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Electronic structure of the pseudo-one-dimensional superconductor Tl2Mo6Se6 according to SCF scattered-wave Xα computations
Solid State Communications, Vol. A3,No.1, pp.19-23, Prin~ed in Great Britain.
1982.
0038-1098/82/250019-05503.00/0 Pergamon Press Ltd.
ELECTRONIC STRUCTUREOF THE PSEUDO-ONE-DIMENSIONALSUPERCONDUCTORTI2Mo6Se6 ACCORDINGTO SCF SCATTERED-WAVE Xa COMPUTATIONS A. Le Beuze and R. L i s s i l l o u r Laboratoire de Chimie Th~orique, L.A.C.N.R.S. n° 254, Universit~ de Rennes I - Beaulieu 35042 Rennes C~dex, FRANCE H. Chermette I n s t i t u t de Physique NuclQaire et (IN2P3), Universit~ de Lyon I , 43 Bd. du I I Novembre 1918 69622 Villeurbanne C~dex, FRANCE M. Potel, R. Chevrel and ~!. Sergent Laboratoire de Chimie Min~rale B, L.A.C.N.R.S. n° 254, Universit6 de Rennes I - Beaulieu 35042 Rennes C~dex, F~ANCE (Received 29 January 1982 by E.F. Bertaut) The e l e c t r o n i c structure of TI2Mo6Se6 has been investigated using the X~ c lus t e r approach. The ground-state eigenvalues show that the Fermi level l i e s in a single degenerated band which supports the experimental results. Contour maps show the anisotropic character of the wawe functions of this Fermi l e v e l . The metal-metal and metal-selenides i n t e r a c t i o n s have been discussed.
cluster is compensated by inclusion of a Watson sphere 9 with the same radius of the outer sphere (O.S.) and bearing a charge +2. The geometry used is an Mo6Se6 u n i t corresponding to the D3d point group symmetry with the z axis being in the c d i rection. Bond distances, atomic spheres r a d i i and atomic s t a t i s t i c a l exchange I0 ~ values are l i s t e d in table I. Extramolecular (O.S.) and in tersphere scaling parameters are obtained by averaging atomic ones. The basis of atomic o r b i tals includes spherical harmonics up to I=3 f o r Mo and O.S. and I=2 f o r Se. The achieved accuracy of s e l f consistency f o r the energies is no worse than ± 0.0001Ry.
TI2Mo6Se6, a new superconductor material hms been synthetised recently I and both i t s c r y s t a l l i n e structure 2 and i t s physical properties 3'4 show a speudo-one-dimensional character. Thus, the c r y s t a l l i n e structure is mainly characterised by the presence of one dimensional (Mo3Se3)~ chains formed by an i n f i n i t e stack of Mo3 and Se3 t r i a n g l e s in staggered positions and may be viewed as the result of a l i n e a r condensation of face sharing Mo6Se6 u n i t . The remarkable monodimensional character of the physical properties is e x h i b i t e d by the anisotro~y in normal state r e s i s t i v i t y ( o f the order of i0 J) and by the fact that the upper c r i t i c a l f i e l d is about 26 times higher than the perpendiculare ones3,4. The authors, therefore, conclude that this anisotropy is a r e s u l t of e l e c t r o n i c i n t r i n s i c e f f e c t s , probably related to the anisotropy of the Fermi surface and thus of the elect r o n i c i n t e r a c t i o n between the Mo3Se3 unit along the chain. So, i t is of i n t e r e s t to i n v e s ti g a te the e l e c t r o n i c structure of such m a t e r i a l . I t is the aim of this paper. For this purpose we have carried out computations using the Self-Consistent Field XmScattered Waves (SCF-Xm-SW)5 framework for an Mo6Se62- cluster. E f f e c t i v e l y , this method is a powerful and convenient approach f o r describing the e l e c t r o n i c structure of large inorganic molecules 6 and crystals 7. Moreower, we have recently shown that i t was s u i t a b l e f o r molybdenum chalcogenide c l u s t e r compounds8. The Xmmethod is used here in the standard " m u f f i n - t i n " approximation with s l i g h t overlapping atomic spheres. We merely considered the T1 ion as i o n i c charges i n t e r a c t i n g on the e l e c t r o nic levels by mean of the t o t a l charge assumed to be -2 in the p e r f e c t l y i o n i c case T I } Mo6Se62". The e f f e c t of the extranegative charge of the
Table 1
Geometric and X~ parameters.
