  The symmetry operator $Q=Y^2$ is introduced to re-describe the Heisenberg
spin triangles in the \{V6\} molecule, where $\mathbf{Y}$ stands for the
Yangian operator which can be viewed as special form of Dzyaloshiky-Moriya (DM)
interaction for spin 1/2 systems. Suppose a parallelogram Heisenberg model that
is comprised of four 1/2-spins commutes with $Q$, which means that it possesses
Yangian symmetry, we show that the ground state of the Hamiltonian $H_4$ for
the model allows to take the total spin S=1 by choosing some suitable exchange
constants in $H_4$. In analogy to the molecular \{V6\} where the two triangles
interact through Yangian operator we then give the magnetization for the
theoretical molecule "\{V8\}" model which is comprised of two parallelograms.
Following the example of molecule \{V15\}, we give another theoretical molecule
model regarding the four 1/2-spins system with total spin S=1 and predict the
local moments to be 1/10u_B, 9/10u_B, 1/10u_B,9/10u_B respectively.
