Self-assembled Transition Metal Coordination Frameworks of ...

Chapter 3
= -2J1{§, -3*, +.§, -$1,} -2.12{.§*, -s, +3‘, -s4} -2J3{§, -s, +§, -$4} (1)
For compounds 1 to 4 J3 is assumed to be zero, because there is no cross­
coupling connection, and it is reasonable to assume that J = J1 = J2 by the
approximation of similar M—X-M angles within each square grid. Assuming all the
four Ni(H)—X—Ni(Il) couplings are equal, i.e. using a single coupling constant J that
takes into account all the exchange pathways to be equal (Scheme 3.2), is a reasonable
assumption in the light of the X-ray crystallographic study of la which reveals a
similar nature of M—S—M angles (~l67°), there is probably a super exchange
mechanism through the intervening sulfur atoms. Therefore, for a square arrangement
of four metal centers, D4,, [2 >< 2] grid, eqn. (l) reduces to eqn. (2) [26],
131 =-2J(.§, -s, +$, -s, +§, -$4 +5‘, -$4) (2)
s1
J1
J2 s2 s1 J s2
J3 \/_> J1 J J
I
S4 I J2 $3 S4 J S3
Scheme 3.2. Magnetic exchange models, showing the general case (left) and
approximation used for 1 to 4 (right). _
Here, the values of the spin angular momentum operator 3‘, (i = 1- 4) are
the same, and using the conventional spin-vector coupling model [52,53] the
corresponding eigenvalues can be obtained analytically and are given by eqn. (3) [51],
E(S',S,3,S24) = —J[S'(S'+l)—S,3(S,3 +l)—S24 (S24 +l)] (3)
where 5'“ = 3', +.§3; $'24 = 6'2 +.§4; 5" = .§'l +5‘, +.§3 +.§'4. For Ni(lI) molecular
squares S l , S 2 , S3 , S 4 = 1. There are nineteen spin states as given below.
............................................................................................................................. .:......................_...,...........................,...........................:.....................
S‘ 5 i s l4%3%2%1%0l i 2 E 3 E ; 5s
114
No.ofspinstates 1 3 6 6 3