QiLing Tools

🔷Point Group Finder - Molecular Symmetry Elements, 3D Model, Flowchart & Character Tables

A molecule's point group is the set of its symmetry operations: proper rotations Cn, mirror planes σ, the inversion centre i and improper rotations Sn. This tool detects the elements numerically from 3D coordinates. It moves the atoms to the centre of mass, then tests C2–C8, S3–S12 and mirror planes along candidate directions — principal axes of inertia, atom directions, and the midpoints, differences and normals of atom pairs — requiring every atom to land on an atom of the same element within an adjustable tolerance. The point group is then assigned with the standard Schoenflies flowchart, and every decision is shown: linear or not, several high-order axes, any Cn, how many perpendicular C2 axes, σh, how many vertical planes, an S2n axis. Single-centre molecules can be typed as formulas and are built from ideal VSEPR geometry, mixed ligands included: H₂O is C2v, NH₃ C3v, CH₄ Td, SF₆ Oh, XeF₄ D4h, BrF₅ C4v, SF₄ and ClF₃ C2v, CH₂Cl₂ C2v, CHCl₃ C3v and PCl₃F₂ D3h. Multi-centre presets include H₂O₂ (C2), ethene (D2h), benzene (D6h), staggered and eclipsed ethane (D3d / D3h), trans- and cis-N₂F₂ (C2h / C2v), allene (D2d), chair cyclohexane (D3d), diborane, CO₂ (D∞h) and HCN (C∞v), and you can paste your own XYZ coordinates. A rotatable 3D model draws the axes (labelled C2, C3…), translucent mirror planes and the inversion centre, and can look straight down the principal or any selected axis. The tool also gives the group order, whether the molecule can be polar (only C1, Cs, Cn and Cnv) and whether it is chiral (no improper rotation), plus character tables for C1, Cs, Ci, C2, C2v, C3v, C4v, C2h, D2h, D3h, D4h, D6h, D2d, D3d, Td, Oh, C∞v and D∞h with linear and quadratic function columns, all checked with the orthogonality relations.

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How to use Point Group Finder

  1. 1Type a single-centre formula (SF4, CH2Cl2…), pick a multi-centre preset, or paste XYZ coordinates
  2. 2Read the point group, order, polarity and chirality, and follow the flowchart decisions
  3. 3Rotate the 3D model, click an element to highlight it or view down an axis, and check the character table below

FAQ

How do you determine the point group of a molecule?
Follow the flowchart. Linear molecules are D∞h if they have an inversion centre, otherwise C∞v. Two or more axes with n ≥ 3 mean a cubic or icosahedral group (Td, Oh, Ih…). Otherwise take the highest-order axis Cn as principal. With n perpendicular C2 axes the group is Dnh (σh), Dnd (n σd) or Dn; without them it is Cnh (σh), Cnv (n σv), S2n (collinear S2n) or Cn. With no axis at all it is Cs (mirror), Ci (inversion centre) or C1.
What are the point groups of SF₄, ClF₃ and XeF₄?
SF₄ is seesaw-shaped with one C2 axis and two mirror planes containing it, so it is C2v. T-shaped ClF₃ is also C2v. Square-planar XeF₄ has a C4 principal axis, four perpendicular C2 axes, σh and an inversion centre, so it is D4h. The tool builds these from VSEPR geometry and detects each element.
How does the point group tell you whether a molecule is polar or chiral?
A dipole moment must be unchanged by every symmetry operation, so only molecules in C1, Cs, Cn and Cnv (including C∞v) can be polar — H₂O (C2v) and NH₃ (C3v) are, CO₂ (D∞h) and CH₄ (Td) are not. A molecule is chiral exactly when it has no improper rotation Sn (including a mirror, S1, and an inversion centre, S2), so its group is C1, Cn, Dn, T, O or I — for example CHFClBr (C1) and H₂O₂ (C2).
How do I read a character table?
Column heads are classes of operations (in C3v: E, 2C3, 3σv — the number is how many operations the class contains). Each row is an irreducible representation (A and B one-dimensional, E two-, T three-dimensional) and the entries are its characters. The linear column shows how x, y, z and the rotations Rx, Ry, Rz transform, which gives IR activity; the quadratic column relates to Raman activity and d-orbital symmetry.

Features

  • Numerical detection of Cn, Sn, σ and i from 3D coordinates with adjustable tolerance
  • Point group assignment by the Schoenflies flowchart with every decision shown
  • Single-centre geometries from VSEPR, including mixed ligands
  • Over a dozen multi-centre presets plus XYZ input
  • Rotatable 3D model with axes, mirror planes and inversion centre; view down any axis
  • Automatic polarity (dipole moment) and chirality verdicts
  • Character tables for 18 common point groups with linear/rotation and quadratic columns