Characterization of the Fermi surface of BEDT-TTF4[ Hg2Cl6] .PhCl by electronic band structure calculations

(1)

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Characterization of the Fermi surface of BEDT-TTF4[

Hg2Cl6] .PhCl by electronic band structure calculations

Luis Veiros, Enric Canadell

To cite this version:

Luis Veiros, Enric Canadell. Characterization of the Fermi surface of BEDT-TTF4[ Hg2Cl6] .PhCl by electronic band structure calculations. Journal de Physique I, EDP Sciences, 1994, 4 (6), pp.939-947.

�10.1051/jp1:1994237�. �jpa-00246956�

(2)

Classification Physics Absb.acls

71.25P 71.45L

Characterization of the Fermi surface of BEDT.

TTF4[Hg~cl~].Phcl by electronic band structure calculations

Luis F. Veiros

(')

and Enric Canadell

(2)

(~) Centro de Quimica Estrutural,

Departamento

de Engenhana Quimica, Instituto

Superior

Tecnico, P-1096 Lisboa Codex, Portugal

(2) Laboratoire de Chimie

Théorique

(*), Université de Paris-Sud, 91405 Orsay Cedex, France

(Received 19 November 1993, ievised 2 Februaiy 1994, act.epted15 Februaiy 1994)

Abstract.

Tight-binding

band _structure calculations for the _room temperature structure of

BEDT-TTF41Hg2CI6"Phcl

show the _existence of closed electron and hale Fermi surfaces, _in agreement with the 2D metallic

conductivity

of this sait. It _is shown that these closed Fermi surfaces result from the

hybridization

of two hidden lD Fermi surfaces. However, _our

study

aise shows that _a transition associated with either _a usual _or _a hidden

nesting

type ^mechanism is

unhkely.

This

explams

why this sait _retains _its metallic properties ^without _any

resistivity anomaly

down _to 1.3 K. Our study _suggests that

BEDT-TTF41Hg2C16"Phcl

is _a somewhat anisotropic 2D semimetal and should exhibit Shubnikov-de Haas oscillations corresponding to a cross-sectional

area of

approximately

13 fb of the first Brillouin _zone.

Charge

transfer salts of the orgamc donor molecule

bis(ethylenedithio)-tetrathiafulvalene (BEDT-TTF, 1)

have led to more than twenty

superconductors Il -3].

However,

superconduc- tivity usually

competes ^with ^different ^electronic instabilities which _can

partially

or

totally destroy

the metallic properties ^of many of these

charge

transfer salts. Some of these instabilities _are

largely

determmed

by

the

topology

of the Fermi surface. It _seems quite ^clear

by

now

[1-3]

