Most organic chemistry deals with closed shell calculations, but every once in a while you want to calculate carbenes, free radicals or radical transition states coming from a homolytic bond break, which means your structure is now open shell. Closed shell systems are characterized by having doubly occupied molecular orbitals, that is to say the calculation is ‘restricted’: Two electrons with opposite spin occupy the same orbital.
Joaquin Barroso (Tue,) studied this question.