However, as reactions do not take place between disjointed molecular orbitals, but electronic states, the final analysis involves state correlation diagrams. A state correlation diagram correlates the overall symmetry of electronic states in the starting material and product. The ground state of 1,3-butadiene, as shown above, has 2 electrons in Ψ1 and 2 electrons in Ψ2, so it is represented as Ψ12Ψ22. The overall symmetry of the state is the product of the symmetries of each filled orbital with multiplicity for doubly populated orbitals. Thus, as Ψ1 is asymmetric with respect to the C2 axis, and Ψ2 is symmetric, the total state is represented by A2S2. To see why this particular product is mathematically overall S, that S can be represented as (+1) and A as (−1). This derives from the fact that signs of the lobes of the p-orbitals are multiplied by (+1) if they are symmetric with respect to a symmetry transformation (i.e. unaltered) and multiplied by (−1) if they are antisymmetric with respect to a symmetry transformation (i.e. inverted). Thus A2S2=(−1)2(+1)2=+1=S. The first excited state (ES-1) is formed from promoting an electron from the HOMO to the LUMO, and thus is represented as Ψ12Ψ2Ψ3. As Ψ1is A, Ψ2 is S, and Ψ3 is A, the symmetry of this state is given by A2SA=A.