A valence-bond approach to the electronic localization in
3/4 filled systems
A. Fritsch, L. Ducasse
To cite this version:
A. Fritsch, L. Ducasse. A valence-bond approach to the electronic localization in 3/4 filled systems. Journal de Physique I, EDP Sciences, 1991, 1 (6), pp.855-880. <10.1051/jp1:1991173>.
<jpa-00246374>
HAL Id: jpa-00246374
https://hal.archives-ouvertes.fr/jpa-00246374
Submitted on 1 Jan 1991
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
J.
Phys.
(1991)
Ii
855-880
1991,
JUIN
855
PAGE
Classification
Physics
Abstracts
31.20R
71.28
71,10
approach
valence-bond
A
filled
systenls
A.
(*) and
Fritsch
Laboratoire
electronic
localization
in
3/4
Ducasse
L.
Thdorique (**),
Physico-Chimie
de
the
to
Universitb
Bordeaux1,
de
33405
Cedex,
Talence
France
(Received 21
Nous
Rkswnk.
propribtds
tir6es
et
de
V~ (second
voisin)
l'expbrience.
Une
anion), dbcoule
d'un premier
tandis
que
la
h
d'une
et
calculs
forte
mbthode
Diagrammatic
Valence
btb
du
type
paramdtres de
des
menb
et
[es
corrblation
valeurs
possible
cristallographiques
et
et
des
un
de
mesures
calcul
de
intersites
V
DUB
de
densitd
de
liaison.
:
des
par
~premier
comparbes aux donn6es
organique, Xcomposbs
conductivitb
: [es
molbcule
semi-conducteur
comportement
L'effet
du
les
btd
ont
btb
ont
M2X (M
sels
essai
U,
exactes
I 300 K
s'ernpilent de manidre rkgulidre ou quasi-r6gul16re,
groupe
localisation
blectronique est modifi6e
100-200K.
Dans
entre
conduisent
I une
fondamental
localisb
description de l'btat
lout
onde
dim6ris6e
structure
une
Un
analyser
pour
solutions
[es
intrasite
obtenues
des
(DUB)
Bond
(lD), dont
(btendu).
Hubbard
1991)
March
I
monodimensionnels
classification
deuxidme
300K
les
a
structures
ont
d'un
ceux
mdtalliques
premier cas,
tenures
des
groupe
accepted
clusters
semi-empiriques
SCF
February1991,
hamiltonien
d'un
moyen
au
mbthodes
de
28
revised
utilisb
avons
dlectroniques
obtenues
voisin)
1990,
November
tenure
second
entre
sont
Ie
en
voisins
qu'il puisse modifier les corrdlations de charge I longue distance ainsi que
magn6tique. Los susceptibilitds magnbtiques x calculbes sun un cycle de 8 sites
comportement
l'expbrience I 300 K et c'est pour V~ voisin de V/2 que la dbpendance de
bon
accord
sont
en
avec
tempbrature
reproduite de fagon la plus satisfaisante.
la
Dans le second cas, des calculs
est
x avec
moddles
tendent I
dim6risation
dlectronique pourrait dtre modifi6e par le
ab initio
montrer
quo la
inter-dim6res
potentiel des anions.
modification
des intdgrales de
transfert
intra- et
rend
Une
rdsistivitd
fonction
tempdrature. Los
qualitativement de la variation
de la
de
la
compte
en
V~
le
demeure
rdsultats
faible
DUB
augmentation
rdgulier
cas
bien
des
sun
de la
anneaux
localisation
observd
h
haute
de
12 sites
lorsque les
tempdrature.
montrent
corrdlations
quo
sont
diffdrence
cette
prises
en
compte,
entraine
en
une
comparaison
nette
du
The
Diagrammatic
Valence
Bond (DUB)
method
has been used to investigate the
properties of
one-dimensionnal
(lD) clusters, for which exact
solutions
obtained
were
within the
framework
Hubbard
hamiltonian.
of an (extended)
The
correlation
U, V
parameters,
and V2 are tentatively
calculated
by means of SCF semi-empirical
methods
and compared to the
data issued from experiment.
From the crystal
and the conductivity data, the M2X salts
structures
Absbact.
electronic
(*)
(**)
Present
URA
address
CNRS
:
503.
Theoretical
Chemistry
Department,
University
of Bristol,
BS81Ts
Bristol,
U-K-
856
JOURNAL
(M
organic
:
with
a
with
a
molecule,
dimerized
regular
which
quasi-regular
or
electronic
in the
anion)
X-
structure
may
be
stacking
ID
classified
in
semi-conductor
are
around
localization
PHYSIQUE
DE
100-200
which
K.
two
at
are
For
M 6
I
groups :
300 K and,
metallic
the
first
at
hand, the compounds
hand, the systems
on
one
on
another
exhibit
which
300 K and
class, the
calculations
DUB
a
change
lead
to
a
picture for the localized ground state. The effect of the next
nearest
neighbor V~ is small although it may affect long distance charge
correlations
and the magnetic
behavior.
The magnetic susceptibility x
calculations
ring lead to a good agreement
on
a 8 sites
and the
with 300 K experimental
data
dependence of x is best reproduced with
temperature
electronic
dimerization
might be
V2 close to V/2. For the second class, it is shown that, the
indicated by model ab initio
modified by the anion potential, as
calculations.
behavior
of the
The
resistivity as a function of temperature is qualitatively
described
by a change in the intra and
interdimer
transfer
integrals. The DUB results on 12 sites rings indicate that this difference leads
localization
the
enhanced
when
correlations
tumed
compared to the high
to
are
on
an
regular system.
temperature
strong
bond
order
wave
Inwoducfion.
superconductivity
in
the
Bechgaard
salts
TMTSF~X
of experimental
amount
; X- : anion) [I], a large
theoretical
work has been
devoted to this family of organic
and
conductors
[2]. However, the
small
number
of organic salts
exhibiting this property, the fact that the
maximum
critical
exceed
11 K, and
the quite
noteworthy
discovery of the high
temperature
not
T~ does
Since
discovery
the
(TMTSF
=
T~ oxides,
have
(BEDTTTF
of
organic
tetramethyltetraselenafulvalene
=
cooled
the
to
contrary
the
to
TMTSF
and
BEDTTTF
salts, the low T superconductivity
apin the
so-called
defined
salts [3], which
show a well
twoK
properties recalling the high 7~ oxides. Moreover, for the first
been quite recently
has
discovered
in
based
salts
some
on
results
have
revived
the
interest
of the
[4]. These exciting
quite «
common
dimensional
packing and some
superconductivity
time, the
molecules
containing
oxygen
materials.
scientific
community for these
dimensionality of these systems
The
Concerning the superconductivity, it is
pears
But,
enthusiasm.
initial
bisethylenedithio-tetrathiafulvalene)
be
for a large
important to note
TMTSF~X [6], p [5] and
properties.
(2D)
increases in the series :
phases
of
the
salts
character
M~X
K [3, 7]
metallic regime competes
(M : organic molecule). In the last two cases, the low temperature
only with the superconducting state. However, an antiferromagnetic
might coexist with
state
superconducting state although no clear experimental evidence
the
supports this assumption
mechanism, microscopic
of
[3]. The superconductivity and its origin (BCS or not-BCS
nature
electron-electron
repulsion) is not the single property to which has been
the screening of the
devoted a large
literature
in the past few years.
The phase diagram of the lD or quasi- ID
salts, represented by the Bechgaard salts TMTSF~X [6] and their sulfur analogs TMTTF~X
tetramethyltetrathiafulvalene)
(antifer(TMTTF=
complicated :
insulator
[8], is
more
spin-Peierls,
magnetic,
metal
superconducting
romagnetic, AF
SP),
have
been
states
non
or
observed.
the
ordering of
anions
modify
Moreover,
non-centrosyrnrnetrical
the
may
distributions
electronic
an
AF
The
one
[9]. For example,
~pressure in the
difficulty in
a
govems
case
theoretical
of
a physical
TMTTF~PF~ [10]
analysis of these
their
electronic
that
the
two-dimensional
constraint
makes
a
SP
state
evolve
to
into
TMDTDSF~PF~ [I I]).
salts lies on
their
complex microscopic
unit
partial
filling
of the
cell,
one-electron
per
anion and the
cation,...) and on the possible
(one, two or
large molecules
more
resulting from the transfer
between
the
various
(kinetic part
interplay
between
terms
electron-phonon coupling, disorder of the anion,
structure
band
part
of
temperature
the
for
hamiltonian,
). Therefore,
it is
interaction,
Coulomb
a
challenge
to
single
out
M 6
APPROACH
VALENCE-BOND
3/4
OF
FILLED
857
SYSTEMS
controlling the behavior of these salts, as it is equally difficult to
relevant
parameters
determination
of
provide a Very accurate
calculation
of their
electronic
An ab initio
structure.
of the ground and
the
organic
is
wavefunctions
of
conductors
the energies and
excited
states
untractable.
description, at a more empirical level,
virtually
Moreover, a unified
theoretical
of the
behavior
of every organic salt is even
still lacking.
correlations
Among the factors which might influence the physical properties, the electronic
leading
(see
be
certainly
for
is
noteworthy
that
the
example
[2]).
It
to
term
appear
a
oneelectron
approach might lead to wrong
for such properties as the symmetries of the
results
excited
in longer polyenes [12], the negative spin
radicals [13] or
lower
densities
in
states
the
excitations
transition
transpolyacetylene
[14],
energies in organic
ion-radicals
metal
or
limitation
is given by the band
complexes [15]. Another example of the
one-electron
model
the M2X salts. This approach leads to a metallic
results
behavior
for every kind
structure
on
formula Ml X~, although the conductivity
of salt based on the unit
show that
measurements
localization [8], without any
the
TMTTF
salts undergo a progressive
structural
distortion, and
dimethylethylenedithio-tetrathiafulvalene)
localized
DIMET2SbF6
(DIMET
is already
at
[16].
temperature
room
The
effects
of the
electron-electron
correlations
have
been
investigated using different
models.
The g-ology models [17, 18], derived in the weak coupling limit where the
theoretical
correlation
considered
perturbation of the
one-electron
formalism, have been
terms
as a
are
applied to the study of the phase transitions, the
and the
localization
NMR
processes
opposite limit of strong coupling, the
relaxation
times.
In the
Hubbard
hamiltonian
is
equivalent to a Heisenberg spin model. This model is currently used to fit the variation of the
magnetic susceptibility of localized
for example in
done
systems with the
temperature,
as
reference [19]. Besides
approaches emphasizing the role of the infinite solid and thus
these
requiring perturbative or group
renormalization
techniques,
methods
have been
local
more
=
developed
in
finite
The
size.
which
attempt
an
difficulty
represents
investigated,
in
combination
applied
to
find
these
difficult
limit
Hubbard
the
task.
