  An open problem in applied mathematics is to predict interesting molecules
which are realistic targets for chemical synthesis. In this paper, we use a
spin Hamiltonian-type model to predict molecular magnets (MMs) with magnetic
moments that are intrinsically robust under random shape deformations to the
molecule. Using the concept of convergence in probability, we show that for MMs
in which all spin centers lie in-plane and all spin center interactions are
ferromagnetic, the total spin of the molecule is a `weak topological invariant'
when the number of spin centers is sufficiently large. By weak topological
invariant, we mean that the total spin of the molecule only depends upon the
arrangement of spin centers in the molecule, and is unlikely to change under
shape deformations to the molecule. Our calculations show that only between 20
and 50 spin centers are necessary for the total spin of these MMs to be a weak
topological invariant. The robustness effect is particularly enhanced for 2D
ferromagnetic MMs that possess a small number of spin rings in the structure.
