This paper uses the theory of creation and destruction operators to give a new simpler proof of the well-known pairing relation between electronic states of alternant hydrocarbon positive and negative ions. The method is like one that Heisenberg used to explain why the atomic spectra of elements such as C (with two electrons in the 2pshell), and O (with two holes) are so similar. It depends on the analogy between electrons in an orbital ψ and holes in the paired antibonding orbital ψ′ of the π-electron shell. A modified pairing relation holds also in a magnetic field. Applications of the operators to other problems are suggested.