The
infinite
of
theory
correlated
states
in
and
a
solid-state
models
clusters
for
of
extrapolation to the solid,
spin-1/2 chains
have
been
Carlo
model [20], and by a
in the
of
Monte
quantum
numerical
Bond
Hubbard
mainly
properties
lies
critical
U, by
extended
or
approaches
local
techniques
Diagrammatic
Valence
of field
variational
the
a
the
solve
to
of
solution
on
finite
chains
(DVB) method [22] has been
models.
and
quantum-chemical
which requires
extrapolation
set
[21]. Recently,
derived
and
(severe)
procedures if
approach gives
The
complete basis
physics, but the DVB results are exact and this
convenient
representation of the
wavefunction.
The applications of the DVB
method
a
very
have been
made in
various
fields as the study of the polyenes [22],
non-linear
optic results
and magnetic properties of the complete family of segregated-stack
[23], electronic
charge
transfer
salts [24],
restriction
lies in the
analyzing
is
one
This
the
size
solid
of the
state
first
recalls
the
paper
two-electron
terms
characteristics
of
the
formalism.
DVB
Then,
the
taking place in an extended
Hubbard
model
are
derived
from the experiments are compared to the values
data
issued from the
approach (transfer integrals), or derived
from
semi-empirical
quantum
dimers.
Finally, the analysis of the organic salts which present
monomers
or
either at
100 K
temperature
at a
temperature,
T~, typically between
room
or
given from thb results
obtained
in the
of lD
clusters.
case
one-
and
values
discussed
band
of
the
:
the
structure
calculations
a
on
localization,
and
200 K, is
Method.
The
DVB
electronic
formalism
applies to
configurations of N~
model
electrons
systems
on
with
N sites
(N~
3
=
per site. A complete
N/2 for this 3/4 filled case)
orbital
one
set
of
is built
858
JOURNAL
following
PHYSIQUE
DE
M 6
I
S~ and
procedure
which
generates
configuration
thus
defined
is
from
the
S~
spin-coupling
of
site
together
with
the
of
the
The
electrons.
of
only
occupancy
every
use
one
orbital per site allows us to draw simple diagrams to symbolize each
configuration.
Crosses
and dots stand for doubly occupied and empty sites respectively. Two singly occupied sites are
by a line in the case of a singlet spin coupling between the corresponding
connected
electrons.
quantized
formalism,
diagram
the
second
each
VB
is
easily
obtained
by
applying
In
to the
the
upon
up
site
eigenfunctions
empty
the
state
orbitals
[25]. A
valence
combination
proper
the
bond
Rumer
electronic
of the
creation
associated
operators
with
the
orbital
basis
limited by the size of the
[22]. As the VB basis is complete, the method is computationally
is
built
of18
electrons
sites
of the singlet space is
cluster : the larger studied
12
(size
system
on
complete
of
the
diagonalization
the
matrix
is
feasible
and
15 730). In this
not
case,
an
relaxation
has been used to
determine
the lowest eigenvalues and
algorithm of
coordinate
eigenvectors [26].
orbitals
orthogonal. This point
It is important to note that, within this method, the site
are
is fully justified by the value of the overlap
first neighbor sites in the organic salts
between
under
study. This represents an
intermolecular
overlap which is only around 10-2, in the
actually
negligible.
intradimer
and
case,
include in the
calculation
We do not
electron-phonon or
electron-molecular
vibration
any
coupling term. Some models emphasize the importance of such terms : analysis of the Raman
of the organic
and
infrared
mechanism
superconductivity
based on the
spectra [27], possible
coupling of the electrons with the molecular
Vibration [28]. On the
contrary, the leading role
of the correlation, in particular in the organic and high T~ oxides
superconductivity, has been
well argumented by
Mazumdar
and
Ramasesha
[29] and we follow this proposal in this study
of
localization.
the
electronic
The
H~
Hamiltonian
is
a
of
sum
and
one
a
a
two
electron
parts,
Hi
and
:
H=Ht+H~=Ht+H~+H~
where
and
Hi
includes
crystal
the
effects
kinetic
the
(organic
core
in H~
well
as
anions) in H~
and
the
as
interactions
between
the
electrons
:
-/£t~~~j((n,n+I)+
H~
(1)
+(n+I,n))
(2)
=
N
I
~
i
i
£
Z
O,
~ii
~(«
(~)
~ia
fl
Expression (2)
that the
calculation
only involves the nearest-neighbor
transfer
assumes
integrals t~,~~ j. The tj~ integrals include the components of the crystal potential so that it is
convenient
write
to
N
~ii
£~I ~
"
£
~pi ~p
~
~ext
(~)
p#i
a~ is
where
and
the
(anions
We
this
core
in
have
the
site
of the
the
organic
retained
formalism,
energy,
V~~
is the
site p, z~ is the
the
H~ may
interaction
effective
charge
potential
of site p
between
and
the
electron
ll~~~ is the
on
extemal
the
site I
potential
conductors).
extended
be
written
Hubbard
as
a
method
sum
of
to
two
evaluate
terms
the
Hu and
correlation
Hv.
terms.
Within
M
VALENCE-BOND
6
APPROACH
=
3/4
SYSTEMS
FILLED
859
N
~
Hu
OF
(5)
~j n~(n~ -1)
2
1
~
Hv
£ £
=
i j
(6)
V~j n~ nj
i
of Hv distinguishes
of electrons
site I. The
evaluation
between
the
the
number
on
Hubbard (the Hv Values are given a priori), and
Pariser-Parr(Hv
0), extended
calculated)
models.
The
neglect of the tri- and
Pople (P.P.P.) [30] (the Hv values
are
tetracentric
results
from
zero-differential
overlap (ZDO)
integrals in these
formalisms
the
approximation.
However, it may be noted that this approximation is well adapted to the study
neighbor 2 p~ atomic
orbitals is
of polyenes, where the
calculated
overlap between two
nearest
where
n~ is
Hubbard
=
conductors,
above, the overlap
organic
noted
as
compared to the transfer integral. Thus, there
is no real need to invoke the ZDO
approximation. In particular, this model might include the
three and four
integrals without lack of consistency.
center
wavefunctions
orthogonal VB diagrams (k) :
The
(1l~) are expanded on the non
large.
indeed
between
On
the
in
contrary,
orbitals
molecular
two
1l~)
is
jj
=
the
small
rather
k)
c~(
represented by
the
(7)
C
vector
k
Using
completeness
the
H is
hamiltonian
of
obtained
the
basis,
VB
H(k)
This
does
method
problem
not
representation
matrix
convenient
a
of
h
the
from
require
jj hj~(j)
=
evaluation
the
of the
(8)
overlap
matrix
leads
and
to
the
secular
:
hC
(9)
EC.
=
Note
Although
:
wavefunction
generally
of
the
this
analyzed
is
involve
diagonalization
through the
overlaps.
the
procedure
large systems,
For
which
overlap
the
of
values
mean
will
represent
(see below).
representation of the
harniltonian
(8),
modify the site occupation,
diagonal,
not
are
if the sites
strictly equivalent, H~ acting on
are
the
do
particular,
matrix
H~(k)
this
term
k)
different
the
this
require
not
of the
the
which
operators
some
consuming part
time
the
matrix,
calculation
Within
and
does
calculation
be
may
lead
will
to
a
N~.
contribution
same
easily
omitted
in
different
a~
for
N~.
=
the
matrix.
interaction
every
t~~
(k),
the
H~, Hu and Hv
components,
extradiagonal.
In
H~ is
while
a
VB
diagram
(k) gives
:
(k)
If the
sites
with
the
lattice
which
is
taken
have
only
as
the
different
the
site
reference
neighborings,
energy will give
energy.
Model.
In
the
quasi
electrostatic
magnitude
Concerning
because
the
lD
salts,
potential.
smaller
the
exact
the
than
interchain
interactions
interchain
The
calculated
the
intrachain
electrostatic
anisotropy
of
the
ones
terms,
through the transfer integral or the
integrals are
around
of
order
an
and
be
conveniently
neglected
[6].
may
decisive
conclusion
is not simple to establish,
difficult
is
For
example, if one
to
assert.
may
interchain
a
potential
act
transfer
JOURNAL
860
considers
is not
between
easy,
However,
of
intuitively
is
interaction
(6)
situation
the
situation
an
which
chain.
each
on
But
evaluation
the
below, and the importance of such
effective
«
localization
charges
shown
as
approach appears to be
primarily the conductivity
affects
@
©fi
©5
x
x
@
x
@
x
I.
Two
VB
on
one
sites
the
diagrams
6
built
may
in
V~y
not be
equation
ruled
out.
progressive
stacking axis.
for the
along the
ix
M
x
m)
(a)
of
terms
account
to
measured
©5
x
of the
interactions
sufficient
lD
»
z
Fig.
M
I
interacting chains represented in figure I, the more
favorable
by the diagram a, which corresponds to a minimization
of the
two
described
the
PHYSIQUE
DE
on
diagram (b) is
chains
2
deduced
from
(a) by shifting
the
charges
chain.
conditions
Cyclic boundary
assumed in our
calculations
that the sites are all
to
are
ensure
anion potentials give the
and
equivalent : the organic cores
contribution
to
same
every
omitted.
diagram and are
As in the
usual
band
calculation
molecule
is
[2, 31, 32], each
replaced by its highest occupied molecular
orbital
(HOMO) providing 3 conducting
electrons
formalism.
HOMO is not explicitly given within the DVB
per two sites (dimer). Note that this
multiplicity of the 12 electrons
The
evaluation
of each
8 sites
system is used for the
on
and the singlet ground state of the 18 electrons
magnetic susceptibility
calculation
12 sites
on
allows a better analysis of the
electron
distribution.
cluster
of-the chain
dimerization
To discuss the possible implications
the
electronic
properties,
on
transfer
integrals, tsi and ts~, sketched in figure 2, have been used. The Sl and 52
two
notation
for the first neighbors V~j
interactions.
The next
neighbor
is also
retained
nearest
is denoted V~. As a convention, the dimer
the pair of sites leading to the largest
represents
V~~
transfer
integral tsj.
tS2> VS2
~Sl, VS1
r
r
o
2p
2p-1
Within
and
a
may
related
spectrum
energy
insight
the
It is of
the
on
the
electron
density.
through
distinct
Value
the
of
not
but
the
operator
=
areas
on
correlated
DVB
explicit, does
not
allow
to
spacings
on
the
N
number
conclusion
in
us
is
localization
the
fully
electrons
the
parameter).
cell
any
the
/
(1l'(H~(1l')
where
on
Nevertheless,
intermolecular
transfer
draw
correlations
of the
are
to
is the
electronic
of the
particular
of
possible
infinite ring,
of tile
orbitals
site
description
not
course
effect
local
existence
the
to
~
(52) integrals (a
interdimer
and
picture, the
the VB
be
decreasing.
which
(Sl)
Intradimer
2.
*
2q+1
2~
~
Fig.
