The generalized (G)MBE of Richard and Herbert 1-4 extends the simple MBE of Eq. ( ) to handle overlapping fragments, meaning those that may share some atoms in common. Many other fragmentation schemes can be viewed as special cases of (or approximations to) the GMBE, 1-3 recovering the conventional MBE in Eq. ( ) when the fragments are disjoint. The fragments used in the present work will be disjoint (specifically, single H 2 O molecules in water clusters), yet the set-theoretical formulation of the GMBE is still useful.