Point-group filtering in unitary coupled-cluster ansätze: exact criticality under the Abelian filter, freeness measured near equilibrium under the full group

Filtering a unitary coupled-cluster ansatz by molecular point-group symmetry has no settled variational cost for groups with degenerate irreducible representations. We prove that the symmetry-adapted subvariety of the amplitude space is a critical subvariety of the energy, for irreducible representa