*
*
*
the
of
straightforward
charge carriers is
existence
of
wavefunction
real
The VB
space.
calculate
any point
a
gap in the
gives
method,
property
some
for
like
effect
of the
delocalization
charge
quantitatively calculated from the expectation
Using expression (2) for H~, one gets :
state.
stabilization
may
be
ground
jjt~~~i(1l'((n,n+
I
)+
+
(n+
I,n
)(1l').
(10)
M
periodic
The
bonds
to
impose
conditions
correspond
which
2.psj
that
ring
the
only intra,
et
psi
/(1l'((2n-1,2n )+
/(1l'((2n,2n+1)+
=
lHtl ~l')
The
Esj (Es~)
expressed
energy
it is
energy
bond
order
following
which
noticeable
the
with
the
on-site
given
of U is
a
as
deals
with
competes
Sl (52)
product of
(2n,2n-1)(
+
(2n+1,2n
effect:
in
a
effects
correlation
the
Mott
figure
3. Tills
decrease
of
of
localization
in
U.
The
correlation
term
shows
that
E(U=0)
(12)
of
tills
term
exact
U Values
of
factor
ring
is
2
:
of
energy
are
the
to
total
wavefunction.
electron
of the
variation
bond
multiplied by
DVB
sites/4
4
a
(13)
Es~)
+
transfer
the
a
)( 1l')
contribution
large
Very
by
52,
(11)
(Esi
=
monoelectronic
the
inter-dimer,
and
1l')
(
ts~)
s~
gives the
bond
Sl,
ps~.
+
psi tsi + 2 .p
the
of
includes
example
function
~~ (2
=
861
SYSTEMS
FILLED
contains
orders,
bond
3/4
OF
:
W
term
that
two
=
2.ps~
so
APPROACH
VALENCE-BOND
6
required
only
transfer
the
bond
a
the
The
as
a
observe
to
obtained
a
for
10 eV.
U
=
,2
0,8
E
°,~
rev)
O,4
o,z
0,0
20
lo
30
Fig.
Energy of
3.
analysis of
give the
The
Cj(
a
the
which
charge
distribution
sites
two
I
bond
in
4
a
electrons/4
charge
distribution
probabilities
to
evaluated
from
is
find
p
the
ring
sites
is
50
40
<ev>
u
as
a
through
made
electrons
on
contribution
of
the
site I and
Hv
U(t
of
function
to
functions
correlation
electrons
q
the
).
I elf
=
total
site j.
on
energy,
which
The
is, for
and j
~ijl'~'(ni~j( ll'),
so
that
the
relation
involving
Cj(
lv'lninjl
v')
is
:
ZP.qlv'slv'£)
=
iP.q.Of
p.q
where
electrons
(1l'j()
on
neighboring
Using
I +n.
is
I
(1l') component
j respectively. We
sites
the
I
and
I +
boundary
I,
and
p,q
collecting
the
and
('4)
=
will
the
conditions,
the
discuss
correlation
the
diagrams
the
in
correlation
functions
intradimer
(Sl)
there
wllich
functions
C)j'+~
C(j~+
between
distribution
p
are
'
sites
and
q
between
I
corresponds
and
to
C)j~,
the
while
tool
the
In
interdimer
analyze
to
of
case
allowing us
multiplicity,
the
the
8
to
C)j~
ring, the complete set
susceptibility,
paramagnetic
function
Zs for the
temperature
to
the
susceptibility
per
site
correlated
of
of
the
~s=£(25+1)exp(leads
functions
These
membered
partition
the
(52) corresponds
one
M 6
I
are
a
very
useful
wavefunction.
calculate
to
PHYSIQUE
DE
JOURNAL
862
the
ar
states
electrons.
was
For
obtained,
spin
each
T
~
(15)
kT
:
£S(S+I)Zs
x
where
is
N
temperature
Electronic
The
number
independent
sites,
of
constant
is
~c~
the
3kTNjjZs
Bohr
2.0023),
(g
(16)
~
The
magneton.
in
=
agreement
with
g
the
factor
is
taken
experimental
as
a
data.
parameters.
method
organic
the
the
g~ ~1]
=
requires the
cation.
These
one-
and
two-electron
parameters
may
be
terms
obtained
which
involve
the
molecular
orbitals
of
modelling experiments, may
through simple
theoretical
approxi-
from
the
by independent approaches, or evaluated
(this is for example realized in the P-P-P- approach in order to calculate the tworepulsion terms).
electron
the
transfer
integrals from infrared data in the
It is possible, by simple models, to
deduce
plasmon range or
thermoelectric
[33]. The results are roughly
coherent
and lead to
power
for
based
intrachain
transfer
integrals between 150 and
200meV
sulfur
salts and 250 to
based salts. The U and V values
have
been
estimated
from IR charge
300 mev for
selenium
from 1.2 to 1.5 eV while V (first neighbor) is
transfer
spectra [33, 34]. The U values
range
around
study of the reflectance
BEDTTTF
salts, Tajima et al.
0.4 eV. In a
spectra of
recent
obtained
U*
(effective U
V) [35].
0.7 eV
U
Theoretically, it has been proposed by Mazumdar
and Soos [36] that the general tendency is
organic
approach
of
the
compounds.
This is in rough
with
2
4
in
lD
U
V
agreement
t,
a
the order
deduced
from the experiment
and the regime might be qualified of
intermediate
strong coupling.
integrals is feasible through band
calculations.
The
calculation
of the
transfer
structure
have
been
calculated
within
the
tight
binding
Quite currently, these band
[31,
32]
structures
calculated
be
mations
=
~
=
~
Hamiltonian
extended
Hiickel
(EHT) [37]. Beyond this
approximation
with the help of the
have
been
made
obtain
simple
approach,
only
the self
consistent
field
to
attempts
two
very
calculations,
based
density
band
39].
These
the
local
approxi[38,
two
structures
on
same
(p-(BEDTTTF)2X),
but
Kasowski
and
mation, deal with the
salts
lvhangbo [39]
same
which
allow
better
representation
of the interintroduce
non-spherical
potentials
a
some
molecular
spacings. The general features of the band at the Fermi level and the shape of the
calculation
surface
similar in the latter
and for the
EHT
model.
Fermi
to be quite
appear
surface
characteristics
that well agree
the
transfer
integrals lead to Fermi
Moreover,
EHT
Shubnikov-de
Haas
experiments in some
representative salts of the
with
those
deduced in the
retained
calculations.
in these
p- and K-phase families [40]. Thus, they have been
complex. Following the P.P.P. scheme, it
The
evaluation
of the U and Vq terms is more
from simple equations.
However, this parametriwould be possible to obtain the Vg terms
M
VALENCE-BOND
6
APPROACH
3/4
OF
SYSTEMS
FILLED
863
atomic
orbitals [30] but no
realized only for the
interactions
between
Then,
semi-empirical
corresponding formula in the
intermolecular
a
case.
method,
CND02
[41], has been used to obtain these
Hartree-Fock
parameters.
of choosing the HF
orbitals
for the
calculation, we would have to
If one
would
think
zation
has
study
deals
evaluate
initially
been
with
the
integral
the
U
U
where
x~ is
pointed
that
the
where
highest
the
out
The
temperatures.
although
tills
is
result
largely depend
slightly smaller for
not
lower
U.
Table
I.
The
the
on
on
molecule
is
The
than
and
for
on
the S
the
than
for
eV
neutral
correspond
calculations
to
a
U
values
:
the Se
TMTTF
and
the
orbital.
orbitals
one,
charged
crystal
so
more
are
that
U is
calculation
Compound
at
calculation
I
neutral
charged
6.45
1.94
TMTTF~PF~
4 K
6.34
6.46
1.88
TMTTF~SbF~
135 K
6.28
6.40
1.90
TMTTF~Br
300 K
6.31
6.42
1.96
DIMET~SbF~
300 K
6.09
6.26
1.72
TMTSF~PF6
300 K
5.82
5.94
1.80
TMTSF~PF6
4 K
5.71
5.80
1.84
Vg
terms
are
where
xi
were
obtained
structure
the
et
in
xi
the
are
from
table
V~j values
interactions
formed
2
:
Vii
The
and
molecular
6.33
(52)
diffuse
The
300 K
listed
do
and
smaller.
TMTTF~PF~
The
values
6 eV,
determined
monomers.
structures
I
at
comparison,
The
around
are
table
in
obtained
data
given for
also
are
be
compounds
collected
are
doubly occupied
the charge. They
ones
should
It
mixed-Valence
shown.
temperature
are
these
crystallographic
from
monomer
to
molecule.
neutral
a
electrons.
taken
related
larger
for
in
charged
a
in
orbital
2
or
xi(v))
xi(~1)
ambiguous
vere
molecule
(CND02)
U
is
U is
as
of
type
these
in
results
compounds
the Se
Integrals
orbital
carry 0,
coordinates
unphysical
DIMET
used
geometries
can
atomic
molecular
HF
of the
orbital
monomer
(calculation I). The
different
occupied
choice
the
ixi(~1) xi(v)i i/r~~
=
II
are
are
by
(xi(~)
=
HOMO's
a
of the
rather
isolated
to
be
xj(v))
charged molecules,
injected in a dimer
or
and
I and
j.
These
calculation.
orbitals
The
results
compounds.
different
found
neutral
calculation
monomer
for
xj(v)(I/r»v(xi(~)
around
U/2. The
intra-dimer
DIMET~SbF~,
which
3 eV, I-e-
close,
except
dimers
[16].
for
(Sl)
inter-dimer
and
exhibits
a
dimerized
864
JOURNAL
Table
II.
to
line
neighbor
integrals
V~~
(first line ), charged
Nearest
neutral
monomers
PHYSIQUE
DE
in
eV.
compound,
(second line ),
monomers
the
charge
one
TMTTF2PF~
300 K
TMTTF~PF~
4 K
TMTTF2Br
300 K
DIMET2SbF~
300 K
TMTSF2PF~
4 K
ratios, Vsj/Vs~ and
both
ratios tend
decreased,
temperature
intermolecular
distance, R, but the
of the
dimerization
The
is
to
a
neighbor
V~~
smaller
terms
dimerization
would
in
ratio
important,
be
Vsi
Vs2
3. 13
3.02
3, 15
3.04
3,16
3.12
3,18
3.14
3.12
3. I
3.14
3.13
3.19
2.20
3.23
2.21
3.21
2.33
3.02
2.98
3.04
2.99
3.02
3.01
3.03
3.03
300 K
TMTSF2PF~
tsj/ts~,
compared
are
per
correspond
(third
dimer
in
III.
Dimerization
ratios
in
some
table
III.
Vfhen
the
depend on the inverse
to
terms
V~~
transfer
integrals vary exponentially with R. This
the first
It is also expected that the
second
case.
if
the
corresponding
transfer
close
terms
to
even
are
decrease.
The
0.
Table
results
6
(DIMET~SbF~)).
