elements of symmetry for 6 marks
Asking for Preferences
Elements of Symmetry in Chemistry (Crystallography/Molecular Symmetry)
Symmetry elements are geometrical entities (points, lines, or planes) with respect to which one or more symmetry operations can be performed.
1. Plane of Symmetry (σ) — Mirror Plane
A plane of symmetry (also called a mirror plane) divides a molecule into two halves that are mirror images of each other.
- σh (horizontal) — perpendicular to the principal axis
- σv (vertical) — contains the principal axis
- σd (dihedral) — bisects the angle between two C₂ axes
Example: H₂O has 2 planes of symmetry; BF₃ has 4 planes.
2. Centre of Symmetry (i) — Inversion Centre
A centre of inversion is a point in the molecule such that any atom moved through it lands on an identical atom on the other side (i.e., for every atom at (x, y, z), there is an identical atom at (−x, −y, −z)).
- Symmetry operation: inversion (i)
- Example: SF₆, centrosymmetric molecules like trans-1,2-dichloroethylene; benzene has an inversion centre.
3. Axis of Symmetry (Cₙ) — Proper Rotation Axis
A rotation axis Cₙ is a line about which rotation by (360°/n) brings the molecule into an indistinguishable configuration.
| Axis | Rotation angle | Example |
|---|---|---|
| C₂ | 180° | H₂O |
| C₃ | 120° | NH₃ |
| C₄ | 90° | XeF₄ |
| C₆ | 60° | Benzene |
The axis with the highest n is the principal axis (Cₙ).
4. Alternating Axis of Symmetry (Sₙ) — Improper Rotation Axis
An improper rotation axis Sₙ involves a rotation by (360°/n) followed by reflection through a plane perpendicular to that axis.
- S₁ = σ (mirror plane)
- S₂ = i (inversion centre)
- Example: Allene (C₃H₄) has an S₄ axis; CH₄ has three S₄ axes.
5. Identity Element (E)
The identity element leaves the molecule unchanged. Every molecule has it. It is included to satisfy group theory requirements (closure, inverse element).
- Corresponds to rotation by 360° (C₁).
- Symbol: E (from German Einheit, "unity")
Summary Table
| Symmetry Element | Symbol | Operation Performed |
|---|---|---|
| Identity | E | No change |
| Proper rotation axis | Cₙ | Rotation by 360°/n |
| Mirror plane | σ | Reflection |
| Inversion centre | i | Inversion through a point |
| Improper rotation axis | Sₙ | Rotation + Reflection |
Key Points for Exam
- Symmetry elements are the geometric entity; symmetry operations are the actions performed with respect to them.
- The total set of symmetry elements of a molecule defines its point group (e.g., C₂ᵥ, Td, Oh).
- Chiral molecules lack σ, i, and Sₙ elements — this is why they are optically active.
- The more symmetry elements a molecule has, the higher its symmetry (e.g., octahedral SF₆ belongs to Oₕ with 48 symmetry operations).
this question is from organic chem
Elements of Symmetry in Organic Chemistry
In organic chemistry, symmetry elements are used to determine stereoisomerism — specifically whether a molecule is chiral or achiral, and to identify meso compounds.
1. Plane of Symmetry (σ) — Mirror Plane
A plane of symmetry divides a molecule into two halves that are non-superimposable mirror images of each other within the same molecule.
- If a molecule has a plane of symmetry → it is achiral (optically inactive)
- Example: meso-tartaric acid has an internal mirror plane despite having two chiral centres → it is achiral
COOH COOH
| |
H—C—OH ←σ→ HO—C—H
| |
H—C—OH HO—C—H
| |
COOH COOH
meso-tartaric acid: top half is the mirror of bottom half
2. Centre of Symmetry (i) — Inversion Centre
A centre of symmetry is a point in the molecule such that every atom has an identical atom at an equal distance on the opposite side.
- Molecule with centre of symmetry → achiral
- Example: meso-2,3-dibromobutane (in its extended conformation) possesses a centre of symmetry
3. Axis of Symmetry (Cₙ) — Alternating Axis
Also called the alternating axis of symmetry or axis of improper rotation (Sₙ) — rotation by 360°/n followed by reflection gives an indistinguishable structure.
- Presence of S₁ (= σ) or S₂ (= i) → molecule is achiral
- A molecule lacking all Sₙ axes (including σ and i) is chiral
Key Rule in Organic Chemistry
| Symmetry Element Present | Chirality |
|---|---|
| Plane of symmetry (σ) | Achiral |
| Centre of symmetry (i) | Achiral |
| Alternating axis (Sₙ) | Achiral |
| None of the above | Chiral |
Application: Identifying Meso Compounds
A meso compound has:
- Two or more stereocentres
- An internal plane of symmetry (most commonly) or centre of symmetry
- Result: optically inactive despite having chiral centres
Example: meso-tartaric acid, meso-2,3-dibromobutane
Axis of Symmetry (Cₙ) — Simple Rotation
A simple rotation axis alone does not make a molecule achiral. A molecule can have a Cₙ axis and still be chiral (e.g., a helicene or BINAP).
⚠️ Only improper axes (Sₙ), which include σ and i as special cases, are the true test for achirality.
Summary for 6 Marks
- Plane of symmetry (σ) — most important; molecule is achiral if present
- Centre of symmetry (i) — less common; molecule is achiral if present
- Alternating axis of symmetry (Sₙ) — rotation + reflection; achiral if present
- Absence of all above → molecule is chiral and shows optical activity
- Meso compounds — have stereocentres but are achiral due to internal symmetry plane
- Cₙ axis alone does not determine chirality — only Sₙ axes matter
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