JEE Main 2025 Jan 24 Shift 1, Chemistry Q5: Molecular Orbital Theory

A productive LCAO requires non-zero net overlap and matching symmetry about the internuclear axis (here, the z-axis).

Two orbitals with different symmetry about the bond axis give equal positive and negative overlap regions that cancel, producing zero net overlap.

Check each pair (z is the bond axis):

A. $2p_z$ (cylindrically symmetric about z) with $2p_x$ (one lobe above, one below the bond axis) $\Rightarrow$ overlap cancels. No MO.

B. $2s$ (spherical) with $2p_x$ (antisymmetric about the bond axis) $\Rightarrow$ cancels. No MO.

C. $3d_{xy}$ and $3d_{x^2-y^2}$ have different symmetries with respect to rotation about z $\Rightarrow$ zero net overlap. No MO.

D. $2s$ and $2p_z$ are both cylindrically symmetric about z; they overlap end-on to give a valid $\sigma$ MO. $✓$

E. $2p_z$ has $\sigma$ symmetry about z, while $3d_{x^2-y^2}$ has $\delta$-type symmetry $\Rightarrow$ no net overlap. No MO.

Only D works. $\therefore$ Option (3).