² orbitals) aligned along the bond axis, while the sigma antibonding MO arises from their destructive interference, leading to a node between the atoms.

Orbital Phases and Nodal Planes

Orbital phase refers to the sign of the wave function in a given region of an orbital. When atomic orbitals combine, their phases must align to produce constructive overlap. In the formation of an antibonding orbital, opposite phases overlap, creating a node—a region of zero electron density—between the nuclei. This concept is crucial for understanding the presence of a node in the sigma antibonding MO.

Energy Level Diagrams and Bond Order

Energy level diagrams are graphical representations that display the relative energies of bonding and antibonding molecular orbitals. They are particularly useful in understanding the electronic structure of molecules. The bond order, calculated as half the difference between the number of electrons in bonding and antibonding orbitals, serves as a quantitative measure of bond strength, and it helps explain the stability and bond characteristics of molecules like Sc?.

Transcript

00:01 Okay, another tough problem.

00:03 In this problem we're going to consider scandium, which is a transition metal element.

00:09 And we're told that many compounds of transition elements like scandium can have a metal -metal bond.

00:17 We're given the information that we should assume the z -axis is the only place that the metal -metal bond can occur.

00:35 Then we're asked which of the 3d orbitals, and remember there are 5 -3 -3.

00:40 D orbitals can be used to make a sigma bond between metals.

00:48 And i'm going to sketch a z, x, and y, and the only d orbital, or d, yep, d orbital that's oriented on the z axis is this orbital, which we call the d, z2.

01:16 So that is the only one that has an orientation right here.

01:23 If you want to go look up the other deorbital you may, but none of the other ones have an orbital that has orientation on the z axis.

01:36 B asks us to sketch the bonding and the anti -bonding.

01:42 And i'm going to, in a different color here, just extend this and this and this.

01:49 And i'm going to draw sort of an overlap, because that didn't work very well, it didn't quite hit my middle, but you get the general idea here.

01:58 So my bonding orbital will be sort of a small little piece up here and a bigger piece down here, and then over here we'll have these, and over here we'll have these.

02:14 That's my bonding orbital, and here's my electron density.

02:20 My anti -bonding orbital will be more of a big piece up here, little piece here with this, and then same thing.

02:48 And you'll see that my node right here, there's no electron density at my node.

02:53 That is b.

02:56 This is a...

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