Fragmentation is a ubiquitous general idea in computational chemistry; the goal is represent a molecule and properties as the union of smaller fragments. In one approach the total energy of molecule is given by the energy of fragements. We have used the fragmentation concept to extend PIPs in two different ways. We review the more powerful and recent approach first. The second, older approach is just briefly mention as it has some features in common with "aPIPs" which we describe in detail in the next section.