Self-assembled Transition Metal Coordination Frameworks of ...

Chapter 5
To fit and interpret the magnetic susceptibility data of complexes, first it is
necessary to find all possible magnetic pathways in the structures. The complexes,
except 20, are expected to be molecular square grids, as would be expected, as in the
case of Ni(II) square grids discussed in Chapter 3. So the Mn(II) compounds 19, 21,
22 and 23 are modeled, with a single coupling constant J that takes into account all
exchange pathways to be equal, by considering the appropriate Heisenberg exchange
Hamiltonian for D4,, [2 >< 2] grid as,
Ii! = —2J($‘, -5*‘, +§, -S‘, +.§, -§4 +.§, -.524) (1)
The corresponding eigenvalues are then obtained using the conventional spin­
vector coupling model [44] and are given [45] by,
E(S',S|3,S24) = 2J[S'(S'+1) — SB (SB +1) — S24 (S24 + 1)] (2)
For Mn(II) molecular squares S I , S 2 , S 3 , S 4 = 52- . There are 146 spin states as
given
E P : 2 I . I :
below,
- : _ y : 1 5 1 : E > 1 V . \ I Y 1 ' , _ g , E : 2 E . : 1 s '-
51
, I|
'2
: - ­'
'
,
:
..........................................................................................
E I
.,_, .........................
I
..) ...................
E
., ......................... .._,
:
......................... ., E......................... .7 ........................ ..r ......................... ., ......................... .,_, ............................................... .1 ..................... .5
Punuuuuuuunuu,H"“""_"""""uuuuuunnnnnuunnnnunuu..“"""".“H“_""..nHn"""“nnx“~ ".H""““n"..""""""""“n“";HU“"“""“"““"n¢“"“““n“n"nm_ “““n_“n“n"“"“;_“nnuuunuunu..________"_"_
§No.ofspinstates§ 1 1 4 6 10 15 21 24 24
=“H.h,H."H.“d“""""““"”“"n"..h"Hu“““"““"u"““nn"n """“““_""__"".""""""“H".L"uh"""""“"n“."“"""""“"“uu“;Hnnnnnhnnnm".“"""""""“_““ ........_....._....-....l-u-.-..............._... A..........................4..-...-.....-....-.-S...".........-.......¢
The allowed values are then substituted in to the modified van Vleck equation,
N 2 2 Zs" s'+1 2s'+1 *”“'>”" N 2 2s s+1
ZM Z fig ( )( _E()§W (1_p)+ fig ( )/>+m,
3k(T-6)) Z(2s+1)e 3kT
(4)
The procedure of generating the exchange equation for such large systems
presents a somewhat daunting task in the case of Mn(II) (S = 5/2) and so we used
MAGMUN4.l [46] software package for calculation of the spin state energy spectrum
for a cluster, and substitution into the van Vleck equation. Then, fitting of variable
temperature magnetic data were done to an exchange expression, eqn. (4), using the
same program MAGMUN4.l.
220