Final answer:
The parity of the number of nodes in the HOMO and LUMO must be the same for cycloaddition to occur.
Step-by-step explanation:
In order for cycloaddition to occur, the number of nodes in the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) must have the same parity. This means that both the HOMO and LUMO must either have an even number of nodes or an odd number of nodes.
For example, if the HOMO has an even number of nodes, then the LUMO must also have an even number of nodes for cycloaddition to occur.
This requirement arises from the symmetry properties of molecular orbitals and is necessary for the orbital overlap required for the cycloaddition reaction.