  We study the correlation function and concurrence for the eigenstates with
zero spin of engineered Heisenberg models to explore the entanglement property.
It is shown that the total nearest neighbor (NN) correlation function of
zero-spin eigenstates reaches its local extremum when the coupling strength is
uniform, and correspondingly the groundstate entanglement of $d$-D cubic AF
Heisenberg model is locally maximized. Moreover, numerical calculations for a
$N$-site quantum spin ring with cosinusoidally modulated exchange coupling,
i.e. $J_i=J(1+\cos(2\pi i/N))$, indicate that the uniform coupling is not the
unique optimal distribution for maximizing the groundstate entanglement and
this modulation of interactions can induce the longer range entanglement.