Compound
leads
each
For
M
I
M2X
compound
salts.
vsi/vs2
tsi/ts2
TMTTF~PF~
300 K
1.04
1.47
TMTTF2PF~
4 K
1.01
1,19
TMTTF~Br
300 K
1.00
1.12
DIMET~SbF~
300 K
1.45
1.98
TMTSF~PF~
300 K
1.01
1.20
TMTSF2PF~
4 K
1.00
1,10
M 6
APPROACH
VALENCE-BOND
calculated
The
Values
which
Values
have
discrepancy
is
molecular
of the
due
the
to
(MO)
alone (the
orbitals
considerations
alternative
MO
on
to
evaluate
larger, by
[33-36]. The
similar
U is
relate
to
the
CND02
the
this
to
term
reason
minimizes
than
the
for
this
all
the
total
although
to
main
Symmetry
energy.
ones), explain the slight
better
the
of 4,
factor
a
which
process
obtain
to
865
SYSTEMS
FILLED
much
are
studies
charge,
molecular
the
3/4
Hartree-Fock
energies
quite
are
their
EHT
method
terms
earlier
in
self-consistent
and
dependence of U and V
deeply the MO energies.
An
correlation
proposed
been
OF
iterative
difference
the
modifies
process
the
between
potential and the electroaffinity, following Pariser and Parr [30]. Using Koopmans'
between
the
of the ar site
theorem
[42], the U term is thus defined as the difference
energy
filled by 2 electrons
filled by I electron.
These MO
orbital
and the energy of the ar site orbital
calculation
corresponding
orbitals
easily
obtained
from
the
and
the
Values are
CND02
U
are
given in table I (calculation 2). They are much smaller than those obtained
above and close to
the experimental
Values.
Besides, they agree with the Value, U
deduced
from the
1.7 eV,
ionization
potential and the electroaffinity in TTF salt [43].
approach leads to V (first neighbor)
Conceming the V term, a similar
I-I eV for
TMTTF~PF~. This represents one third of the values of table II, but it is still larger than the
experimental value
around
0.3-0.4 eV [34, 35]. A possible explanation lies in the
CND02
the neglect of the
neglect of the penetration integrals, in order to
overlap
compensate
integrals [41]. These integrals take into account the attractive effect of the atomic
the
cores
on
distances
valence
electrons
of the neighboring site. The
intermolecular
typically larger
are
than 3.5 A, and correspond to overlaps no larger than 10-2 and actually negligible, as already
outlined.
unbalance
the
electrostatic
potential
Consequently, such a compensation tends to
experienced by the
electrons.
Therefore, a more
method
dealing with
conduction
accurate
ionization
=
=
such
should
effect
an
lead
to
decrease
a
of
V.
formally
involves
strict
core-peel
a
using
Hartree-Fock
molecular
orbitals
consistent
with such a scheme.
Besides, Klein and Soos [44]
of site
have
shown
that, in
Hubbard's
derivation
representations,
kinds
of
intrasite
many
electronic
could
included
energies,
transfer
integrals
be
in
site
correlation
terms.
processes
or
possible to include
contributions
by appropriately choosing the
It is also
many-electron
transfer
integrals, as noted for example by Heeger [45] or Kondo [46]. In a similar
manner,
the
Pariser
and
approximation
(calculation 2 of Tab. II) implicitly takes into
Parr
account
significant part of these many body effects, that is the core
relaxation
with the charge of the
and
calculations
clearly show that it is possible to obtain explicitly reliable
monomer
our
Values for the
correlation
interaction
is properly (although
terms, provided that the core-peel
important to note
that
separation. The explicit
calculation
(calculation I of Tab. II) is not
It
is
still
approximately)
encountered
To
reports
bypass
on
changes in
(represented
the
in
the
the
handled.
calculation
problem
Variation
the
electron
of
of
the
the
of the
the
the
exact
V
is
in
to
progress
overcome
the
difficulties
term.
Values
wavefunction
distribution
by tsj/1s~ and/or
parameters
work
Further
of
approach
DVB
due
of
the
to
the
the
parameters,
characteristics
variation
on
of
these
the
present
parameters
electronic
paper
and
rather
on
the
dimerization
Vsi/Sj~).
Results.
presented in two
depending
the
degree of the
electronic
parts,
on
dimerization,
dimerized
in
compounds
such
DIMET~SbF~
[16], or
met
:
as
small
dimerization, in regular and quasi regular systems, represented by the TMTTF~X with
octahedral
anions [8]. The
corresponding results have been presented in a condensed
form
elsewhere [47].
The
results
dimerization
are
large
JOURNAL
866
DIMERIzED
The
SYSTEMS.
semiconductors
at
more
are
calculation
tsj
correlation
terms
then
model.
indirect,
is
given
are
for
N
when
difference
1.7.
This
ratio
the
onsite
sites,
by
but
the
integrals tsj
increases
but
and
throughout
effect
of the
model
Hubbard
the
different
0)
V
and
=
intersite
the
successively
terms
of
value
0
U
first
and
for
=
is
The
Each
system.
6 eV.
~
I.4 eV,
U
=
(Fig. 4).
U
of the
U
increase
an
localization
on
with
size
the
to
U
without
move
bonds
the
insensitive
between
:
may
effect
asymptotic
an
This
effect
decrease
the
only for Sl. This is directly related to the
the Hfickel limit, Esj/Es~ is roughly equal to
Thus, the apparent
dimerization
is
IA eV.
5 fb
ts~. In
for U
2.85
to
rather
bond
the
which
used
V~.
reaches
for 52,
is 36 fb
salts [8],
TMTTF
been
study
to
first
use
analyse
we
are
and
=
increased
we
neighbor
interdimer
the
transfer
in the
properties,
increases
U
pronounced for
character
bonding
more
of the
=
is
in the
have
3/4 filled system, the charge carrier
occupied sites. Consequently, the
by the variation of the energies of
12
=
decreases
tsi/ts~
a
demonstrated
as
energy
In
doubly
of
number
eV
and
(Q.cm)-'
50
DIMET~SbF~
[16]. In order
of
0.10
second
and
around
integrals
model,
Hubbard
Vsi and Vs~,
Hubbard
the
results
the
on
:
localized.
They are
only 10-3 (Q.cm)-'
are
for
while it is
and ts~
electronic
eV
=
extended
the
neighbor,
of
0,17
M 6
I
representative of this class
example, the conductivity
salts
temperature
room
DIMET~SbF~ [48],
regular. The transfer
300 K in
at
PHYSIQUE
DE
=
correlation.
0,2
+
EST
o
ES2
0,0
2
a
4
S
6
lo
u
Fig.
Variation
4.
Hubbard
according
that
table
as
to
3/4 filled
this
In
function
type gives
larger
3.
(ev~
of U
in
dimedzed
section,
intersite
of the
have
12
sites).
=
neighbors.
The U value
for (DIMET)2SbF6 [34].
we
(N
salts
be
0.2 eV
has
the
and
of its
to
be
1.3 eV
proposed
compounds. The
indeed
energies
bond
potential Vo,
also
dimerized
the
dimerization
structural
evaluated
averaged
in
chosen
was
It
and
been
influences
the
the
correlation
dimerization
3, by
or
rise
=
Vo
+
3/2
and
Vs~
=
Vo
/2
the role of Vo in
localization is direct. It plays the same role as U in the
diagonal correlation
minimum
for the diagrams
which
present
energy is
of singly and doubly occupied sites. An electron
transfer in a diagram of this
diagram whose diagonal energy is increased by Vsj (for an
interdimer
to a
band.
alternance
transfer)
function
formulae
the
half-filled
an
a
collected
data
Vsi
In
first
as
between
Vsi and Vs~ would
qualitatively suggest that the
II
a
Es~ (ev~
and
extended
potential.
functions
Esj
spectroscopic
difference
of
intersite
using
model
to
the
results
of
bands,
The
Vs~ (for
an
intradimer
transfer).
The
latter
stabilization
is
evidently
enhanced
by
a
M
VALENCE-BOND
6
The
energies
bond
only
is
noticeable
small
induces
Variations
Vo
or
varying from
( Vo
0.4 eV
0 to
and
thus
to
Es~
models.
two
a
the
intersite
52
cell,
so
that
the
such
a
ratio
the
For
0.2 eV
This
one.
leads
decreases
=
the
in
evidenced
0.4 eV.
=
interdimer
as
&,
dimerization
Vo, the
similar
given in figure
sufficiently large
of Es~. Therefore,
is
by
more
values
), one finds
only 1.9 in
The
of
inclusion
ratio
the
of
of
Esj/Es~
Esj,
so
the
The
may
table IV.
that
Esi/Es~
uncorrelated
case,
correlation
the
to
within
while
U
small
even
Value
the
the
of
than
stronger
bond
St
extended
the
of
multiplied by 1.7 for
experimental suggestion
bond is 5 times
intradimer
by
52,
on
value
non-zero
Whatever
is
than
Sl
on
modified
be
of
867
larger
is
which
parameter.
Vsj and Vs~ close
that
the
this
results
than
SYSTEMS
FILLED
of Vo,
effect
Values
the
3/4
OF
The
5.
are
for
Values
of
APPROACH
the
strength
Hubbard
is
model
bond-order
(BOW) picture. A dimerization
of 5
strong
means
wave
is virtually empty. For these compounds, the hole is localized in the
short
calculation
do not
segments used in the DVB
represent a limitation
very
that
bond
unit
for
discussion.
0,2
EST
°'~
*
6=0.2
°
6=0.4
°
6=0.0
.
6=0.2
0,0
0,2
0,4
0,3
0,5
0,6
Y0
0,2
ES2
°"
°
6=0.4
°
6=0.0
0,0
0,2
0,4
0,3
0,5
0,6
VU
Fig.
U=1.3
Table
5.-Variation
of
Esi
and
Es~ (elf)
as
a
function
of
V~
and
8
dimedzed
in
salts
(N
=12;
elf).
IV.
Esj/Es2 for d@ferent
values
of Vo
and
3 in
dimerized
salts
(U
1.3 eV
=
3
Vo
0.0
0.2
0.4
0.2
3.46
4.85
6.00
0.4
3.74
5.10
6.31
0.6
3.56
4.96
6.08
).