that _even _minor modifications in the

crystal

structure of these salts _can have

large

effects _on their Fermi surface and

hence,

_on their

physical properties. Thus,

there _is _a need to understand how the

crystal

structure and Fermi surface of these salts _are related. For this

S s s ^~

= l

~~~s~ ~s~l~~

BEDT-TiF

(*) CNRS URA 506.

(3)

940 JOURNAL DE PHYSIQUE I N° 6

purpose extended Hückel

tight-binding

band structure studies have been of

major

value

[4].

Recently, magnetoresistance

studies _on

high purity crystals

^of ^BEDT-TTF ^salts have

given

important information

concerning

the Fermi surface of _some of these

organic

metals

[5-7].

However, fuit

exploitation

of these results is sometimes difficult without _a

previous knowledge

of the

general shape

of the Fermi surface. In

general,

the main results of the

magnetoresistance

studies _are in excellent

agreement

^with ^the ^calculated ^extended ^Hückel ^Fermi ^surfaces.

Thus,

extended Hückel studies of the Fermi surface of BEDT-TTF metallic salts _are not

only

useful

in

understanding

the

origin

of their transport

properties

but aise in

providing

a basis for the

interpretation

of the magnetoresistance measurements and in

building

_a link between the Fermi surface and the

crystal

structure.

Recently, Lyubovskaya

et ai.

[8]

have

reported

the

synthesis

of _a _serres of

organic charge

transfer sains with the

general

formula

BEDT-TTF~,[HgX~]~

PhX

(X

=

Cl, Br).

Four of these salts _are menais _at _room

temperature [8-9]. However,

their low temperature ^behaviour seems to

depend

on the _nature of the anion and the solvent. For

instance,

whereas BEDT-

TTF4[Hg~clô].Phcl

is _a metal down _to 1.3 K

[8-10], BEDT-TTF41Hg~Brô].PhBr undergoes

a metal to semiconductor transition _at 125 K

Il Ii

Here _we report our results conceming the

electronic band _structure and Fermi surface of

BEDT-TTF41Hg2Cl~].Phcl

for which the

crystal

structure has been

recently reported by D'yachenko

et ai.

Il 0].

Our

tight-binding

band

structure calculations

[12]

_use an extended Hückel Hamiltonian

[13]

and a

double-(

basis

set

[14]

for ail _atoms except

hydrogen.

It _tums out that

BEDT-TTF4[Hg2Clô].Phcl

has _a

pecuhar

Fermi surface and it _is a

likely

candidate for the observation of

angular magnetoresist-

ence oscillations.

Crystal

structure and donor donor interactions.

The

crystal

structure of

BEDT-TTF4[Hg~cl~].Phcl loi

contains

layers

of the donor BEDT-

TTF molecules

altemating along

the _a direction with

layers

of the

[Hg~clô]2-anions.

The

aurons occur as dimeric _units and _two ends of the dimer make _a weak interaction with _a solvent

molecule

leading

to

[Hg~cl~ Phcl](

_units. A

perspective

view of _a donor molecule

layer

^of

BEDT-TTF4[Hg~clô].Phcl (in

the

crystallographic

bc

plane)

is shown in

figure

la~ Each donor molecule of

figure

la is viewed

approximately along

the direction of its central C=C bond. The repeat ^unit ^of ^this ^slab ^contains

eight

donor molecules pairwise related

through

inversion centers,

resulting

_m four symmetry

inequivalent

BEDT-TTF molecules

(A, B,

C and

D in

Fig. lb).

As _can be

easily

seen from

figure

la the four different BEDT-TTF molecules

belong

to two different conformational types

(A, C)

and

(B, D).

Structurally,

the slab of

figure1

_can be described _as _a _serres of

parallel

inclined stacks running

along

the

(b

+ c direction

(hereafter designated

_as the _a

direction).

The four different

BEDT-TTF molecules form _a sequence B-A-C-D

along

^the ^stack ^and _every stack is related _to its

adjacent

ones

through

inversion _centers.

Altematively,

the slab of

figure

_can be descnbed

as a serres of

step-chains running along

the

ydirection.

This arrangement gives rise _to

14different

types

^of interactions between donor molecules: 4

along

the adirection

(ai.

_a4 in

Fig.

lb and

Tab.1),

5

along

the p direction

(pj p~),

and 5

along

the y direction

(yj y~).

Short mtermolecular S... S contacts smaller than 3.85

À _(see

_Tab.

_I)

are observed for both the

step-chains (.. yj-y~-y~..)

^and the mclmed stacks

(...

_a _-a~-a _~-a

~

),

as well _as for the w-type ^chains

(... p~-p~-p j-p

~ running

along

the p

direction

(see Fig.

l).

Despite

some differences _in the intramolecular geometnes, the calculated energies of the

highest occupied

molecular orbital

(HOMO)

of the four different BEDT-TTF molecules _are very similar.

Consequently,

the HOMO bands of the donor molecule

layers

will result from _a strong mixing of the HOMOS of the four different donors. In order to discuss the rote of the

(4)

'

£X

' 7

' '

~f~

^,'

~~~Ù

1'

'

'~

/

~

~~Î~

'-

"",C ,'

~ lj~

'~

~

1' "'

Ù

/

~ i~

Ôl'

~~Î~

, /

~

', /

',

",

/

~ ~Î~~

/

"

", _/ '

~ ~

",,/

(a)

A c

= B _D

la '-

l' '''-fi (

_

~ ^/ / ^'

~/ ~

-..,~___ ÷A

_.~'

,

, c

/~

2 '1

[

~

/~

7~

%

'

/ D

~ ⁱ _; ^/

/~ Î~ fi"'Ù~"; Î

~/"~~..--. ^A

/~

¹³

~( ( %/~

f,

",,

B

~__~_

~o /^Iii D

e

', j?"'~

' ''- /

', /

' '- /

(b)

Fig. l. la) Perspective _view of _a BEDT-TTF layer of

BEDT-TTF41Hg~CIô

Phcl. Each molecule is viewed

approximately along

its central C C bond. lb) Schematic

representation

of

figure

la

showmg

the different types ^of ^molecules ^and ^donor., ^donor intermolecular interactions.

different types ^of ^chains ⁱⁿ ^the transport properties ^of

BEDT-TTF4[Hg~Cl6l.Phcl,

_we

calculated the

p~o~~_~o~~

interaction

energies[15] corresponding

to the 14different

donor... donor interactions of the BEDT-TTF

layers.