Atomic distances d Mo.Mo i n t r a t r i a n g l e :
2.6630
d $e.Se
5.2310
intratriangle :
d intertriangle :
2.250
Sphere r a d i i and a parameters R Mo =
1.5261 ~
~ o = 0.70441
R Se =
1.6070 ~
aSe : 0.70638
R(OS)=R(WS)=4.8299 ~
19
~(0S)=~(IS)=0.70589
20
PSEUDO-ONE-DIMENSIONAL
We r e p o r t here some p r e l i m i n a r y r e s u l t s . X ~ ground s t a t e eingenvalues diagram o f an ~o~ ~Se2c l u s t e r is p i c t u r e d on the r i g h t p a r t o f f~gu L re I . In o r d e r to discuss the various metal-met a l and m e t a l - s e l e n i d e i n t e r a c t i o n s , r e s u l t s obt a i n e d f o r an Mo6 m e t a l l i c c l u s t e r (DRd symmetry) are also shown on the l e f t . Table I I presents an a n a l y s i s o f the charge d i s t r i b u t i o n o f the v a l e n ce l e v e l s in the various regions o f the Mo6Se6 u n i t ( a c c o r d i n g l y to the angular momentum c o n t r i bution to the t o t a l charge i n s i d e the atomic spher e s ) . The l e v e l s are l a b e l l e d according to the i r r e d u c i b l e r e p r e s e n t a t i o n s o f the D3d p o i n t group.
Mo6Se62-
Mo6 // 2a2g
,'
if
,/
~=mm
~l / Z
iI , II /
' . -" :/ " / .//'
-02-
/
/ i l~
/
3eg =::J
-a v
-O3.
>-.
lalU
2eu
2~
leu 2~cJ
-
-
,' /"
5c~u
,~' .." ."_,J'~,,_.... . . _"_ _
~ .11,u" "" / -~-
8eu 6cmu 7e 9 7eu
,/
/iI / t i "
/
/
--"
";~-
"- - - "/"-
2e9
-0.4-
8e9
./
"~f i i i~ / / # # i/
m~ i,i Z w
/
,I~ ,' :~-':;k" . . . . : / ,', 5" . . . .
2CAJ 4eu
3eU 302u
t
It" ,'
5e 9 la~J__ 4a'~ - 4e9
4a~g
3~u 3a2q i~u
,/
,l
-0.1_
/
//.,
6o~ ,'
~--
6e~
__2~u 6eu 5e~ j'
,/ / .+ . / "
5eu I~
,,~.."
/ ./ ...-y
k,'," . - ; - "
__4eu 4e~
~ 3eu 3cr-..u 14C~c~
-05-
Ia9
......
3~ ' 3e~
~'7- --
\ __
-0.5.
Fi gure I
2eu 2ecj 2~ 9 2~J
Valence e l e c t r o n i ~ energy l e v e l s o f Mo6 and Mo6Se6~- c l u s t e r s .
