For the formation of a $\pi$-bond, the orbitals involved must have the correct symmetry and orientation to allow for effective sideways overlapping. The lobes of the orbitals must be parallel to each other and perpendicular to the internuclear axis.

Why Option (B) is correct:

In option (B), we have the sideways overlapping of a $d_{x^2-y^2}$ orbital and a $p_y$ orbital. The $d_{x^2-y^2}$ orbital has its lobes lying along the x and y axes. The $p_y$ orbital has its lobes along the y-axis. When these orbitals attempt to overlap sideways, their symmetries do not match effectively for $\pi$-bond formation. The positive lobe of one orbital might overlap with the positive lobe of the other, but simultaneously, the positive lobe of one might overlap with the negative lobe of the other, leading to zero net overlap (destructive interference).

Option Analysis:

• A) $p_x+p_x$ sideways overlapping: This is a classic example of $\pi$-bond formation. Both $p_x$ orbitals have the same symmetry and can overlap effectively sideways along the x-axis (assuming the internuclear axis is the z-axis or y-axis).
• B) $d_{x^2-y^2}+p_y$ sideways overlapping: As explained above, these orbitals have incompatible symmetries for effective $\pi$-bond formation due to the nodal planes and orientation of their lobes.
• C) $d_{xy}+d_{xy}$ sideways overlapping: Both $d_{xy}$ orbitals have the same symmetry. Their lobes lie between the x and y axes. They can undergo effective sideways overlap to form a $\pi$-bond (or even a $\delta$-bond if aligned appropriately, but $\pi$-bond is possible).
• D) $d_{yz}+p_y$ sideways overlapping: The $d_{yz}$ orbital has lobes between the y and z axes, and the $p_y$ orbital has lobes along the y-axis. These orbitals can have effective sideways overlap to form a $\pi$-bond, especially if the internuclear axis is along the x-axis.

Correct Answer: (B)