^The ^results are

reported

in table I. The strongest interaction

energies

_are those associated with the

step-chains running along

the _y

direction

(0.21-0.30

eV). Even if the shortest sulfur... sulfur contacts are those of the chains

running along

the p

direction,

the w-type interactions between the HOMO orbitals

imposed by

the nature of these chains result _in reduced interaction energies

(0.Il-0.15

eV). These

interactions _are however

considerably

stronger ^than ^those ^within ^the ^inclined ^snacks

along

the

a direction

(0.04-0.09 eV).

Thus, from the electronic viewpoint, ^the ^BEDT-TTF ^slabs of

JnLR~'L »F PHY~'QLL' T 4 ~ 6 JU'r1,'4 4

(5)

Table I. S... S distances smaller than 3.85

À

_and _absofute _i,ali~es

of

trie

p~o~o_~~~o

mteractmn eiieigies

(eV) foi-

the

dij$eient

BEDT-TTF...BEDT-TTF inteiac.tioiis _m

BEDT-TTF~[Hg~cl~]

Phcl

(see Fig.

l

for labelliiig).

Interaction type ^S ^S ^distances

(À) p~o_,j~

(eV)

a-type

ai 3.820 0.045

a~

3.847,

3.855 0.059

a~ 3.800, 3.841 0.085

a~

(4.023, 4.026)a

0.038

P-type

pi 3.395,

3.403, 3.430, 3.514, 3.809 0.133

p,

^3.411

(x 2),

3.589

(x 2),

3.759

(x 2)

0.148

pî _3.463,

_3.470,

_3.480, _3.534,

_3.826 _0.138

p~

3.400, 3.479, 3.575, 3.576, 3.888 0.131

p~

^3.408

(x 2),

3.616 (x

2)

Ù-118

y-type

vi

3.580, 3.647, 3.764,

3.840, 3.969 0.277

Y2 3.599, 3.691,

3.716,

3.721 0.234

Y~ 3.821 (x

2),

3.855 (x

2),

3.856 (x

2)

0.287

Y4 3.725 (x

2),

3.779, 3.789 0.295

y~ 3.676 (x

2),

3.853 (x

2)

0.213

id) ^Shortest ^S... ^S contacts of this interaction type.

BEDT-TTF41Hg~Clô].Phcl

seem to be best described _as _a series of

step-chains along

the _y direction interacting

through

weaker _w- and «-type contacts

along

the other directions of the slab.

It is worth

pointing

out that the _neat

partitioning

of the

p

interaction energies of table _in three groups is not a

peculianty

of the present ~ystem, The interaction

energies

calculated for

other BEDT-TTF slabs which

geometncally

_can be considered to be built from

parallel

indined stacks like

BEDT-TTF~ReôSe~CI~[guest] (guest=DMF,

THF, dioxane)

[16]

BEDT-TTF~XCI~, H~O (X

=

Ni [17a], Cu

[17b, ci)

_or

BEDT-TTF~[M(CN)~] (M

= Ni,

Pt)

Il 8],

ail have the _same characteristics

(a)

strong ^values

(0.2-0.3 eV)

for the interactions

along

the

step-chains, (b)

medium values

(0.15-0.11 eV)

for the interactions

along

the w-type

chains,

and

(c)

smaller values

(<

0.1 eV for the interactions

along

the inclined chains. This _is _in clear

contrast with the situation for the BEDT-TTF slabs built from

parallel

columnar snacks like

BEDT-TTF~ReO~ [19], p-BEDT-TTF~X (X

= I~, IBr~)

[lsa]

_or

BEDT-TTF41M(C204)il (M

= Cu, Pt)

[18],

for which the interaction energies associated with the donor,.. donor

interactions

along

the columnar chains _are

always by

far the stronger ones.

Thus,

in

general,

the columnar snacks _are the natural

building

blocks for the second type of BEDT-TTF

slabs,

but

they

are the

step-chains

which _are the appropnate ones for the first type ^of BEDT-TTF

slabs. A more detailed account of these results will be

presented

elsewhere

[17b].