At view o f these datas we see t h a t the top o f the valence band corresponds t o s t a t e s o f predom i n a n t l y 4d c h a r a c t e r and s p a t i a l l y l o c a l i s e d on
SUPERCONDUCTOR T12Mo6Se 6
Vol. 43, No. I
Mo whereas the l o w e r p a r t is mainly dominate by Se-4p s t a t e s . The highest occupied l e v e l c o r r e s ponds to a f u l l occupation of the 6alg MO o f mainly Mo-4d c h a r a c t e r i n v o l v i n g p r i m a r l y dz 2 o r b i t a l s o r i e n t e d in the c d i r e c t i o n w i t h a few c o n t r i b u t i o n o f 4dxz,yz and 5s Mo o r b i t a l s . These m e t a l l i c o r b i t a l s i n t e r a c t weakly w i t h Se-ap ones (5 % Se-4p c h a r a c t e r ) . At 0.02 Ry above, l i e s the 5a2u level which i s , s t i l l , mainly l o c a l i s e d a t the Mo s i t e s ( d x z , d y z o r b i t a l s ) but shows a s t r o n g e r a n t i b o n d i n g h y b r i d i z a t i o n w i t h Se-4p o r b i t a l s (16 % Se-4p c h a r a c t e r ) . This strong a n t i b o n d i n g e f f e c t e x p l a i n s the i n v e r t e d o r d e r o f these two l e v e l s in the m e t a l l i c Mo6 cluster. In f a c t , in terms o f band s t r u c t u r e the Fermi l e v e l , corresponding to 26 e l e c t r o n s per Mo.6 u n i t , which would a r i s e from l i n e a r combinat l o n s o f Bloch sums o f the two s i n g l e degenerated MO s t a t e s 5a2u and 6alg o f an Mo6Se6 u n i t , would have a broad low d e n s i t y o f s t a t e s . The l a r g e d i s p e r s i o n o f t h i s band along the chain r e s u l t s from the high c o n t r i b u t i o n o f Mo-4d o r b i t a l s having l a r g e components in the c d i r e c t i o n ( i . e . 4dz 2 f o r 6alg and 4dxz, yz f o r 5a2u MO). Contour maps o f these two MO are p i c t u r e d on f i g u r e 2. Curves 2a and 2b concern r e s p e c t i v e l y the 6alg and 5a2u MO drawn in the yz plane. The former e x h i b i t s the weak i n t r a t r i a n g l e (MoRSe3) h y b r i d i z a t i o n o f Ho-4dz 2 o r b i t a l s w i t h [he-Se-4pz ones, when the second shows the c h a r a c t e r i s t i c behavior o f an a n t i bonding d~-p~ ( d y z , p z ) i n t r a - t r i a n g l e i n t e r a c t i o n ; l i k e w i s e , we can also note the a n t i b o n ding i n t e r - t r i a n g l e i n t e r a c t i o n . On the o t h e r hand, f i g u r e s 2c and 2d show the 6alg MO drawn in two p e r p e n d i c u l a r planes to the z d i r e c t i o n a t z:O. and z = l . l a.u. r e s p e c t i v e l y . These l a s t curves suggest a t u b u l a r e l e c t r o n i c d i s t r i b u t i o n a l l along the z axis as a consequence o f the s t a k i n g up o f the F~o-4dz2 and Se-4pz orbitals. In f a c t , theses curves lay to emphasize on the e l e c t r o n i c monodimensional c h a r a c t e r o f the Fermi l e v e l o f t h i s chains compounds. This t h e o r e t i c a l r e s u l t supports the experiments conclusion o f a very l a r g e Fermi v e l o c i t y in the d i r e c t i o n o f the chain and the low d e n s i t y o f s t a t e s e s t i m a t e d to be equal to 0 . I s t a t e s / e V . atoms, spins. This contrasts with the result obtained8,11 f o r r e l a t e d compoundsPbMo6S 8 (Chevrel phases) where the Fermi l e v e l a t 22 electrons/Mo 6 corresponds to an h a l f occupation of a 2eg band which corresponds to the 6eg f o r an Mo6Se62cluster. Just below this l a s t , l i e the 2alu and 6eu MO states corresponding to the t2u one in Mo6X82- (Oh p o i n t group). Like in Chevrel phases, the s t r o n g e r upward s h i f t observed f o r the 6eg Mo-d s t a t e , when we compare Mo6 and Mo6Se62l e v e l s , is a consequence o f the l a r g e a n t i b o n ding i n t e r a c t i o n f o r the eg s t a t e o f Mo-4d o r b i t a l s w h i t h Se-4p ones (Selenide c o n t r i b u t i o n of 23 % f o r 6eg NO compared t o - 4 - 5 % f o r 2alu and 6eu MO's). The uppermost of the Se-4p band corresponds t o the la2g Se s t a t e and represents non bonding Se-4p e l e c t r o n s , l i k e w i s e f o r the 4eg MO, these two l e v e l s corresponding to the It2g o f the cub i c Mo6X8 u n i t in Chevrel phases. The remaining Se-4p s t a t e s h y b r i d i z e s t r o n g l y w i t h Mo s t a t e ; t h u s , i t may be seen t h a t the Se-p band have s i g n i f i c a n t l y Mo-s and d c h a r a c t e r . P a r t i c u l a r y ,
Vol. 43, No.
