Chemistry Reference
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Fig. 8.2 Definition of the
halogen displacements
q l
X -
lth M
As the last remark about this hamiltonian, we mention another type of e-l lattice
coupling that modifies the electron transfer. Such type of coupling appears very
typically in the model of polyacetylene [ 7 ], but it is missing here. The reason is that
our transfer term originates from a super transfer via the halogen p z orbital and that
the halogen displacement Q l only gives a second-order effect to it.
Next, we rewrite the hamiltonian slightly to make the following discussion more
transparent [ 1 ]:
H ePH2 ¼t 0 X
s¼";#
X
:ÞþU X
n l" n l# þ V X
N
1 ðC 1 s C ls þ
N
N
h.c
n l n 1
1
1
S X
N
1 ðq 1 q l Þn l þ
2 X
N
S
q l :
(8.2)
1
=K , and the
displacements are replaced by q l by the definition of Q l ¼ða = Þq l . Note that S
has the dimension of energy and that q l is dimensionless.
In the extended Peierls-Hubbard model, we neglect the contributions of the
other electron orbitals. Thus, as candidates of other models, it is very natural to
introduce such orbitals that may be located close to the corresponding d z 2 orbitals.
Based on the results of first-principles calculation, which we briefly summarize in
the next subsection, we know that the most important orbital to be added is the
halogen outermost p z orbital. In fact, as we have already mentioned, they play the
role of an “island” in the super transfer that we have already mentioned. Moreover,
this orbital is rather close to the Ni 3 d z 2 orbital and comes into the Hubbard gap of
the latter, as we will see in the forthcoming sections. For these reasons, we construct
the following dp model [ 8 , 9 ]:
Here,
the e-l coupling strength S is introduced by S a
2
X
X
X
tðlÞðC 1 s C ls þ
H dp ¼
h.c
:Þþ
eðlÞn l þ
U p n l" n l#
ls
l
odd
X
X
X
þ
U d n l" n l# þ
VðlÞn l n 1 þ
V pp n l n 2
even
l
odd
X
X
K l
2 Q l ;
þ
V dd n l n 2 þ
(8.3)
even
l
where C ls
and C ls are assigned to the orbitals of the metal and halogen sites with l
being even and odd, respectively. As for the other parameters, their meanings will
be almost self-explanatory in Fig. 8.3 and we reserve the details including actual
site-dependent expressions for later discussions.
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