Crystal Structures and Properties of MMX-Chain Compounds Based on Dithiocarboxylato-Bridged Dinuclear Complexes - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 188

4 t 2
U

J ¼

j t U ¼ n 1

2

DE X denote the total energy and the total spin angular momentum
for the spin state X (X

S

where E X and

¼

broken symmetry low spin (LS) state ( S ¼

0) and high

spin (HS) state ( S ¼ 1), respectively). The equation for J values corrects a spin

contamination error in LS state. And n is an occupation number of the highest
occupied natural orbital, which is a magnetic orbital calculated by UB3LYP
method [ 43 ]. From DFT results and above equations, the estimated parameters
are J ¼ 975 cm 1 , n ¼ 0.226 eV, respectively. A

result of the similar calculation using UBH and HLYP method with a tetra-MM
units model also estimated U ¼

1.268, U ¼ 1.68 eV, and t ¼

1.03 eV and t ¼ 0.116 eV [ 42 ]. Assuming the

bandwidth W ¼ 4 t is valid since the 1D Ni MMX system is 1D strong electron

correlated system, 4 t is 0.904 eV (0.464 eV for the tetramer model). Accordingly,
band energy gap, E g ~ U 4 t is 0.776 eV (0.566 eV for the tetramer model). On

the assumption that the energy difference between the di-MM and tetra-MM
models approximates error limits, the E g is 570-780 meV, which is consistent
with the E opt observed for 7-10. Therefore, the intense absorption band observed
near 650-670 meV has been attributed to the transition from the LH d s * band to

UH d s * band.

9.3.5 Electrical Conductivity

Yamashita et al. have reported that the single crystals of [Ni 2 (MeCS 2 ) 4 I] 1 (7)show
semiconducting behavior with a small activation energy E a of 100-250 meV and a
relatively high conductivity at RT of 10 2 Scm 1 s RT ¼ 2.5 [ 29 ]. Temperature

dependences of the electrical conductivity Et (8), n -Pr (9),

n -Bu (10)) are shown in Fig. 9.36 [ 38 ]. The electrical conductivity of 8-10 are
1.6

s of [Ni 2 (RCS 2 ) 4 I] 1 (R ¼

10 4
Scm 1 at 287 K, respectively, which are oneortwoorderofmagnitudesmaller
than that of 7. The compounds 8-10 show typical semiconducting behavior in the
temperature range measured and the activation energy E a of 8-10 estimated from the
Arrhenius equation, a plot of ln

10 3 Scm 1 10 4 Scm 1

at 290 K, 7.6 at 290 K, and 6.0

vs. T 1 , are 198(1), 143(3), and 339(2) meV,
respectively. These values are relatively close to that of 7 [ 29 ]. 10 satisfies the
relationship of 2 E a ¼ E opt ,where E a is an activation energy estimated by the electrical
conductivity and E opt is the optical band gap, whereas the relationship of 2 E a ¼ E opt
does not hold for 8 and 9. This is presumably attributable to a decrease in the E a by
impurity existing in the sample.

s