The

(6)

distinction is however

important

in the _context of the present ^work ^because ^it ^has a

key

^rote ⁱⁿ the discussion of

possible

hidden Fermi surface

nesting

mechanisms

[18, 20].

Band structure and Fermi surface.

The

analysis

of the previous section makes clear that there _are strong interactions between the

BEDT-TTF HOMOS

along

the

step-chains

and that the interactions between those of the

different

step-chains

_are

quite

^sizeable. This suggests ^that

BEDT-TTF~ [Hg~cl~

Phcl should be _a somewhat

anisotropic

two-dimensional

(2D)

conductor. The repeat ^unit ^of ^the ^donor ^slabs contains

eight

BEDT-TTF molecules _so that there will be

eight

HOMO bands. With the formai oxidation

required by

^the stoichiometric

formula, (BEDT-TTF )( +,

there _are twelve electrons per ^unit cell _to fill the

eight

HOMO bands.

Thus,

it is not clear if the system ^should ^be a 2D

semiconductor or a 2D

menai,

_i e., whether there is _or _non _a band gap between the sixth and

seventh HOMO bands. The calculated band structure for the BEDT-TTF slabs of

BEDT-TTF~[Hg~cl~]

Phcl is shown _in

figure

2a. It is clear that the sixth and _seven bands (from

bottom) slightly overlap

_so that the system ^is a semimetal. The calculated Fermi

surface,

shown _in

figure 2b,

contains electron

pockets

centered _at M

(or

^the

equivalent point S)

and hole

pockets

centered _at Z. Both the electron and hole

pockets

are closed _so that the system

should have 2D metalhc

conductivity,

in agreement ^with ^the

experimental

results.

The Fermi surface of

figure

2b is quite ^unusual ^and ^contains a nested

portion.

As shown in

figure

2c, this Fermi surface _can be

thought

of _as

originating

from the weak

hybridization

of _an almost ideal lD electron Fermi surface

along

the

(b*

+

c*) direction,

and _a

warped

lD hole Fermi surface

along

c*. Detailed examination of bands _a and b in

figure

2a shows that this _is

actually

the _case. For instance,

along

r

~

M,

bands _a and b result from _a

weakly

avoided

crossing

between _a very flan band and _a

dispersive

_one

(The

intended band

crossings

_are

indicated with dots m

Fig. 2a).

However, band _a _is

quite dispersive along

^the r

~

S direction

(although

this is masked

by

the fact that when

raising

in energy the band intends _to _cross the two next bands

leading

to the

belly

_appearance of the bands

along

this

fine). Thus,

band _a is _an mtended 1D band

along

_a direction

approximately perpendicular

to the

(b

^* + c.^* direction. If avoided

crossings

were

ignored,

this band would lead to the hidden ID Fermi surface

along (b*

+

c*)

of

figure

2c. It _is also easy to see that band b _at r

undergoes

an avoided crossing with band _a

along

^both r

~ Y and r

~ Z. If these avoided crossings were

disregarded,

band b

would be _a lD band

approximately perpendicular

to c*. However, the

dispersion

of this

intended band b

along

r

~ Z is greater than the

dispersion

of the intended band _a

along

r ~ M. This _means that band b is _an intended

pseudo

1D band and

consequently,

as shown _in

figure

2c, its associated hidden lD Fermi surface will be

slightly warped.

Once _it is realized that the Fermi surface of

figure

2b _can be deconvoluted into _two 1D Fermi surfaces, two questions come into mind.

First,

where _are in the structure the chains

leading

to the two lD Fermi surfaces of

figure

2c ?

Second, why

the system seems to be _immune to some

kind of Peierls distortion associated with these hidden lD Fermi surfaces ? The chains _in the

crystal

structure should be

perpendicular

to the direction of the hidden lD Fermi surfaces.

Neither the

step-chains

nor the w-type ^chains

(1.e.,

the chains associated with the strong donor... donor

interactions)

fulfill this condition. Let _us recall that there _are

eight

^donor

molecules per unit cell of the slab. Thus, there _are

eight

bands

resulting

from the combinations of the

eight

HOMOS of the unit cell. The

eight

combinations, must be such that

they

^make strong nearest

neighbors

interactions

along only

_one direction _to grue use to the hidden lD Fermi surfaces, due _most

likely

to the

special topology

of the lattice. Work is _in progress ^to

probe

a

possible relationship

between the

topology

of the lattice with inclmed stacks and the _occurrence of hidden nesting.

