Molecular Symmetry Analyzer

Determine molecular point groups, analyze symmetry operations, and understand character tables.

Molecule Analysis
Point Group Finder
Character Tables
Water
H₂O
C₂v
Ammonia
NH₃
C₃v
Methane
CH₄
Td
Benzene
C₆H₆
D₆h
CO₂
CO₂
D∞h
SF₆
SF₆
Oh
Boron Trifluoride
BF₃
D₃h
PCl₅
PCl₅
D₃h
Custom Molecule
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Custom

Use the flowchart below to determine the point group of your molecule:

Is the molecule linear?
No
Does the molecule have two or more Cₙ axes with n≥3?
No
What is the highest order rotation axis (Cₙ)?
C₂
Are there n C₂ axes perpendicular to the principal axis?
No
Is there a horizontal mirror plane (σh)?
No
Are there n vertical mirror planes (σv)?
Yes
C₂v
Determined Point Group
Analyzing Symmetry...

Understanding Molecular Symmetry

Molecular symmetry describes the spatial arrangement of atoms in a molecule and the operations that can be performed on the molecule without changing its appearance. Symmetry analysis is fundamental to understanding molecular properties, spectroscopy, and quantum chemistry.

Key Insight: The symmetry of a molecule determines its point group, which in turn dictates its vibrational modes, electronic transitions, and many other physical and chemical properties.

Symmetry Elements and Operations

1

Identity (E): The "do nothing" operation. Every molecule has this symmetry element.

2

Rotation Axis (Cₙ): An imaginary line about which rotation by 360°/n leaves the molecule unchanged.

3

Mirror Plane (σ): A plane that reflects the molecule onto itself. Can be horizontal (σh), vertical (σv), or dihedral (σd).

4

Inversion Center (i): A point through which all atoms are inverted (x,y,z → -x,-y,-z).

5

Improper Rotation Axis (Sₙ): A combination of rotation by 360°/n followed by reflection through a plane perpendicular to the rotation axis.

Common Point Groups

Point Group Symmetry Elements Example Molecules
C₁ E only CHFClBr
C₂v E, C₂, σv(xz), σv(yz) H₂O, SO₂
C₃v E, 2C₃, 3σv NH₃, CH₃Cl
C∞v E, C∞, ∞σv HCl, CO
D₃h E, 2C₃, 3C₂, σh, 2S₃, 3σv BF₃, PCl₅
D∞h E, C∞, ∞σv, i, S∞, ∞C₂ H₂, CO₂
Td E, 8C₃, 3C₂, 6S₄, 6σd CH₄, CCl₄
Oh E, 8C₃, 6C₂, 6C₄, 3C₂, i, 6S₄, 8S₆, 3σh, 6σd SF₆, [Fe(CN)₆]⁴⁻

Applications of Molecular Symmetry

Symmetry analysis is crucial in many areas of chemistry:

  • Vibrational Spectroscopy: Determines IR and Raman activity of molecular vibrations
  • Electronic Structure: Symmetry-adapted linear combinations (SALCs) for molecular orbitals
  • Crystallography: Space groups and crystal structures
  • Chemical Reactions: Selection rules and reaction pathways
  • Molecular Properties: Polarity, chirality, and optical activity

Chirality and Symmetry: A molecule is chiral (and therefore optically active) if it does not possess any improper rotation axis (Sₙ). This means chiral molecules cannot have a plane of symmetry (σ), center of inversion (i), or improper rotation axis (Sₙ).

Frequently Asked Questions

A symmetry element is a geometric entity (point, line, or plane) about which a symmetry operation is performed. A symmetry operation is the action of moving the molecule in such a way that its final orientation is indistinguishable from its original orientation. For example, a rotation axis (Cₙ) is the symmetry element, while rotation by 360°/n is the symmetry operation.

Use a systematic approach: 1) Check if the molecule is linear, 2) Look for high symmetry (multiple high-order rotation axes), 3) Identify the highest order rotation axis (principal axis), 4) Check for perpendicular C₂ axes, 5) Look for mirror planes (horizontal, vertical, dihedral), 6) Check for inversion center and improper rotation axes. Our point group finder tool implements this systematic approach.

A character table summarizes the symmetry properties of a point group. It lists the irreducible representations (symmetry species) and their characters (traces of transformation matrices) for each symmetry operation. Character tables are used to determine selection rules in spectroscopy, construct molecular orbitals, and analyze vibrational modes.

Symmetry determines which vibrational modes are IR-active (require a change in dipole moment) and which are Raman-active (require a change in polarizability). It also determines the symmetry of electronic transitions and their selection rules. Without symmetry analysis, interpretation of spectroscopic data would be much more difficult.

Yes. A molecule will have a permanent dipole moment if it belongs to one of the Cₙ or Cₙv point groups. A molecule is chiral (and optically active) if it does not possess any improper rotation axis (Sₙ), which includes planes of symmetry (σ) and centers of inversion (i).