868
JOURNAL
PHYSIQUE
DE
M
I
6
result is confirmed by the
calculation
of the charge
correlation
functions C(f + ~. They
intradimer
(sites
and
for
interdimer
given
in
figure
for
the
I
and
2)
the
(sites I
6
case
case
are
and fi§. The ground state, which is nlainly built on the diagrams exhibiting alternating singly
C(j~+'
larger
doubly occupied sites, corresponds
the
values
of C(j~+'
and
and
to
(C(j~ + '
C(j~ + ' by symmetry). For Sl, the probability of having 3 electrons on the dimer
(C(j~ + C(j~) is 90 fb, and does not depend on Vo, as expected. This probability is still the
delocalization
in
largest for 52, but C(j~ and C(j~ are reduced. Their decrease is due to the
C(j~
C)j~
C(j~)
equalize
(and
the
probabilities
the Sl
bond
which
tends
to
to
or
C(j~ to have 2 or 4 electrons on 52. Tills is particularly true for Vo 0.2 eV, wllile the
potential barrier through Sl is zero. For larger Vo values, this effect decreases and the charge
correlation
outside the dimer (Sl) or the unit cell. This is illustrated by the charge
propagates
functions
between
sites I and the other sites (I + n ) of the system : figure 7 (the
correlation
while n =11
corresponds to the
interdimer
intradimer
correlation,
I gives the
case
n
correlation
and
quickly
decreases
large
between
sites I
2
for
correlation).
The
very
situation
is
completely
uncorrelated
with
6,
the
almost
2.
For
n
n
This
=
=
=
~
=
f~17
f~
II
17
22
~
17
12
~
17
21.
o,5
o,4
~
C12
C21
=
~(j
0,3
0,2
o,1
0,0
0,3
0,2
0,5
0,4
0,G
VU
a:sl
o,5
o,4
~
o,s
c12
=
c21
~((
0,2
o,1
0,a
0,2
0,5
0,4
0,3
0,6
VU
b:s2
Fig.
6.
of Vo in
C~~. (a)
Charge
dimerized
Intradimer
correlation
salts
case
(N
functions
12 ;
sl, (b)
U
C(f
between
+
1.3 elf ;
Interdimer
0.2
8
case
=
s2.
neighbor sites for ~p, q )
elf). In the caption, these
=
(1,
2
)
functions
as
a
function
are
denoted
M
APPROACH
VALENCE-BOND
6
3/4
OF
SYSTEMS
FILLED
869
o,s
0,4
C12
O
C21
0,3
*
Cll
'
~~~
0,2
o,1
0,0
0
6
4
2
8
1 0
1 2
n
Fig.
-Charge
7.
dimedzed
correlation
(N
salts
12
Hubbard
model
because
it
allows
number
of
doubly
the
preceding
a
«
sites
between
0.4 elf ;
=
and
I
ev~.
0.2
8
I
~p,q)
for
+n
(1, 2)
in
=
caption,
the
In
functions
these
=
are
have
We
it is
that
that,
respectively,
neighbors.
second
to
discriminate
Vs~, type A is
favored.
The
effect
diagrams
competition
which
the
between
behavior
The
will
of
the
close
to
interesting
minimal
same
these
diagrams
those,
obtained
between
be
quite
V~ is
present
depends
with
the
equivalent
and
model
Vs~ is comparable
singular
show
extended
to
us
behavior
to 2
<
in the
shown
favored.
the
preceding
increases
V~
the
that
so
almost
are
;
is
same
from
have
0
that
on
sites
Esj
Esj/Es~
would
on
be
by
described
is
by
Es~ increase
only from 5.I
and
goes
a
because
strong
energies.
bond
the
different
by 52.
linked
localization
influence
0.15 eV,
ratio
correlation
the
the
small
a
to
dimerization
charge
The
charge
section
expected that V~ would
when
distributions
electron
different
V~, the
expected
is
Vsj, type Z
correspond to
if Vs~ « 2 V~
diagrams
these
so
Vo
occupied sites (Fig. 8). The
values of Vsj, Vs~ and V~ :
relative
if 2 V~
if
=
by C~~.
denoted
on
C)j~+"
functions
1.3 elf ;
U
=
The
5.5 fb
and
BOW,
results
10 fb
4.9.
to
52
fi~~
A
x
x
~
~i~
~
(4V2)
B ~VS2
x
i
~
+
4V2)
/
~x
~x
/
~
~
'
~
x
B'
(VSI
~
+
4V2)
xx
z
Fig. 8.
potential
(2vs2)
Representative diagrams with
energies (referenced to 4 U; N
z'
a
=
(2vs1)
large weight
8).
in
the
ground
state
and
their
corresponding
JOURNAL
870
PHYSIQUE
DE
M
I
6
(Figs. 9 and 10) clearly show a strong
change
this is a direct
of
not
consequence
trapped
the
dimer
whatever
the
the
Value
of
are
on
C(j~+~m0.5
C(j~+'
invariably.
The
correlation
strongly
depends
that
52
V~ so
on
around
0,15 eV (in that
0), a change in the regime occurs, as
2 V~
V~
Vs~
V~
case
defined
above.
The charge
between
the dimers is almost fully
uncorrelated
evidenced
by
as
the long
distance
correlation
charge reported in figure10. Thus, for the
where
case
the
On
the
contrary,
results
charge
the
on
correlation
of V~. Through Sl, the
correlation
of the 52 bond.
electrons
weakness
The
influence
does
=
=
Vs~
2
=
dimer
V~, the
electronic
with
contrasts
simple
larger than
would
be
comparable
diagrams, and
Finally,
to
necessary
be
the
Cjj
+
include
odd
effect
dimers
values
results
show
that
the
correlation
in
the
the
effect
turn
the
for
the
this
C(j'+~
and
regime of large
which
the
against
favor
A
dimerization
dimerization
charge
the
interaction
apparent
of
inside
complement
C(j'+~
However,
of N.
increases
conclusions
of
They justify the previous
them to
extend
of triplet spin
excitons [49], and
systems.
results
third-neighbor
Including these potentials would
second regime would be
recovered.
the
These
V~~0.2eV,
For
of the
correlation
strong
dimer.
the
energies.
for
~
the
isolated
outside
bond
'
of
ts~.
to
these
no
and
+ ~
made
correlation
given by
C )j~
is
system
almost
picture
BOW
become
V~, it
=
on
would
the
Z
of these
properties
the
correlation.
a,5
0,4
0
3
°
Cl 2
+
Cl
=
C21
'
~~~
,
a,2
o,1
0,0
0,1
0,0
0,2
0,3
Y2
a:sl
0,4
0,3
C12=C21
u
.
Cil
.
C22
0,2
0,1
0,0
0,2
0,1
0,3
Y2
b:s2
Fig.
9.
V~ in
functions
of
Charge
correlation
dimerized
are
denoted
salts
(N
functions
Cjf
=12
U=1.3eV;
by C~~. (a)
;
+
neighbor sites
0,4eV;
8
Vo
sl, (b) Interdimer
between
=
Intradimer
case
for ~p, q
=
0.2eV~.
case
52.
(1, 2)
=
In
the
as
a
caption,
function
these
M
APPROACH
VALENCE-BOND
6
3/4
OF
871
SYSTEMS
FILLED
C12
D
C21
0,3
*
Cli
,
c22
o,1
0,0
0
2
6
4
8
0
2
n
Fig,
Charge
(N
lo-
dimerized
caption,
these
12 ;
=
functions
U
C)j
functions
correlation
salts
1.3 eV ; Vo
denoted
by C~~.
=
are
between
+ "
=
0.4 eV ;
sites
and
I
0.2 eV
8
I +
V2
=
n
~p,
for
Vsj2
=
q
0.15
=
(1,
=
eV).
2
In
)
in
the
antiferromagnetic
order
observed
The
Consequences for the magnetic properties.
at low
finite
paramagnetic
susceptibility
result
Tin
DIMET~SbF~ [48] leads to a
This
has
at 0 K.
Hamiltonian
infinite
chain
of1/2 spins [48]. In this
been
modelled
by a Heisenberg
on
an
model, the U term is not a molecular entity. For a finite ring, the ground state may be singlet
triplet depending on the number of sites (even or odd), or on the
To be
parameters.
or
electronic
distribution,
the
susceptibility
calculations
consistent
with
results
the
have
our
on
been performed on a ring of 8 sites which gives a singlet ground
The
state in the present
case.
T dependence of the static susceptibility has been performed for the ring of
susceptibility per site is independent of the size N of the cluster at high T, in
the Curie limit, and
almost
independent of N at the maximum (see for example [50]). The low
behavior
is
sensitive
factors
including the change of the dimerization,
and
Various
T
to
therefore
of the
closed
transfer
integrals, upon lowering T, the difference
between
and
open
chains, the fact that the results
corresponding to N
4 n or 4 n + 2 might lead to
different
detail in the
section
reporting on
ground states, etc. This point will be discussed in more
regular systems. We then focuss on the shape of the plateau and of the maximum and on their
calculation
of the
only.
8 sites
The
=
b
a
~~X~~
X~ /
0 0 eV
~RT
~
0. I S eV
~
,
2
0 25 eV
I
i
o
o
0
200
l00
300
100
0
TIK)
Fig,
Variation
I I.
V~ (N
=
8 ;
Heisenberg
U
=
of
x(~/X(300j
1.3 eV ;
fit [51].
Vo
"
with
0.4 eV ;
200
300
T(K)
dimerized
Tin
0.2
8
=
ev~
salts
;
(b)
:
(a)
calculated
ESR
result
for
results
for
different
DIMET2SbF~
with
values
of
spin 1/2
872
JOURNAL
dependences
T
The
the
on
for
and
electronic
maximum
calculations
The
small
:
T~a~
obtained
when
means
of
cluster
of
small
size
and
using
justify
the
use
of the
Table
(N
U
=
DVB
=
of
M
a
with
the
6
temperature
Vo
an
=
increase
of
into
x(n
These
account.
T~~~.
in the
rings
the
for
it
occurs,
an
to
the
increase
of
relation
between
experiment
quantitative
comparable to
the
better
quite
are
calculations
[51]. These
of
range
analysis
experimental [51] magnetic
0.2 eV).
A
results
Hamiltonian
parameters
finite
on
around
which
compared
induces
of V~
evidence
experimental
for a
0 disagree qualitatively
with
no
V~
molecular
and
1.3 eV ;
with
increase
spin-1/2 Heisenberg
method
Calculated
V.
8
x~~/x(300K)
that
is
There
taken
V~ is
by
show
sharp
and
obtained
the fit
variation
The
parameters.
T~~~ and a decrease of xmax/x(300 K).
results
these
numbers.
The
obtained
is
I
Values
strongly depend
experimental Values.
agreement
PHYSIQUE
of V~ are
reported in figure I la.
