Ch4: Predicting Molecular Geometry

Greenhouse Gases, Heat Capture & Molecular Structure

• Previous lecture takeaway:
  • Green-house gases (CO$2$, H$2$O, CH$4$, N$2$O, etc.) absorb IR radiation
    → vibrational excitation
    → higher average kinetic energy
    → higher temperature.
  • N$2$ and O$2$ do not absorb IR despite being the most abundant gases.
  • Key difference lies in molecular structure, symmetry, electronegativity differences and therefore molecular polarity.
  • Current goal: Relate structure (geometry + electron distribution) to the ability to interact with IR radiation.

Electron Domains & Fundamental Shapes

• Electron Domain (ED) = any region around a central atom where electrons are located.
• A single bond, a double bond, a triple bond or a lone pair each count as one domain.
• Count domains only around the central atom (denoted A).
• Five ideal (electron-domain) geometries:
  • 2 domains
    → Linear | $180^\circ$ bond angle
  • 3 domains
    → Trigonal planar | $120^\circ$
  • 4 domains
    → Tetrahedral | $109.5^\circ$
  • 5 domains
    → Trigonal bipyramidal | $90^\circ/120^\circ$ (axial/equatorial)
  • 6 domains
    → Octahedral | $90^\circ$

Bonding vs Non-Bonding Domains

• Bonding domain = shared pair(s) in a bond (shown as a line in a Lewis diagram).
• Non-bonding domain (lone pair) = unshared electrons on the central atom.
• Lone pairs still count toward the ED geometry but distort the observed molecular shape because:
  • Lone pair–bond pair repulsion > bond pair–bond pair repulsion.
  • Result: Observed (molecular) geometry can differ from the ED geometry when $E \neq 0$.
  • Ex: NH$_3$ → 4 domains ⇒ ED geometry = tetrahedral, but 1 lone pair ⇒ observed shape = trigonal pyramidal.

VSEPR Theory (Valence Shell Electron Pair Repulsion)

• Qualitative rule: Electron pairs arrange themselves to minimise repulsion → maximise mutual distance.
• Gives the idealised geometries listed above.
• Deviations (bond angles slightly < ideal) arise when lone pairs or multiple bonds are present.

VSEPR Notation (AXE or ABE)

• Standard symbols used in the course:
  • A = central atom count (usually 1, written as A).
  • B (or X) = number of terminal atoms bonded to A.
  • E = number of lone pairs on A.
• Example (water):
  • Lewis: H–O–H with 2 lone pairs on O.
  • Notation: $\text{A} \text{B}2 \text{E}2$ (often written AX$2$E$2$).
  • Lookup in VSEPR table → ED geometry = tetrahedral; molecular shape = bent / angular.

Master Table: From Notation to Shape

Worked Examples from Class

1. Ammonia, NH$3$

• Lewis: N with 3 H bonds + 1 lone pair.
• Notation: $\text{A}\text{B}3\text{E}1$
• ED geometry: tetrahedral.
• Molecular shape: trigonal pyramidal.
• IR activity: polar molecule → strong dipole; can absorb IR.

2. Water, H$2$O

• Notation already derived: $\text{AB}2\text{E}2$.
• ED geometry: tetrahedral.
• Molecular shape: bent; bond angle $\sim 104.5^\circ$ (compressed from $109.5^\circ$ by 2 lone pairs).

3. Carbon Dioxide, CO$2$

• Lewis: O=C=O, no lone pairs on C.
• Notation: $\text{AB}2$.
• ED geometry = molecular shape = linear.
• Non-polar → IR active only via asymmetric stretch.

4. Formaldehyde, CH$2$O

• Central carbon with 3 regions (2 C–H, 1 C=O counted as 1 domain), 0 lone pairs.
• Notation: $\text{AB}3$.
• Shape: trigonal planar.

5. Phosphoric Acid fragment (PF$4$ example used)

• Central P bonded to 4 F, 0 lone pairs.
• Notation: $\text{AB}4$.
• Shape: tetrahedral.

6. Ethylene, C$2$H$4$

• Two central atoms (C and C) → treat each separately.
• Around each C: 3 domains (2 C–H + 1 C=C) → $\text{AB}3$.
• Geometry at each C: trigonal planar.
• Overall molecule planar; each C carries its own geometry.

Step-by-Step Procedure (Algorithm)

1. Draw complete Lewis structure.
2. Identify the central atom(s).
3. For each central atom:
   • Count bonding domains (single, double, triple all = 1).
   • Count lone pairs.
4. Build AXE (or ABE) notation.
5. Use VSEPR table to find:
   • Electron-domain geometry (ideal, determined solely by total domains).
   • Molecular geometry (observed, depends on $E$).
6. Quote ideal bond angles, then adjust qualitatively:
   • Lone pair present → angle < ideal.
   • Multiple lone pairs → even smaller.
7. Relate geometry to molecular polarity and potential IR activity.

Practical / Philosophical Implications

• Geometry ↔ polarity ↔ ability to absorb IR → climate science relevance.
• Understanding VSEPR equips chemists to predict reactivity, solubility, phase behaviour.
• Ethical: Accurate structural prediction crucial for designing less harmful molecules (e.g., refrigerants with low global warming potential).

Numerical & Symbolic Reminders

• Ideal angles to memorise: $180^\circ$ (linear), $120^\circ$ (trigonal planar), $109.5^\circ$ (tetrahedral), $90^\circ/120^\circ$ (TBP), $90^\circ$ (octahedral).
• Lone-pair compression rule: $\theta<em>{\text{observed}}$ < $\theta</em>{\text{ideal}}$.

Study Tips

• Re-draw each example without looking at notes; derive AXE, then self-check.
• Build or view 3-D models (ball-and-stick or software) for octahedral & TBP shapes.
• Quiz yourself: given AB$3$E$2$, what is shape? (T-shaped) Why? (3 bonding + 2 lone pairs in TBP arrangement.)
• Link to prior chapter: Ensure comfort with Lewis structures—formal charges,