An explicit implication of symmetry on the molecular structure can be shown in case of the simplest bi-nuclear system: a hydrogen molecule ion or a di-hydrogen cation, H 2 + . A natural trial wave function for the H 2 + is determined by first considering the lowest-energy state of the system when the two protons are widely separated. Then there are clearly two possible states: the electron is attached either to one of the protons, forming a hydrogen atom in the ground state, or the electron is attached to the other proton, again in the ground state of a hydrogen atom (as depicted in the picture).