 Solution

A symmetry orbital is a molecular orbital when it is also an eigenfunction of the effective one-electron Hamiltonian operator. If an irreducible representation occurs once in a complete invariant model space, a symmetry-invariant Hamiltonian acts as a scalar on that copy by Schur's lemma. Its basis functions are then degenerate eigenfunctions. When the same symmetry occurs in several copies, those copies can mix; one must diagonalize the corresponding block. Merely having a one-dimensional symmetry label is insufficient if other orbitals have that same label.