Question

Which of the following linear combinations of atomic orbitals will lead to the formation of molecular orbitals in homonuclear diatomic molecules (internuclear axis in z-direction)?
(1) \( 2p_z \) and \( 2p_x \) 
(2) \( 2s \) and \( 2p_x \) 
(3) \( 3d_{xy} \) and \( 3d_{x^2-y^2} \) 
(4) \( 2s \) and \( 2p_z \) 
(5) \( 2p_z \) and \( 3d_{x^2-y^2} \) 
 

• A. E only
• B. A and B only
• C. D only
• D. C and D only

Hint:

When combining orbitals for molecular orbital formation along the internuclear axis, ensure that the orbitals have components along the axis. For the z-axis, \( 2p_z \) and \( 2s \) orbitals are suitable combinations.

Answer 1

The Correct Option is C

To identify linear combinations of atomic orbitals that form molecular orbitals in homonuclear diatomic molecules with the internuclear axis oriented along the z-direction, one must examine the symmetry and alignment of the atomic orbitals.

1. \( 2p_z \) and \( 2p_x \): Overlap is ineffective due to the \( 2p_z \) orbital's z-axis alignment and the \( 2p_x \) orbital's x-axis alignment. This combination is not possible.
2. \( 2s \) and \( 2p_x \): The spherically symmetric \( 2s \) orbital and the x-axis-aligned \( 2p_x \) orbital lack the necessary alignment for combination. This combination is not feasible.
3. \( 3d_{xy} \) and \( 3d_{x^2-y^2} \): Both these d-orbitals are situated in the xy-plane and their symmetry is incompatible with z-axis bonding in diatomic molecules. Consequently, they cannot form molecular orbitals.
4. \( 2s \) and \( 2p_z \): The \( 2s \) orbital's spherical symmetry and the \( 2p_z \) orbital's z-axis alignment facilitate effective combination, as the z-axis orientation is suitable for bonding in homonuclear diatomic molecules. This combination will form molecular orbitals.
5. \( 2p_z \) and \( 3d_{x^2-y^2} \): The \( 2p_z \) orbital is z-directed, while the \( 3d_{x^2-y^2} \) orbital lies in the xy-plane, rendering it unsuitable for forming molecular orbitals along the z-axis. This combination is not possible.

Therefore, only the combination of \( 2s \) and \( 2p_z \) results in molecular orbital formation under the specified conditions, making "D only" the correct selection.