in the Born Oppenheimer Approximation, one expands the molecular wavefunction $\Psi(x,X)$ in terms of the electronic wavefunctions $\phi(x;X)$: $$\Psi(x,X)= \sum_k(c(X)_k\phi(x;X)_k)$$ ($x$ are the electronic coordinates and $X$ are the nucleonic coordinates)
Now, since the electronic wavefunctions are eigenstates of the electronic Hamiltonian, the constitute a complete basis of the electronic space. Thus any electronic wavefunction can be expanded in terms of the eigenfunctions. But, how can we be sure that any molecular wavefunction can be expanded in terms of the electronic wavefunctions? How can we be sure that the molecular Hilbert space is not larger than the space which is spanned by the eigenstates of the electronic Hamiltonian?