We should have the capability to deal with a cluster with frozen atoms 1 frozen atoms: - no translational symmetry - reflection only through the frozen atom - rotation only around the frozen atom 2 frozen atoms: - rotational and reflection only around (through) the line between them 3 frozen atoms: - no rotational symmetry - reflection symmetry through the plane of the frozen atoms 4 or more frozen atoms: - no symmetry except permutational Of course if you have three atoms on a line then you have the symmetries of a 2 frozen atom system, etc. In particular this means: - rotation around points not at the origin, and around lines - reflection through points not at the origin, through lines, and through planes
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