Concept

Site symmetry — where it appears

The subgroup of a molecule's operations that leave one particular atom where it is. It constrains what that atom's own orbitals can do, and the symmetry-adapted combinations a reduction produces are built by projecting from one atom onto its whole orbit.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

phosphorus pentafluoride — D3h. The molecule with the point group found from its coordinates rather than looked up: every candidate operation was applied and kept when it permuted the atoms among themselves.

Site symmetry, and what it constrains

A molecule's group is not the only group in the problem. Each atom sits at a position with a symmetry of its own, and what that local group permits decides how many kinds of environment a structure really has.

symmetry · Representation

phosphorus pentafluoride: 3 environments. The atoms of phosphorus pentafluoride sorted into orbits under its own symmetry group — two atoms are in the same orbit when an operation of the group carries one onto the other, which makes them indistinguishable by any measurement. There are 2 of F, 1 of P, and a spectrum that resolves environments counts those rather than atoms.

A spectrum counts environments, not atoms

Phosphorus pentafluoride has five fluorines in two inequivalent sets, so its magnetic resonance spectrum should show two signals. It shows one — and the reason is not a symmetry the molecule has but a motion faster than the measurement.

spectra · Spectrum

Named alongside it

The objects these essays reach for when they reach for this one.

Group order Orbit (group theory)Point group Stabiliser (group theory)Character table Coordination number Degeneracy Equivalent atoms Local symmetry Selection rules Symmetry operation VSEPR

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