The nested portions in

figure

2b

(1.e.,

the flat portions

parallel

_to the b* ₊ c*

direction),

(7)

-8

uJ

-8

v r z r r

(a)

(b)

/ /

j' ^,' ^/ ¹

' 1' ' >' ,' ' ' ,~

' ,~~>," _,' ~'i ,,' i r ~,

~ '

'/ ,

&' ^/ ,' [,'

J~ '/ ~" ,,/ ^' ^,' ^~n

,"( ,' ,Ô ,' ' ~" ,'/

," ,f'

,

,,' ',' ,'

,,~~,,'

_'

," ^' ^' ,' ,'( _' ,' ,t /

,' ^/ ^' ^,' ^' ,' ,' i /

'

,)", '

Î,"

" /

,,'~

' ' ,' _'i _," ,' 1' _,'

' ~'

, ,,' , /" ,'

' / '' ' , é'

,' '/ >'

, , ,

' ,'/

"Î ,' ' ,,

' 'j

"','Î'

'

"'ÎÀ"'," ^,"'Î'

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~' ' ' ,' l'

,

' /

,' )" ' ' "

' /~

, ," ," ,~' ^,~ '

',' ,'

, ,' S' , , ,' , ,' ,'

~'

,'~'

^/ ^"

,f' '"',("

,'1 ' ' ,/ ,',

1','~

,,' ]" ,' ,,~>,' , ,,6 , ~/

,"'

_' ,' _," ,'$ ,' _," (" '

' ,' ,' >'

(c)

Fig.

2. (ai Dispersion relations for the HOMO bands of the donor slabs

in

BEDT-TTF4 ÎHg~CI~ Phcl, where the dashed fine refers _to the Fermi level. Dots _are used _to indicate the

intended band crossings discu~sed _in the _text. r, Y, Z, M and S refer to (0, 0). (h~/2, 0),

(0, _t */2 ). (h*/2, c*/2 and (- h~/2, _t */2 ), respectively. (b) Fermi surface associated with the partially filled bands of (a). (c) ^Hidden ID Fermi surfaces associated with (b).

(8)

represent

only

a moderate fraction of the Fermi surface. Thus the

driving

force for a

penodic

lattice distortion is

probably

small.

However,

_our

analysis

shows that the Fermi surface of

figure

2b _can be

approximately

deconvoluted into _two lD Fermi surfaces. In such _cases, it is essential _to

analyze

^if a

periodic

lattice distortion

(or

even a

spin density wave)

associated with

a hidden

nesting

mechanism

[18,

20,

21]

can occur. The concept ^of ^hidden ^Fermi ^surface

nesting [20]

_is that some weak local structural

changes, possibly slight displacements

of the BEDT-TTF molecules

perpendicular

to the stack direction, or

slight

rotations of the BEDT- TTF

molecules,

_can

modify

the relative

magnitudes

of the transfer

integrals, affecting

the

dimensionality

of the system ^and

ultimately leading

to the appearance of the otherwise hidden nested Fermi surfaces. Essential for this mechanism _is that the energy

gained by

the

penodic

lattice distortion (or the

spin density wave)

associated with the hidden

nesting

more than compensates the energy needed for the reduction of the interstack interactions. Thus,

only

when the system ^is

structurally prepared

to

readjust

the Fermi surface with

just

minor structural

changes,

it will

undergo

the structural transition

stabilizing

this hidden

nesting

vector.

BEDT-TTF~ReO~

_seems _to be _a system

undergoing

_a Peierls distortion

through

^this type ^of

mechanism

[20]. However,

there _are three _reasons

why

this mechanism is

unlikely

to be

effective in

BEDT-TTF~ [Hg~cl~

Phcl.

First,

the

hybridization

_gaps between the _two hidden

ID Fermi surfaces _are

quite

sizeable.

Second,

it has been

recently argued [18]

that,

independently

of the

magnitude

^of the

hybridization

_gaps, BEDT-TTF slabs built from columnar stacks are

structurally prepared

to sustain _a hidden nesting type ^mechanism ^but ^this ^is

non the case for those built from inclined columnar snacks. These two observations lead to the conclusion that the

energetic

cost for

readjustment

of the Fermi surface will be

quite

_important.

Third, there is _no _common

nesting

vector for the two hidden 1D Fermi surfaces.