Value of the susceptibility x~~~, and the
temperature T~~~, at
characteristics
collected
in table V and
V~. These
are
on
different
(see Fig. I16)
DE
of
on
a
coupling
the magnetic properties.
an
intermediate
susceptibilities
in
dimerized
salts
0A eV
=
=
V~(eV)
()$)()~
T~~~(K)
0.0
Xmax/X300K
3.5
7.9
10-3
10-4
10-4
8.9
10-4
1.5
90
8.5
80
9.0
10-4
10-4
1.6
80
7.0
10-4
1.5
28
1.0
0.15
60
9.4
0.20
77
0.25
96
p-(ET)2IC12
(ET)2AuC12
DIMET~SbF~
1.9
1.7
1.7
In the
TMTTF~X salts, the conductivity
show a
SYSTEMS.
measurements
regime at room
and a
semi-conductor
behavior
below the
temperature
temperature
of the resistivity
minimum
delocalization
is assured in mean-field,
T~ [8]. For a rigid lattice,
and
band
theory is simpler than VB approaches.
showing
intermediate
For
systems
an
REGULAR
metallic
T~
m
100-200
K, the
size
of the
localization
is not
of the
DVB
evaluated
formalism.
by this
ology formalisms
approximate,
are
mean-field
cluster
well
This
used
treatment
in
modelled
the
by short
limitation
mean-field
leads
would
treatment
to
a
size of the
electron-hole
pair
of the
order
Consequently, it might be argued that
and that its modelling is out of reach of the
founded
only if the size of the e-h pair
calculation.
DVB
segments
be
well
were
an
perturbative
exact
result.
However,
models
like
the
g-
corresponding results
treatments,
are
modelization.
Furthermore, in RG models, the
compared to the exact DVB
choice of the cut-off
and
guides should be extracted directly from
some
energy is important
the physical properties. On the contrary, the exact
DVB data point to a small
extension
of the
e-h pair.
Moreover, this result is independent of the size of the ring (8 or 12 sites) and fully
justifies the limited size of the cluster used in this study. Further
be made
comments
can
on
the approach of
localization
by the g-ology model and on the g~ parameters. It is difficult to
fix
link the
of the salt. For example,
authors
parameter g~ to the microscopic
nature
some
by
fitting
the
experimental
different
Besides,
the
has
[17].
parameter
at
g~
pressures
g~
T~
been
dimerization
shown to depend on the gj
[53]. However, our
parameter and on the stack
[17, 18, 52, 53]
and
the
M
VALENCE-BOND
6
calculation
of the
type
dimerization.
calculated
relation
the
and
of the T~
established.
The
be
The
approach
DVB
and
this
on
may
do
not
priori
a
the
is
valuable
a
attempt
an
as
to
first
a
for
the
study
the
effect
related
results,
cumulative
where
of
effect
TMTTF
show
salts
[54].
This
This
structure.
the
the
of
cautionary
this
decrease
a
the
t;j
and
possible
the
essentially
because
calculation
[55] has
B, located at
H, located
atom
influence
of
and
3.5
the y axis
on
last
of the
overlap
performed
A apart
on
at
turn
now
we
the
d
z
A
a
been
the
(low 1~ system is
the previously
localized
more
of
calculated
the
to
to
shown
arise
to
the
from
This
which
effect
included
is
description
has
this
suggestion.
local
more
supports
been
The
v(p)jxj(R))
+
the
the
term
on
the
model
from
leads
This
dimerization
contraction
:
to
axis,
a
parameters.
A
model
a
between
on
stacking
the
contradictory
has
electronic
V(p
and
due
the
been
transition
note,
larger
one.
apparently
[17,18].
(x;(R)lT(R)
T(p ) is the kinetic
component
organic stack and the potential
evaluate
of
hamiltonian
dimerization.
the
and j is
site I
=
the
in
from
localization
electronic
correlation
between
problem
the
each
continuous
evaluation
results
is
might possibly modify the
The
anions
in the
g-ology model
phenomenologically
[51]. We present
proposed by
Laversanne
integral
of
of
parameters.
decreased
dimerized
less
the
to
discussed
where
discriminate
to
us
mind
(52) spacing than of the
intramolecular
(Sl)
of the tsj/ts~ ratios reported in table III. Then, the
variations
the
allow
back
tool
track
principle
regimes. Keeping in
than
electronic
of
structures
temperature
be
intermolecular
transfer
873
implies
V
parameters
g,
low T
the
the
of
crystal
the
rather
T and
discussion
the
The
SYSTEMS
the
to
appears
viewed
be
property,
high
the
between
when
FILLED
compounds.
localization,
to
comparison
But
3/4
OF
that gj would not depend strongly on the
should
be
related
only to the stack
parameter
g~
of the
structural
data on the stack
dimerization
(or of the
values in a large series of compounds
shows that no simple
U and
terms
Thus,
molecule.
tsj-ts~)
can
between
term
correlation
organic
of
APPROACH
Coulomb
organic
the
cores
3pz
represented
the
and
integral,
transfer
sulfur
between
term
in
and
the dimer and
represent
the z axis. The
transfer
ar
the
as
12
:
electron
of
order
to
In
orbitals,
atomic
figure
a
anions.
latter
arises
ab
initio
an
sulfur
two
with
interact
integral
a
atoms,
A
hydrogen
between
the
two
z
o
s
~
s7
)
d
I
§
s~
2
0
1)
Fig.
lo
and
Model
12.
sulfur
atoms
t
are
of
S~ and
the
the
St~
transfer
2
4
d
8
6
IA)
h)
change in the transfer integral due to the anion potential
interacting with a hydrogen atom H (b) ab initio results
integrals in absence and in presence
respectively of H.
(a)
:
Model
D
=
to
of
t,
two
where
874
JOURNAL
orbitals
sulfur
pzA(p)
3
and
nucleus
have
to
t
are
21<
d<
which
is
should
this
distance
that
given in
on
the
transfer
integrals
Kid
law,
and
K=
a
anion
extrapolation
the
center
a
kinetic
anions
to
of
anion
an
the
dimer
For
For
51,
the
in
real
0.066eV.
of
possible,
strongly
yet
not
the
field.
hi.
in
component
is
where
-t,
H, gives
of
(d
~~
species
actually
may
integral.
confirms the hypothesis
This very simple approach thus
integrals by the anion potential. However, a more
accurate
Inspection of the TMTTF~X crystal
that
shows
structure
the
under
-1.44eV.I
molecular
of the
effect
decrease
to
the
to
D=
respectively
presence
figure12b.
and
compared
be
to
electrostatic
the
the
between
0.29eV,
is
is
and
orbitals
the
are
potential of the hydrogen
A negative charge
would
difference
the
in
and
Xj(lL)
and
matrix.
Therefore,
absence
t
that
straightforward
noted
in
follows
curve
the
decrease
a
be
confirms
this
roughly
Although
on
Hamiltonian
core
integral.
integrals
negative charge
a
81,
this
the
the
transfer
of
material,
from
extracted
effect
the
negative,
is
D
be
can
contribution
M 6
pzB(p)
3
opposite
an
and
I
given by the above equation, where Xi (lL)
respectively. This integral involves the
is
and
PHYSIQUE
DE
contribute
transfer
affected
more
assumed
for
from
evolve
effect.
by the
Sl only,
tsj
eV
=
=
t
picture,
corresponding to
investigated.
localized
Regular
a
decrease
varying
figure13.
V
=
ts~
=
change
qualitative
the
equality
into tsj
in
the
From
Hubbard
model
decrease
is 16 9b for
52 in the
for
between
The
0.3 eV,
dimerized
and
0
0.3
or
with
slight
a
equality
correlation
it will be
in
if
a
(t
of
transfer
effect is
difficult.
spacing might be
Sl
decrease
of
0.05
dimerized
(t
system
eV is
of V is
0,15
eV;
U
around
V~
E
the
charge
0.15 eV.
For
energy
U varying
for
eV
small
=1.5eV
with
:
),
Es
).
be
to
cases,
have
been
requires
the
increase
of
an
between
0 and
compared to the 36 9b
by only 7 9b for V
decreases
effect
The
of
V~ is
transfer
is
(V -2V~(
this
of
parameters,
=
more
a
Two
calculation
DVB
case
0,15
describes
integrals,
transfer
bond
=
effect
against
the
of the
which
measurements.
tsj and ts~, the
decrease
The
=
0,15 eV,
=
conduction
difference
the
regular
a
barrier
minimum
intradimer
Thus,
t s~
<
the
between
than
case.
eV
the
one.
of the
of this
=
0.10 eV
=
agreement
smaller
is
renormalization
a
evolution
=
more
a
52
of
reasonable, at high T, the transfer
integrals [54] would
0.10 eV, to tsj
0.15 eV
ts~, while including the anion
Similarly, the low T EHT result [54]
delocalized
situation.
seems
»
to
interdimer
the
t, U, V (first neighbor), V~. The
eV, this
I.4
eV
would
s~
chain.
parameters
U in
which
0.15
=
than
anion
corresponds
This
0.15
tsj
set
shown
and
the
W
t=O.lsev
+
t=0,10ev
o,o
O,I
O,O
O,2
O,3
V2(ev~
13.
Influence
of V2
on
the
energy
of the
bond
in
regular
salts
(U
=
I-S eV ;
0.3
V
=
in
for
overall
(eV)
0,1
Fig.
it
to
eV).
M 6
APPROACH
VALENCE-BOND
decrease
the
in
model.
It
by
of V
of
the
is 16 9b for
energy
609b
was
screening
decrease
bond
second
bond
energy.
3/4
FILLED
SYSTEMS
875
uncorrelated
Hiickel
regard to the
if
take
into
the
systems. Thus,
account
we
that
the
main
contribution
the
U gives
to
appears
0,15 eV,
=
with
dimerized
Es~ in the
for
the
t
OF
neighbors,
it
charge
correlation
along the ring is reported in figure 14. It is already negligible for the
difference
lies in the value
second
neighbor, as found in the dimerized systems. A substantial
The
correlation
of the
the
dimer
probability
variation
the
to
amounts
negligible
may
neighbor
95 9b in the
dimerized
to
the
the
meet
related
be
delocalized
more
first
between
the
to
of
nature
sites
case,
with 2
situation
or
of the
small
decrease
the
electrons.
probability to have 3 electrons in
only
70 9b. Thus, there is a nonnow
This
possibility of the charge
electrons.
4
of
the
bond,
which
corresponds to
energy
while
the
it is
o,s
0,4
~'~
O,2
w
Cl 2
+
Cll
w
C22
C21
=
o,i
o,o
2
6
4
12
lo
8
n
Fig.
