Elements of Symmetry

Elements of Symmetry are geometric features like planes, axes, or centers that describe balance and repetition in a molecule’s structure.

• An element of symmetry is a feature (like a plane, point, or axis) that describes how a molecule can be transformed into an indistinguishable configuration.
• A molecule is achiral if it has any element of symmetry.

There are three primary types:

1. Plane of Symmetry (σ)

   • Also called a mirror plane
   • An imaginary plane that divides the molecule into two identical mirror-image halves
   • If present, the molecule is achiral
   • Example:
     • In meso-tartaric acid, a vertical mirror plane passes through the molecule, dividing it into two symmetric halves.

2. Center of Symmetry (i)

   • Also called a center of inversion
   • A point in the molecule such that:
     • For any atom, an identical atom exists directly opposite at an equal distance
   • Molecules with a center of symmetry are achiral
   • Example:
     • Benzene has a center of symmetry in the middle of the ring.

3. Axis of Symmetry (Cn)

   • An imaginary axis around which the molecule can be rotated by 360°/n, and it looks the same
   • For example, a C2 axis means the molecule looks the same after a 180° rotation
   • Note:
     • The presence of an axis alone does not confirm chirality or achirality, but in combination with other elements, it helps identify symmetry.

Relevance to Optical Activity:

• A molecule that possesses a plane of symmetry or a center of symmetry is typically achiral and thus not optically active.
• No plane of symmetry, no center of symmetry, no improper rotation axis (S_n​) → likely to be chiral.

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