Question

How many of the following combination(s) of the orbitals can form a $\pi$-bond, if the internuclear axis is z-axis.

$p_x + p_x$

$d_{xy} + d_{xy}$

$p_z + p_z$

$p_x + p_y$

$s + p_x$

$p_y + p_y$

$d_{yz} + d_{yz}$

$p_y + d_{yz}$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (D)

4

Answer 2

A $\pi$-bond is formed by the lateral (sideways) overlap of atomic orbitals. For effective sideways overlap, the overlapping orbitals must have the correct symmetry with respect to the internuclear axis. When the internuclear axis is the z-axis, a $\pi$-bond is formed by the overlap of orbitals that have a nodal plane containing the z-axis.

Let's analyze each combination:

1. $p_x + p_x$: The $p_x$ orbital has a nodal plane (yz-plane) that contains the z-axis. The lateral overlap of two $p_x$ orbitals along the z-axis results in electron density concentrated above and below the z-axis, with the yz-plane as a nodal plane. This forms a $\pi$-bond.
2. $d_{xy} + d_{xy}$: The $d_{xy}$ orbital has two nodal planes (xz-plane and yz-plane) that contain the z-axis. The lateral overlap of two $d_{xy}$ orbitals along the z-axis results in a $\delta$-bond, which has two nodal planes containing the internuclear axis. This does not form a $\pi$-bond.
3. $p_z + p_z$: The $p_z$ orbital is oriented along the z-axis. The overlap of two $p_z$ orbitals along the z-axis is a head-on overlap, which forms a $\sigma$-bond.
4. $p_x + p_y$: The $p_x$ orbital is along the x-axis and the $p_y$ orbital is along the y-axis. When the internuclear axis is the z-axis, these orbitals are perpendicular to each other and cannot overlap effectively to form a bond. Orbitals must have the same symmetry with respect to the internuclear axis to form a bond. $p_x$ and $p_y$ have $\pi$ symmetry with respect to the z-axis, but they are orthogonal.
5. $s + p_x$: The $s$ orbital is spherical and has $\sigma$ symmetry with respect to any axis. The $p_x$ orbital has $\pi$ symmetry with respect to the z-axis. Orbitals with different symmetries ($\sigma$ and $\pi$) cannot overlap to form a bond.
6. $p_y + p_y$: The $p_y$ orbital has a nodal plane (xz-plane) that contains the z-axis. The lateral overlap of two $p_y$ orbitals along the z-axis results in a $\pi$-bond, with the xz-plane as a nodal plane.
7. $d_{yz} + d_{yz}$: The $d_{yz}$ orbital has one nodal plane (xz-plane) that contains the z-axis (the other nodal plane is the xy-plane, which is perpendicular to the z-axis). The lateral overlap of two $d_{yz}$ orbitals along the z-axis results in a $\pi$-bond, with the xz-plane as a nodal plane.
8. $p_y + d_{yz}$: The $p_y$ orbital has $\pi$ symmetry with respect to the z-axis (nodal plane xz). The $d_{yz}$ orbital also has $\pi$ symmetry with respect to the z-axis (nodal plane xz). Orbitals with the same symmetry can overlap. The overlap between $p_y$ and $d_{yz}$ along the z-axis occurs in the yz plane, above and below the z-axis, forming a $\pi$-bond.

The combinations that can form a $\pi$-bond when the internuclear axis is the z-axis are:

• $p_x + p_x$
• $p_y + p_y$
• $d_{yz} + d_{yz}$
• $p_y + d_{yz}$

There are 4 such combinations.