Bent's Rule
Hybridization, s-Character & Molecular Geometry
1. What is Bent's Rule?
In advanced chemical bonding, simple hybridization often fails to explain the exact bond angles and lengths in unsymmetrical molecules (like $CH_2F_2$ or $PCl_3F_2$). Bent's rule refines this understanding.
Statement: "Atomic s-character concentrates in hybrid orbitals directed towards electropositive substituents, while p-character concentrates in orbitals directed towards electronegative substituents."
In simple terms:
- Electronegative atoms (like F) "pull" electrons away, so the central atom uses orbitals with less s-character (more p-character) to bond with them.
- Electropositive groups or Lone Pairs "stay closer" to the nucleus, so the central atom uses orbitals with more s-character.
2. Key Relationships
Understanding these relations is crucial for applying the rule:
$$ \% \text{ s-character} \propto \text{Bond Angle} $$
$$ \% \text{ s-character} \propto \text{Electronegativity of Orbital} $$
$$ \% \text{ s-character} \propto \frac{1}{\text{Bond Length}} $$
- More s-character: Orbitals are shorter, fatter, closer to nucleus (stronger attraction). Forms large bond angles (closer to $180^\circ$ for sp).
- More p-character: Orbitals are longer, thinner, directional. Forms small bond angles (closer to $90^\circ$ for pure p).
3. Applications & Examples
A. Trigonal Bipyramidal Geometry ($sp^3d$)
In $PCl_5$, there are two types of positions:
- Equatorial: $sp^2$ hybrid (33% s). Higher s-character. Shorter bonds.
- Axial: $pd$ hybrid (0% s in ideal model, or significantly less s). Lower s-character. Longer bonds.
Application 1: Lone Pairs
Lone pairs love s-character (to be close to nucleus). So, they always go to Equatorial positions (e.g., $SF_4, ClF_3$).
Lone pairs love s-character (to be close to nucleus). So, they always go to Equatorial positions (e.g., $SF_4, ClF_3$).
Application 2: Electronegative Atoms
Electronegative atoms (like F) prefer less s-character. So, they go to Axial positions.
Example: In $PCl_3F_2$, the two F atoms occupy the axial positions.
Electronegative atoms (like F) prefer less s-character. So, they go to Axial positions.
Example: In $PCl_3F_2$, the two F atoms occupy the axial positions.
B. Distorted Tetrahedral ($CH_2F_2$)
Comparing Bond Angles:
- C-F Bond: F is electronegative. C uses less s-character (more p). More p means angles closer to $90^\circ$. So, $\angle F-C-F < 109.5^\circ$.
- C-H Bond: H is electropositive. C uses more s-character. More s means angles closer to $120^\circ/180^\circ$. So, $\angle H-C-H > 109.5^\circ$.
Result: $\angle H-C-H > \angle F-C-F$.
Practice Quiz
Test your logic on Bent's Rule.
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