Charge
(N
14.
regular
functions
systems
are
correlation
12
=
denoted
t
=
functions
0,10 eV ;
Cjj~
between
+~
1.5 eV
U
sites
=
=
I
0.3 eV
V
and
V~
I
+
(1, 2) in the
~p, q)
eV). In the caption, these
for
n
=
0. IS
=
by C~~.
noted
that the multiplicity of the ground
might depend on various
above
state
3/4 filled systems, Hiickel theory predicts that the ground state will be a triplet for
shown
that the
4 n ring. Besides,
Klein
and Seitz [56] have
electronic
properties of a linear
limit, by a Heisenberg
chain
atomic
model
with
Hubbard
might be modelled, in the
antiferromagnetic
exchange a function of band filling. For a regular cyclic system, we have
checked
whatever
that the gound
the U value. The Klein and
state is indeed
state,
a triplet
Seitz result does not
be
valid
for
ring
whilst
result
a
appear to
our
agrees with previous data of
Mazumdar
and Dixit [24] about the multiplicity of a ring with N # N~. The
different
results
for the rings and the chains might be closely related
obtained
different
their
topologies.
to
multiplicity as a
function
have
calculated
ground
of the
For
8, we
the
N
state
dimerization
0,135
while
fixing
of
the
transfer
integrals
and
0,135
the
3,
3
ts~
+ 3
: tsi
(with
these
correlation
0A
eV
0.2
eV
1.3
eV
Vsj
Vs~
terms
to : U
parameters,
; V~
the case 3
studied here, and 3
0.035 eV
corresponds
0 corresponds to the regular system
dimerized
unless 3 m 0.035 eV
case). It is found that the triplet is the ground state
to the
(dimerized case). For this value, the singlet ground state is lower by only 0.0006 eV.
the triplet ground state leads to a divergence of the susceptibility at 0 K
In the regular case,
forbids to reproduce the
magnetism. The magnetic susceptibilities have
and
observed
Pauli
been
calculated
only at 300 K and are given in table VI for two sets of correlation
parameters
We
factors.
have
For
=
=
=
=
=
=
=
=
=
876
JOURNAL
Table
VI.
(N
salts
Room
8
V~
=
U
=
1.5
eV
V
1.I
eV
V
and
different
for
larger
than
decreases
8.8
eV
8,I
values
regular
in
0,15
x
for
this
part,
7.5
x
7,I
x
10-4
10-4
7,4
x
7.0
x
10-4
10-4
the
susceptibilities are
integral. The
calculated
somewhat
(around 6 x 10~~ uemcgs/mole [51ii. They increase when t
results
satisfactory with regard to the small size of the
are
correlation
large susceptibility and justify the values of the
the
effect
data
The
account
10-4
10-4
x
0.20
transfer
of the
increases.
U
or
eV
0.4
experimental
the
They
cluster.
0.3
=
=
(300 K) (uem,cgs/mole)
X
0.10
=
=
U
M 6
I
V/2).
(eV)
t
susceptibilities
magnetic
temperature
PHYSIQUE
DE
terms.
summarize
To
intrasite
the
neighbor potential
only 20 9b (for t
uncorrelated
However,
plays
term
0.10
=
This
of
absence
leading
of the
role.
correlation
If
related
be
may
a
in this
gap
one,
the
«
decrease
the
such
and
the
first
of
is
bond
similar
character
by
small
of
of the
energy
gives results
metallic
checked
rather
is
screening
of the
model
bad
be
cannot
localization
complete
a
correlated
the
to
state
on
assumes
one
by the second neighbor
eV). In this aspect, the
term
model.
the
a
the
to
these
salts.
on
finite
calculations
systems.
Quasi-regular
tsj
chain.
and ts~
electrostatic
0,15 eV
=
different
=
eV,
transfer
but
to
the
first
of the
contributions
correspond
would
parameters
The
0,10
a
integrals
neighbor
dimerized
are
V is not,
molecules
and
the
anions
less
than
T~,
that
temperature
and
since it is
are
is for
we
have
considered
additive.
the
used:
the
that
This
set
of
semi-conducting
regime.
The
Hubbard
model
gives identical
(see for example
results
to
the
case
of
dimerized
salts
which
has
been
Fig. 4). In particular, the Es~ decrease by U is
of the
variation
of the one-particle self-energy
renormalization
factor zj (in the
reminiscent
in the g-ology
notation
of Solyom [52])
evaluated
continuum
model.
This
factor
corresponds
renormalization
of the dispersion
and
incorporates
local
and
the
long range
to a
energy,
interactions, and the stack
dimerization
Coulomb
(see for example [53]). It is proportional to
the
level and it has been
Fermi
shown [18] to be
the single particle density of states
at
of a finite g~, as
significantly depressed due to the
in the
(TMTTF)~X
met
presence
compounds. The single transfer energies Es~ and zj are related, because both account for the
the
localization.
effect of the
dimerization
mediated
by the
correlation
However, it is not
on
possible to
obtain
relationship
between
the
results,
because
the
factor
two
exact
an
zj~ might also include the effect of the many-body effects on the energy of the bond
description of the electronic system, in
Est. Thus, the DVB approach leads to a more
accurate
distribution
of the
electron
density on the various
bonds of the system.
of the
terms
Figure 15 shows that the effect of V is larger on 52 than on Sl until V is larger than 0A eV,
dimerized
The
maximum
of
dimerization
for
similarly to the
0.3eV<
occurs
case.
This
domain
corresponds to the values of V deduced from the experiment. The
V
0A eV.
the
only by 396 for 0< V~<
ratio Esj/Es~
decreases
effect
of V~ is less
important:
by 80 9b in the
V/2
Hiickel
model, Esj/Es~ is 1.6 and
increases
correlated
0.3 eV.
In the
from a small
decrease (2 9b) of
0.15 eV.
This
results
regime : U
1.5 eV, V
0.3 eV, V~
is
the
correlation
Esj and a large decrease of Es~ (459b). In the quasi-regular
systems,
discussed
previously
<
=
=
=
«
selective
»,
as
in
the
dimerized
=
salts.
M
APPROACH
VALENCE-BOND
6
3/4
OF
SYSTEMS
FILLED
877
3,2
3,o
2,8
/Es2
Esi
2,6
2,4
2,2
O,O
O,2
Fig.
ts~
rev)
ground
integral
or
slightly
a
susceptibility
section,
the
it
of
value
smooth
The
The
effect
of
Table
VII.
(N
=
the
of
V in
quasi-regular
the
behavior
of
1.5
U
=
I-I
infinite
the
of
a
(tsj
systems
0.15eV
=
a
of
chain
spins with
the
eV,
of the
differs
limit,
so
to
of
the
semi-conducting regime
integrals due to the
in
the
2
weakening
that
it is
not
possible
interdimer
to
relate
this
bond.
this
transfer
mean
of
changes
salts is
anion-cation
from
derived
cases
of the
these
in
transfer
triplet
a
results
integrals
transfer
temperature
with
modelled
assumption
results
The
increasing
:
are
the
not
localization
gap.
temperature
susceptibilities
x
(300 K)
(uem,cgs/mole)
quasi-regular
in
=
0.3
eV
tsi (eV)
ts2 (eV)
0,15
0.10
9.0
0.17
0.12
8.1
0.20
0.15
7.3
0,15
0,10
8.0
10-4
10-4
10-4
=
0,4
V
the
only
interaction.
V/2).
V~
eV, V
dimerization
metallic
a
appreciable
an
Room
8 ;
from
correlation
the
extrapolable to
the opening
to
=
follows
x
dimerization
induces
dimerization
U
function
a
that
the
appears
susceptibility.
the
transition
change in the
a
as
eV).
of x less than 20 K [8]. These
data
be reproduced
cannot
The 300 K
calculated
in
increase
given
table
The
of the
VII.
x are
decrease
of U lead to a
decrease
of x. By comparison
with the
state.
preceding
salts
1.5
=
maximum
the
by
U
low T, the
At
of
dimerization
Electronic
15.-
0.10 eV ;
=
O,6
O,4
V
eV
=
X
(3°° K)
0,17
0,12
7.2
0.20
0,15
6.9
10-4
10-4
10-4
t
878
JOURNAL
PHYSIQUE
DE
M
I
6
Conclusion.
has
It
been
This
model
the
within
based
the
on
regular
or
behavior
from
an
site
molecular
localized
the
for a strong
localization
effect
account
may
hanfiltonian
describing a 3/4 filled
Hubbard
extended
allows
salts
when
a
correlation
the
similar
interactions
understanding
better
phenomelogical
more
involves
and
This
structures.
of the
discriminates
method
DVB
correlation
is
dimerized
chain
that
shown
electronic
approaches
is in
for
in
the
origin
of the
the
site
band.
of
cases
of
intermediate
the
which
of the
spin
the
This
range.
made
is
of
the
dimer.
Providing
intrasite
that
the
correlation
electronic
taken
is
core
leads
term
into
less
values
to
than
calculation
the
CND02
account,
which agree with
of
the
deduced
those
2 eV
from
intersite
larger than what is commonly retained, due to the
terms
are
semi-empirical
CND02
method
electrostatic
for long range
interactions.
A
sensible
parametrization of this method
should yield better
results.
more
of
dimerized
salts, the
(interdimer) bond is even
weakened
In the
weaker
by the
case
while
the
correlation,
bond
is only slighly
modified.
Conceming the magnetic
stronger
properties, a comparison of the theoretical and experimental results shows that the second
neighbor intersite term is an important parameter. The value of the 300 K susceptibility, the
maximum
of x (T) and the
which it occurs,
fairly well reproduced by the
temperature
at
are
calculations.
the screening of the first
DVB
When
neighbors'
interaction
by the second
electrostatic
neighbors is taken into
the
of these
salts
corresponds to
account,
structure
isolated
uncorrelated
dimers
with 3 electrons
and
each, so that the localized regime could
on
correspond to a BOW state. Through the charge
correlation
functions, the DVB
method
additional
information
provides some
in
of
spatial
correlation
of
the
electrons.
terms
inclusion
of the regular salts, the
of the
anion-cation
interaction
renormalizes
In the
case
transfer
integrals. Going from a regular to a quasi-regular model, where it is sufficient to
the
consider
only dimerized
transfer
integrals, allows us to simulate the
localization
observed
experiment.
inadequacy of
The
the
when
the
case,
but
the
to
The
DVB
induce
some
smaller
a
extent,
shows
formalism
large
behavior
The
decreases.
temperature
due
to
the
localization
the
effect
effects,
of the
latter
model
non-dimerization
of the
of
intermediate
depending
on
is
the
sinfilar
correlation
the
structure
of
dimerized
potential
which
the
the
to
intersite
is
term.
sufficient
to
stacks.
that
of the DVB
the size
limitation
of the complete
basis
extrapolation
the
infinite
of
the
results
is hardly
to
system
severe.
conceivable, and the prevision of a gap opening, related to the conductivity
is
measurements,
possible. The study of the optical properties of the 8- and 12-site rings would be quite
not
the absorption
useful in order to
relate
frequencies of the charge transfer
spectra to the
correlation
Finally the exact DVB results may constitute a reference for
different
parameters.
approximate
of the
solutions
hamiltonian.
This, in turn,
would
model
allow
more
an
evaluation
of the properties of
extended
systems and, particularly, a study of the effect of the
interchain
interactions
in the
competition
different
between
the
ground states.
However,
formalism
it
be
may
is
noted
The
Acknowledglnents.
It is
a
pleasure
to
with
Z.G.
method
performed
Centre
thanks
National
acknowledge
Soos,
to
the
S.
Centre
Universitaire
fruitful
Ramasesha
de
Sud
discussions
and
Comp6tences
de
Calcul
about
the
S.Mazumdar.
en
Calcul
(CNUSC,
Diagrammatic
The
Nurnbrique
Montpellier,
calculations
Intensif
France).
