Chemistry Reference
In-Depth Information
Fig. 9.1 Schematic electronic structures for the MMX-chain compound in the limit
U !
0;
(a) averaged-valence (AV) state, (b) charge-polarization (CP) state, (c) charge-density-wave
(CDW) state, and (d) alternate charge-polarization (ACP) state [
31
]
system based on a dinuclear unit containing a metal-metal bond with a formal bond
order of one-half. Important features of MMX compounds are expected to arise
from the increase of the internal degrees of freedom resulting from the mixed-
valence state of the dinuclear unit. This property enables various electronic
structures, which are represented by the four extreme valence-ordered states as
shown in Fig.
9.1
[
31
].
The valence state, expressed as a -M
2+
-M
3+
-, represents an extreme case, which
is more accurately represented as -M
(2+
d
)+
-M
(3
d
)+
-or-M
(2.5
d
)+
-M
(2.5+
d
)+
-. The
value of
d
depends on the degree of orbital hybridization and lies between
the limiting cases of 0 and 0.5. These valence-ordered states are classified based
on the periodicity of the 1D chains as follows. The averaged valence (AV) and charge-
polarization (CP) states in which the periodicity of the 1D chain is -M-M-X-
correspond to a metallic state with an effective half-filled conduction band mainly
composed of M-M d
*-X p
z
hybridized orbitals or to a Mott-Hubbard semicon-
ducting state. In contrast, the periodicities of the 1D chains in the charge-density-
wave (CDW) and alternate charge-polarization (ACP) states are doubled. Except
for the averaged valence (AV) state, the valence-ordered states should undergo
lattice distortions due to valence alternation. The magnitude of the on-site Coulomb
repulsion
U
in MMX compounds is expected to be relatively small compared with
MX compounds due to the sharing of one unpaired electron through a metal-metal
bond. This facilitates valence delocalization and enhances valence fluctuation in the
mixed-valence state. Furthermore, an MMX-chain compound should have a strong
AF interaction arising from the superexchange interaction between the
S ΒΌ
s
1/
2 spins of the M
3+
ions through the large overlap of the metal d
z
2
and halogen p
z
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