Consequently,

even after read

justment

of the Fermi surface, the

driving

force for the

penodic

lattice distortion would _not be very strong. ^We ^conclude that a hidden

nesting

_type mechanism _is also

unlikely

and

thus, BEDT-TTF~[Hg~cl~]

Phcl retains ils metallic

properties

without any

resistivity anomaly

until very low temperatures.

The Fermi surface of

figure

2a contains closed electron and hole

pockets.

Since

BEDT-TTF4 lHg~cl~

Phcl is metallic down _to 1.3 K it should be

possible

to

study

its Fermi surface

by

magnetoresistance experiments. ^Ouf

study

suggests the existence of Shubnikov-de Haas oscillations

corresponding

_to _a cross-sectional _area of

approximately

13 % of the first

Brillouin _zone. Since this value has been obtained from the _room temperature structure, the actual value obtained from the low temperature measurements could be

slightly

different. Let

us note that the cross-sectional _area of the electron and hole Fermi surface

pockets

^is

stnctly

the _same. This _is _in _contrast with _recent results for the molecular

superconductor

BEDT-TTF~ReO~ H~O [?

Ii. In this sait, the electron Fermi surface consists of two symmetry related closed

pockets

with _a cross-sectional _area which is half that of the hole Fermi surface

pocket, leading

to the observation of _two different Shubnikov-de Haas

frequencies.

It _is also

worth pointing out that,

although

the Fermi surface of

figure

2a

corresponds

to a 2D

semimetal, our

analysis

of

figure

2b in _terms of two hidden lD Fermi surfaces suggests ^that

BEDT-TTF~[Hg~cl~]

Phcl should be somewhat

anisotropic,

with better

conductivity _along

the

perpendicular

to a direction between b* ₊ c* and c*.

Concluding

remarks.

Tight-binding

band _structure calculations for the _room temperature structure of

BEDT-TTF4 lHg~cl~

Phcl show the existence of closed electron and hole Fermi surfaces, _in

agreement ^with ^the ^2D ^metallic

properties reported

for this sait. These Fermi surfaces exhibit

some nestmg ^features but

they

_seem to be non strong

enough

to lead to a

periodic

lattice distortion. However, our

study

also shows that these closed Fermi surfaces result from the

(9)

hybridization

of two hidden lD Fermi surfaces. This observation suggests ^the

possibility

of _a

periodic

lattice distortion

through

a hidden nesting type ^mechanism. ^However it is shown that

there _are structural and electronic factors

against

this mechanism. Thus,

BEDT-TTF~ [Hg~cl~

Phcl exhibits metallic

properties

down _to 1.3 K without any

resistivity anomaly. Magnetoresistance

experiments ^and a detailed

study

of the

resistivity anisotropy

would be

interesting

in order _to further caracterize the unusual Fermi surface of this sait. In

view of the present results, it would be very

interesting

to

study

the _structure and

physical properties

of the other sains with

general

formula

BEDT-TTF,,,[HgXi]

PhX IX

= Cl, BT

recently reported by Lyubovskaya

et ai.

[8].

Acknowledgments.

L.F.V. thanks

Fundaçao

Calouste Gulbenkian for _a travel grant.

References

[1] Williams J. M., Ferrare J. R., Thom R. J., Carlson K. D., Geiser U., Wang H. H., Kini A. M.,

Whangbo

M.-H.,

Organic Superconductors

(Prentice Hall _: New Jersey, 1992).

[2] lshiguro R., Yamaji K., Organic

Superconductors (Springer-Verlag

Berlin, 1990).

[3] Williams J. M., Schultz A., Geiser U., Carlson K. D., Kini A. M., Wang H. H.. Kwok W.-K., Whangbo M.-H.. Schirber J. E.. S<.ience 251 (1991) 1501.

[4] For _instance, _see chapter 8 of reference il].

[5] Tokumoto M., Swanson A. G., Breaks J. S., Agosta C. C., Hannahs S. T., Kinoshita N., Anzai M.. Tamura M., Tajima H., Kuroda H., Andersen J. R.,

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V. Z.

Kresin and W. A. Little Eds. (Plenum : New York, 1990), _p. 167.

[6] Wosmtza J., frit. J. Med. Phj~s. B 7 (1993) 2707.