Valence
Bond
have
(C3NI)
been
at
the
M 6
APPROACH
VALENCE-BOND
3/4
OF
879
SYSTEMS
FILLED
References
[Ii
JtROME
[2]
Proceedings of the
Tiibingen (FRG),
[3]
DELHAES
D.,
P.,
D.,
[4]
[6]
[7]
[8]
[9]
[10]
[I Ii
[12]
[13]
[14]
[15]
[16]
II?]
J. J.,
NIGREY
Inorg.
France
France
28
(1989)
of
41 (1980) L-95.
Synthetic Metals,
B.,
HILTI
(1990)
51
M. A.,
BEND
Chem.
A.,
FRITSCH
Phys.
J.
M.-H.,
WHANGBO
P. J.,
in
L.,
DucAssE
Phys. Left.
Technology
Synth. Met.
J.
and
l179 ;
A. M.,
KtNI
MAYER
C.W.,
SCHULTz
A. J.,
4516.
H., KINI A. M., CARLSON K. D., GEISER U., KwoK W. K., THOMPSON
M., REN J. and WHANGBO M.-H., Inorg. Chem. 29 (1990) 1659.
M. V.,
KoNoNovIcH
P. A.,
KARTSOVNIC
YAGUBSKn
E. B., SHCHEGOLEV I. F., LAUKIN V. N.,
Zh. Eksp. Tear. Fiz. 39 (1984) 12 ; JETP
A. V, and
Lett.
ZVARYKINA
BURANOV L. I., Pis'ma
39 (1984) 12.
JtROME
D, and
SCHULTz
H. J., Adv. Phys. 31 (1982) 299.
NozAwA
K., SUGANO T., KINOSHITA M., SATO S.,
URAYAMA
H., YAMOCHI H., SAITO G.,
OSHIMA K.,
KAWAMOTO
A. and TANAKA, J. Chem.
Lent. (1988) 55.
Low-Dimensional
and
Crystalline
Materials,
P.Delhaes
CouLoN
C., Organic and Inorganic
Eds. ~Plenum Press)
NATO
ASI
168 (1987) 201.
M. Drillon
Series
Chelnistry and Properties of Materials
with
Quasi-OneMORET R, and
POUGET J. P., Crystal
Dimensional
Structures, J. Rouxel Ed. (D. Reidel Publishing Company) 1986, p. 87.
K., J. Phys. France 44
CREUzET F.,
D., FABRE J. M. and
BECHGAARD
PARKIN S. S. P.,
JtROME
(1983) 975.
K., J.
AUBAN P.,
JtROME
BECHGAARD
D., LERSTRUP K., JOHANNSEN I., JORGENSEN M. and
Phys. France 50 (1989) 2727.
HUDSON B. S., KOHLER B. E. and
States, E. Kim Ed. (Academic, NewSCHULTEN K., Excited
York) 6 (1982)
and
references
therein.
Chem. Phys. 27 (1957) 984
MCCONNELL
H. M. and
CHESNUT
D. B., J.
CARRINGTON
A. Q., Rev.
Chem.
Sac, 17 (1963) 67.
MEHRING
M., GRUPP A., HOPER P. and KASS H., Synth. Met. 28 (1989) D399.
Association, R. Foster Ed. (Academic,
KLEIN D. J.,
Molecular
New-York) 1
Soos
Z. G. and
(1975) 1.
and
inorganic low
GALLOIS
B,, Organic and
DucAssE
L,,
ABDERRABBA
A., FRITSCH
A.
dimensional
crystalline materials, P. Delhaes and M. Drillon, Eds.
NATO
ASI
Series
168
(1987) 313.
CARON L. G, and
BOURBONNAIS
C., Physica 143B (1986) 453 ;
C., WzIETEK P., CREUzET F., JtROME D., BATAIL P, and BECHGAARD K., Phys.
BOURBONNAIS
E.,
Rev.
[18]
II 9]
and
published
be
to
Science
on
G. C.,
PAPAVASSILIOU
K.,
BECHGAARD
S.,
FLANDROIS
NovoA
J. M,
A.,
M.
BEND
J.
[5]
M.,
EVAIN
WILLIAMS
and
M.
Conference
September 1990,
J.,
and
J.
RIBAULT
International
AMIELL
ZAMBOUNIS
JUNG
A.,
MAzAUD
H.
J.
Lett.
C.,
CouLoN
(1989)
62
J.,
V.
EMERY
WANG
WILLIAMS
BRUINSMA
1532.
and
R.
LAVERSANNE
BARISIC
R., AMIELL
J.
S., Phys.
and
Rev.
Lea.
48
(1982)
P., J. Phys. C
DELHAtS
1039.
Solid
:
Stale
Phys.
19
(1986)
L-753.
[20]
[21]
[22]
HIRSCH
J.
E.
and
SCALAPINO
EMERY
V.
J.
and
NOGUERA
For
recent
a
review
Structure,
references
[23]
[24]
[25]
[26]
[27]
Soos
Z.
G.
MAzUMDAR
RUMER
see
:
Soos
Klein
D.J.
D. J., Phys.
C., Phys. Rev.
Z.
and
G.
and
827
Rev.
Left.
60
(1983)
(1988)
RAMASESHA
N.Trinajstic
Eds.
S.,
7169
29
(1984)
5554.
631.
Valence
(Elsevier,
Theory and
Bond
Chemical
Amsterdam,
1990) p.81 and
therein.
and
S.
RAMASESHA
and
DIXIT
S.
S., J. Chem. Phys. 90 (1989) 1067.
N., Phys. Rev. B 34 (1986) 3683.
WEYL H.,
Nachr.
Ges.
Gbitingen
Wiss.
G., TELLER E. and
S., J. Camp. Phys. 45 (1982) 100.
R., MENEGHETTI
M., PEDRON D. and
Math.
Phys.
27
(1988)
Kl
(1932)
RETTRUP
Bozio
PECILE
C., Synth.
Met.
B109.
499.
880
[28]
[29]
[30]
JOURNAL
K.,
YAMAJI
PARISER
S.
PARR
Farad.
413.
27 (1988) A105.
Phys. 21 (1953) 466 ; 21 (1953)
(1953) 1375.
S., Synth.
Met.
Chem.
J.
Sac.
49
767 ;
M., HOARAU J., PESQUER M., GALLOIS B. and
Phys. 19 (1986) 3805 ;
Bordeaux
PhD Thesis,
University (1987).
State
M.,
M.-H.,
WHANGBO
G.,
R.
(1987)
61
M 6
I
ABDERRABBA
Solid
ABDERRABBA
[32]
Commun.
RAMASESHA
Trans.
J.
C
State
and
and
R.
A.,
DUCASSE L.,
POPLE
[3 Ii
Solid
MAzUMDAR
PHYSIQUE
DE
WALSH
M.,
W.
HADDON
C.
R.
and
F.,
WUDL
Solid
J., J. Phys.
GAULTIER
Commun.
State
43
(1982)
637 ;
Thesis, Tokyo University (1985)
M., J. Phys. Colloq. France 44 (1983) C3-847.
C. S.,
review
JACOBSEN
Low-Dimensional
see ;
T.,
MORI
GRANT
[33]
For
a
D.
[34]
[35]
PhD
P.
Jdrome
DELHAtS
L.
and
P.
H.,
TAJIMA
and
Caron
(Plenum Press)
Eds.
C.,
GARRIGOU-LAGRANGE
M.,
TAMURA
H.,
KURODA
MoRi
Phase
ASI
Semi-Conductors,
and
(1987)
(1988) 27.
B155
Transitions
and
T.
Conductors
NATO
13
H., Bull.
INoKucHi
p.
253.
Chem.
Sac.
(1987)
801.
Jpn 63 (1990)
538.
[36]
[37]
[38]
[39]
[40]
MAzUMDAR
S.
KAsowsKi
R.
K.,
OSHIMA
POPLE
J.
HEEGER
A.
KONDO
K.,
FRITSCH
A,
and
J.,
Conducting
Press, 1979) p.
SODS
Physica
and
L.
of
R.,
B
2810.
State
Chem.
H.,
Approximate
Commun.
29
62
(1990) 360.
YAMOCHI
H.
and
G., Phys. Rev.
SAITO
B 38
molecular
orbital
Devreese,
R. P.
(McGraw-Hill,
theory
New-
104.
ID
Mol.
L.,
solids, J. T.
60
Phys.
(1988)
20
and
V. E.
(1971)
Solid
176.
Systems
Lower-Dimensional
State
Doren
1013.
AMIELL
J.,
and
Molecular
press
Intemational
the
(FRG),
DUPART
E.,
September
DELHAtS
Devices,
Conference
1990,
Commun.
P.,
NATO-ASI,
Science
on
to
and
published
be
MORAND
(1986) 765.
MCCONNEL
H. M., J. Chem. Phys. 43 (1963) 3780.
[49] Soos Z. G. and
Soos Z. G., Synth. Met. 1 (1979) 77.
S. and
MAzUMDAR
[50]
Bordeaux
University (1987).
[51] LAVERSANNE R., PhD Thesis,
[52] SOLYOM J., Adv. Phys. 28 (1979) 201.
[53] BARISIC S., J. Phys. Collogue France 44 (1983) C3-991.
[54] GRANIER T., GALLOIS B., DUCASSE L., FRITSCH A. and FILHOL A., Synth. Met.
MINI
HUzINAGA S., ANDzELM J., KLOBUKOWSKI
GAMESS
with a basis
[55] Program
Basis Sets for
Molecular
Gaussian
ANDzELM E., SAKAI Y. and TATEWAKI H.,
(Elsevier, Amsterdam, 1984).
[56] KLEIN D. J. and SEITz W. A., Phys. Rev. B lo (1974) 3217.
MANIGAND
Van
781.
(Plenum Press) in the
A., Proceedings of
FRITSCH
Synthetic
Metals,
Tdbingen
:
C.,
Evrard
69.
1989
CouLoN
C.,
G.,
Phys.
98 (1980)
DUCASSE
and
LAVERSANNE
Z.
Mod.
Rev.
Technology
Synth. Met;
[48]
Solid
Inorg.
URAYAMA
L.,
D.
Highly
Spetses (Greece),
DUCASSE
H.,
(1981)
833
1397.
C. B.~
M.-H.,
INOKUCHI
BEVERIDGE
(Plenum
D.
KLEIN
SOMMERS
and
WHANGBO
T.,
Rev.
(1963)
39
A., Physica 1 (1933)
T.
A. J.,
Eds.
[44]
[45]
[46]
[47]
and
KOOPMANS
HEEGER
M.
and
G., Phys.
1970).
York,
[42]
[43]
Z.
Phys.
938.
A,
J.
V.
MoRi
(1988)
[41]
Soos
Chem.
WEGER
J..
KOBLER
and
R., J.
HOFFMANN
J.P.
in
and
58
24
(1988)
M.,
343.
RADzio-
Calculations