Chemistry Reference
In-Depth Information
Fig. 12.2 Extended
Peierls-Hubbard model for
MMX compounds
t
MXM
-
α
(
y
b,i
+y
a,i+1
)
t
MM
V
MXM
V
M
M
V
2
MM
X
MM
X
y
b,i
y
a,i+1
U
M
d
z2
X
-
β
y
a,i
K
MX
K
MXM
t
MXM
, is assumed to be linearly modified by the length change
y
b
,
i
+
y
a
,
i
+1
with
coefficient
. The energy level of the M d
z
2
orbital is assumed to depend linearly on
the change in the MX bond length with coefficient
a
. The repulsion strengths are
denoted by
U
M
for the on-site pair of electrons with opposite spins,
V
MM
for the
nearest-neighbor pairs within the unit,
V
MXM
for the nearest-neighbor pairs
accompanied with an X site in-between, and
V
2
for the next-nearest-neighbor
pairs. They are not assumed to depend on the positions of the X ions for simplicity.
The elastic constants are denoted by
K
MX
for the MX bond length and
K
MXM
for the
distance between the neighboring binuclear MM units. The latter constant is needed
when counterions hinder the MM units from being displaced.
Here, the periodic boundary condition is imposed. The electronic ground state is
determined by the exact diagonalization method except for the photoinduced
dynamics in the last part. The lattice displacements
y
a
and
y
b
are treated as classical
variables and determined in a self-consistent manner with the electronic ground
state, unless otherwise stated, so that the system is in the lowest energy configura-
tion, except for the photoinduced dynamics in the last part.
b
12.3 Kinetic Versus Interaction Terms
Electronic phases of R
4
[Pt
2
(pop)
4
I]
n
H
2
O[R
¼
Na, K, NH
4
, (CH
3
(CH
2
)
7
)
2
NH
2
,
P
2
O
5
H
2
2
] are suggested to be classified according to the distance
between the nearest-neighbor M ions accompanied with an X ion in-between,
d
MXM
[
7
]. In order to study the effects of changing
d
MXM
, we first obtain ground-
state phase diagrams by varying
t
MXM
. Considering these pop systems containing
charged MMX chains and counterions, we set
K
MXM
to be infinitely large,
prohibiting displacements of M ions and allowing displacements of X ions only.
The site-off-diagonal electron-lattice coupling
etc., pop
¼
is then irrelevant. As a conse-
quence, the ACP phase is not realized here. In addition, leaving detailed studies of
a
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