Second, we construct simplified space tables [Eq. (18)] by systematically moving one electron from any one fragment to any other fragment up to r times in all possible ways, where r is a non-negative integer chosen by the user. For each increment or decrement of , the corresponding local spin S (K) can (in general) either increase or decrease by 1 2 . A schematic for this is presented in Table .2. Rootspace depiction