[7] la) Kartsovnik M. V., Laukhin V. N., Pesot~kii S. I. Schegolev I. F., Yakovenko V. M., J. Phys. I Fianc.e 2 (1992) 89 _;

(b) Kartsovnik M. V., Kovalev A. E., Kushch N. D., J. Phys / Fiafic.e 3 (1993) II 87 _;

(c) Kovalev A. E., Kartsovnik M. V., Kushch N. D., Sand Stale Comm. 87 (1993) 705.

[8]

Lyubovskaya

^R. N., Afanas'eva T. V.,

D'yachenko

O. A., Gritsenko V. V.,

Mkoyan

Sh. G..

Shilov G. V., Lyubovskii R. B., Laukhin V. N., Makova M. K., Khomenko A. G., Zvarykina A. V., I=v Akad. Naiik. SSSR, Ser. Khim. (1990) 2872.

[9] Lyubovskaya R. N., D'yachenko O. A., ^Gritsenko V. V., Mkoyan Sh. G., Atovmyan L. O.,

Lyubovskii

R. B., Laukhin V. N., Zvarykina A. V., Khomenko A. G., Synlh. Met. 41-43 (1991) ^1907.

10]

D'yachenko

O. A., Gritsenko V. V., Mkoyan ^Sh. G., Shilov G. V., Atovmyan L. O., /=i>. Akad.

Naiik. ,ÇSSR, Ser. Khini. (1991) 2062.

iii Gritsenko V. V.,

D'yachenko

O. A., Shilov G. V.,

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R. N., Afanas'eva T. V.,

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12] Whangbo M.-H., Hoffmann R., J. Am. Cfieni. Soc. 100 (1978) 6093.

13] Hoffmann R., J. Chem. Ph»,i 39 (1963) 1397. A modified Wolf~berg-Helmholz ^formula (Ammeter J., Bürgi H.-B., Thibeault J., Hoffmann R., J. Am. Cheni. Soc, 100 (1978) 3686) _was used to

evaluate the

nondiagonal

_H~~ values.

14] Clementi E., Roetti C., Al. Nu<.l. Data Tables 14 (1974) 177. The exponents and parameters were

taken from

Whangbo

M.-H., Williams J. M.,

Leung

P. C. W., Bene M. A.,

Emge

T. M.,

Wang H. H., Carlson K. D., Crabtree G. W., J. Am Cheni. Soc., 107 (1985) 5815.

15] (a) Whangbo M.-H., Williams J. M., Leung P. C. W., Bene M. A., Emge T. J., Wang H. H., Inoig. Chem. 24 (1985) 3500.

(b) Williams J. M.,

Wang

H. H.,

Emge

T. J., Geiser U., Bene M. A., Leung P. C. W., Carlwn K.

D., Thora R. J., Schultz A. J.,

Whangbo

M.-H., Piog- Innig Chetn. 35 (1987) 51.

(10)

(c) Since overlap is

explicitely

included in extended Hückel calculations, these interaction energies (p ) should net be confused with the conventional transfer integrals il ). Although ^the two

quantities

are obviously related and have the _same physical meaning, the absolute values of p are somewhat greater ^than ^those ^of1.

(16] ^Pénicaud A., Boubekeur K., Batail P.. Canadell E., Auban-Senzier P., Jérome D., J. Am Chem.

Soc., ils (1993) 4101.

(17] la) Martin J. D., Canadell E., Fitzmaurice J. C., Slawin A. M. Z., Williams D. J., Woollins J. D., submitted for publication.

(b) Veiros L. F.. Canadell E., to be

published.

(c) Day P., Kurmoo M., Mallah T., Marsden C., Friend R. H., Pratt F. L., Hayes W., Chasseau D., Gaufrier J.. Bravic G., Ducasse L.,./. Ami. Cheni. Soc. l14 (1992) 10722.

(18] Martin J. D.. Doublet M.-L., Canadell E., /. Phj>.i. / Fiance 3 (1993) 2451.

[19]

Whangbo

M.-H., Bene M. A., Leung P. C. W.. Emge T. J., Wang H. H., Williams J. M., Solid Slale Conimiifi. 59 (1986) 813.

(20] Whangbo M.-H., Ren J., Liang W.. Canadell E., Pouget J. P., Ravy S., Williams J., Beno M., Dini,q Cheni. 31 il 992) 4169.

[2 Ii Kahlich S., Schweitzer D.~ Rovira C., Paradis J., Whangbo M.-H., Heinen I., Keller H. J., Nuber B., Bele P., Brunner H., Shibaeva R. P.. Z Phv.i. B, Cnfid Mal., _in press.