Which of the following linear combination of atomic orbitals will lead to formation of molecular orbitals in homonuclear diatomic molecules [internuclear axis in z-direction] ? A. \(2 \mathrm{p}_{\mathrm{z}}\) and \(2 \mathrm{p}_{\mathrm{x}}\) B. 2 s and \(2 \mathrm{p}_{\mathrm{x}}\) C. \(3 \mathrm{~d}_{\mathrm{xy}}\) and \(3 \mathrm{~d}_{\mathrm{x}^{2}-\mathrm{y}^{2}}\) D. 2 s and \(2 \mathrm{p}_{\mathrm{z}}\) E. \(2 p_{z}\) and \(3 d_{x^{2}-y^{2}}\)

Chemical Bonding and Molecular Structure — JEE Main · 2025 · 24 Jan 2025 · Shift 1 Question with Solution

Which of the following linear combination of atomic orbitals will lead to formation of molecular orbitals in homonuclear diatomic molecules [internuclear axis in z-direction] ?
A.

2 p_{z}

and

2 p_{x}

B. 2 s and

2 p_{x}

3 d_{xy}

and

3 d_{x^{2} - y^{2}}

D. 2 s and

2 p_{z}

2 p_{z}

and

3 d_{x^{2} - y^{2}}

(A)E Only
(B)A and B Only
(C)D Only✓ Correct
(D)C and D Only

Answer: (C)

Solution

Two atomic orbitals combine into molecular orbitals in a homonuclear diatomic only when they have comparable energy and the same symmetry with respect to the internuclear axis (taken as z), so that their net overlap integral is non-zero.

A.

2 p_{z}

has

σ

symmetry along z while

2 p_{x}

has

π

symmetry — the symmetry mismatch gives zero net overlap — no bonding.

B. 2s has

σ

symmetry,

2 p_{x}

has

π

symmetry — again mismatched, no net overlap.

C.

3 d_{x y}

and

3 d_{x^{2} - y^{2}}

are the two components of the same

δ

-symmetric pair but differ in phase orientation relative to the internuclear axis, so their net overlap integral vanishes by symmetry — no bonding.

D. 2s and

2 p_{z}

both have

σ

symmetry about the internuclear axis with comparable energy in light homonuclear diatomics, so they overlap effectively end-on and mix (the s–p mixing responsible for the reordering of the

σ_{2 p}

and

π_{2 p}

levels seen from

L i_{2}

through

N_{2}

) — bonding occurs.

E.

2 p_{z}

(n = 2) and

3 d_{x^{2} - y^{2}}

(n = 3) differ too much in energy, and in symmetry (

σ

δ

), for effective overlap — no bonding.

Only combination D, 2s with

2 p_{z}

, leads to molecular orbital formation.

JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Single correct option

JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Chemical Bonding and Molecular Structure

Solution

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