Self-assembled Transition Metal Coordination Frameworks of ...

Copper(II) complexes
When two or more paramagnetic metal ions are present in the same molecular
entity, the magnetic properties can be totally different from the sum of the magnetic
properties of each ion surrounded by its nearest neighbors. These new properties
depend on the nature and magnitude of the interaction between the metal ions through
the bridging ligands [46]. The model often used to describe the magnetic behaviour of
metal ions in isolated dimers is provided by the isotropic Heisenberg exchange
Hamiltonian, suggested originally by Heisenberg, Dirac and van Vleck [47]
1§r=-2J5‘, -$2 (1)
= -./(s" -$3 - §;>
The two metal ions interact through several intervening ligands and the
exchange interaction .1 is given by the summation over the two centers of the dimeric
molecule. These interactions lead to new quantum numbers (S '= |S, +S2|,
|S, + S2 —l , [S1 — S2|) and corresponding molecular states, a spin singlet S '= O
and a spin triplet S '= l for isolated dicopper(II) complexes. The corresponding eigen
values of eqn. (1) will be
E(S') = —.][(S'(S'+l) — S|(S| +1) — S2 (S2 + 1)]
The gap between the singlet and triplet states of dicopper(Il) compounds will
then be 2.] and for an antiferromagnetic interaction singlet state and for a
ferromagnetic interaction triplet state will be the ground state. The model often used
to describe the magnetic behaviour of isolated dicopper(H) complexes is provided by
modified Bleaney-Bowers equation [48] (derived from eqn. (1)),
N2,B2 1 -2.1 " N2,62p
Z/t4=€k?w—|Il+§€XP(?):I (1"P)+'€T+Na’ (2)
179