LCAO Method, MO diagrams of diatomics, VSEPR theory (geometries / Bent's Rule)

LCAO, MO Diagrams of Diatomics, VSEPR Theory & Bent's Rule

1. LCAO method (Linear Combination of Atomic Orbitals)

Molecular orbitals are formed by adding/subtracting atomic orbitals:

• Bonding MO ($\psi_A + \psi_B$): electron density piles up between nuclei → lower energy, stabilizes bond.
• Antibonding MO ($\psi_A - \psi_B$, marked *): node between nuclei → higher energy, destabilizes.
• Rules: combining AOs must have (a) similar energy, (b) same symmetry about molecular axis, (c) good overlap.

For 2p orbitals this gives $\sigma_{2p}$ (head-on overlap), $\pi_{2p}$ (sideways overlap), and their antibonding partners $\sigma^\*_{2p}$, $\pi^\*_{2p}$.

2. MO diagrams of homonuclear diatomics

Filling order for heavier elements (O₂, F₂): $\sigma_{2s} < \sigma^\*_{2s} < \sigma_{2p} < \pi_{2p} < \pi^\*_{2p} < \sigma^\*_{2p}$. For lighter elements (Li₂ to N₂), s–p mixing swaps order: $\pi_{2p}$ fills before $\sigma_{2p}$.

Bond order $= \frac{1}{2}(N_b - N_a)$ where $N_b$ = bonding electrons, $N_a$ = antibonding.

Molecule	Config (valence)	Bond order	Magnetism
N₂ (14 e⁻)	$(\pi_{2p})^4(\sigma_{2p})^2$	3	diamagnetic
O₂ (16 e⁻)	$(\pi_{2p})^4(\pi^\*_{2p})^2$	2	paramagnetic (2 unpaired — MOT's famous success; VBT fails here)
F₂	+ $(\sigma_{2p})^2(\pi^\*_{2p})^4$	1	diamagnetic
CO, NO (heteronuclear)	skewed diagram (O more electronegative → its AOs lower)	CO: 3, NO: 2.5	NO paramagnetic

Higher bond order → shorter bond, higher dissociation energy.

3. VSEPR theory (shapes from electron domains)

Count steric number = bond pairs + lone pairs; lone pairs repel most (lp–lp > lp–bp > bp–bp).

Steric no.	Arrangement	Example (lone pairs) → shape
2	linear	BeCl₂ (0) linear; —
3	trigonal planar	BF₃ (0) planar; NH₃-like analogue SO₂ (1) bent; H₂O-like analogue —
4	tetrahedral	CH₄ (0); NH₃ (1) pyramidal; H₂O (2) bent 104.5°
5	trigonal bipyramidal	PCl₅ (0); SF₄ (1) see-saw; ClF₃ (2) T-shaped; XeF₂ (3) linear
6	octahedral	SF₆ (0); BrF₅ (1) square pyramidal; XeF₄ (2) square planar

4. Bent's rule

Atomic s-character concentrates in orbitals toward electropositive substituents; p-character toward electronegative ones.

• CH₃F: C–F bond has more p-character (F electronegative) → F–C–H angle < 109.5°.
• H₂O vs H₂S: O more electronegative lone-pair demand gives H–O–H 104.5° but H–S–H ~92° (almost pure p-bonding on S).
• PCl₅ vs PF₅ axial/equatorial differences explained by apicophilicity (electronegative F prefers axial, low s-character sites).

Exam Points

• Draw MO diagram of N₂ vs O₂ and explain O₂ paramagnetism (5 marks — most asked).
• Bond-order/magnetism numericals for B₂, C₂, O₂⁺, O₂⁻, NO (3 marks).
• VSEPR shapes of NH₃, H₂O, SF₄, ClF₃, XeF₄ + statement of Bent's rule with one example (5 marks).