To determine which combination results in [tex]\(d\)[/tex]-bond formation when the internuclear axis is along the [tex]\(x\)[/tex]-axis, let's analyze the interactions between the orbitals provided in the columns.
Firstly, let's get a grasp on the notation and the possible overlaps:
1. (P) [tex]\(d_{yz}\)[/tex]:
- This is a [tex]\(d\)[/tex]-orbital with lobes lying in the [tex]\(yz\)[/tex]-plane.
2. (Q) [tex]\(s\)[/tex]-orbital:
- This is a spherical orbital.
3. (R) [tex]\(d_{xz}\)[/tex]:
- This is a [tex]\(d\)[/tex]-orbital with lobes lying in the [tex]\(xz\)[/tex]-plane.
4. (S) [tex]\(p_z\)[/tex]:
- This is a [tex]\(p\)[/tex]-orbital aligned along the [tex]\(z\)[/tex]-axis.
Now, looking at the options provided:
1. (P), (7), (i):
- [tex]\(d_{yz}\)[/tex] with an unidentified orbital (7) and a 1 lobe - 1 lobe overlap. The provided table does not include (7), so this is invalid.
2. (P), (3), (iii):
- [tex]\(d_{yz}\)[/tex], [tex]\(d_{yz}\)[/tex], and 4 lobe - 4 lobe overlap. However, for [tex]\(d_{yz}\)[/tex] on the [tex]\(x\)[/tex]-axis, the [tex]\(d_{yz}\)[/tex] orbitals would actually overlap in the [tex]\(yz\)[/tex]-plane.
3. (R), (3), (iv):
- [tex]\(d_{xz}\)[/tex], [tex]\(d_{yz}\)[/tex], and zero overlap. Given that [tex]\(d_{xz}\)[/tex] is aligned along the [tex]\(xz\)[/tex]-plane and [tex]\(d_{yz}\)[/tex] is aligned along the [tex]\(yz\)[/tex]-plane, their overlap along the [tex]\(x\)[/tex]-axis would indeed result in zero overlap.
4. (P), (2), (ii):
- [tex]\(d_{yz}\)[/tex], [tex]\(p_x\)[/tex], and 2 lobe - 2 lobe overlap. Here, [tex]\(d_{yz}\)[/tex] has lobes in the [tex]\(yz\)[/tex]-plane and [tex]\(p_x\)[/tex] has lobes along the [tex]\(x\)[/tex]-axis, leading to a 2 lobe - 2 lobe overlap along the [tex]\(x\)[/tex]-axis.
Therefore, when the internuclear axis is the [tex]\(x\)[/tex]-axis, the combination that results in a [tex]\(d\)[/tex]-bond formation by ensuring a 2 lobe - 2 lobe overlap is:
(P), (2), (ii).