I
Table 2
Levels
PSEUDO-ONE-DIMENSIONAL
SUPERCONDUCTOR TI2Mo6Se 6
21
2Ground-state electronic structure (SCF SW Xa) of the Mo4Se5 cluster. The Fermi level is flagged by the arrow.
s
p
d
81 85 55 84 71 75 72 32 76 57 52
13 5 16 6 14 3 8 11 i 6 16
4 2 8 2 7 I 4 2 ] 5 2
0 7 8 7 7 15 12 38 16 25 22
3 4 3 2 I i I I 1 I
26 13 7 6 3 5 12 3 2 6 12 9 9 14 8
2 1 5 5
5 23 4 5 20 19 74 23 26 65 74 60 34 62 44 I 47 49 44 54 53
91 90 86 85
I i i 2
p
d
2 1 2 1 I 4 1 7 2 5 5 3 3
3alu 3a2g 9eg 2a2g 9eu 8eg 8eu 6a2u 7eg 7eu 5a2u
-0.0346 -0.0432 -0.0587 -0.0601 -0.0648 -0.0902 -0.1335 -0.1427 -0.1481 -0.1618 -0.2306
6alg 6eg 2alu 6eu 5eg 5eu la2g 4a2u 5alg 4eu 4eg 3eu 3a2u lalu 4alg 3alg 3eg 2eu 2eg 2alg 2a2u
-0.2510 -0.2638 -0.2925 -0.3051 -0.3243 -0.3508 -0.3677 -0.3316 -0.3355 -0.3994 -0.4010 -0.4598 -0.4737 -0.4781 -0.4780 -0.5238 -0.5262 -0.5664 -0.5720 -0.5887 -0.5912
2 23 5 16 3 18 5
14 5 7 4 3 2
56 56 86 86 74 70 8 66 59 21 5 23 37 14 44 62 35 22 45 17 34
leg leu la2u lalg
-1.1284 -i.1378 -1.1531 -1.1716
3 I 7
4 4 i I
4 I I0 5
1 1 4 I I 5
2 I I
17
INT
Se
Mo
Energy (Ry i
2 5 5 i0 4 6 5 2 8
the two lowest l y i n g 2alg and 2a2u Se-4p s t a t e s i n t e r a c t mainly w i t h the 3alg-5s and 2a2u-4dxy s t a t e s o f the m e t a l l i c Mo6 u n i t , the a n t i b o n ding c o u n t e r p a r t being pushed a t the top o f energy range o f the Mo6Se62- c l u s t e [ . . In o r d e r to improve the energy ~ i s ~ r i b u t i o n of Se-4p l i k e l e v e l s and Mo-4d ones i n s i d e the valence band we have p i c t u r e d in f i g u r e 3 t o t a l d e n s i t y o f s t a t e s (DOS-curve I) and l o c a l d e n s i ty of s t a t e s (LDOS-Mo-4d and Se-4p corresponding to curves 2 and 3 r e s p e c t i v e l y ) . T r a n s i t i o n p r o b a b i l i t i e s have not been considered. Two peaks (A) and (B) can been seen in t h e o r e t i c a l DOS. The a n a l y s i s of the LDOS curves 2 and 3 allows to conclude t h a t the peak (A), e s p e c i a l l y close to the Fermi l e v e l , is mainly dominated by Mo-4d l i k e s t a t e s , which would be emphasized by t a k i n g i n t o account the p h o t o i o n i s a t i o n cross s e c t i o n s . Moreover, as mentioned above, a strong
i
2 I I i 2 2 4 2 2
OUT
4
1
Se-4p, Mo-4d h y b r i d i z a t i o n occurs at higher energy and is at the o r i g i n o f the second peak (B). In f a c t , these curves show t h a t covalent bond plays an i m p o r t a n t r o l e in the s t a b i l i t y o f t h i s chains compounds as one can see on the t o t a l e l e c t r o n i c d i s t r i b u t i o n o b t a i n e d from t a b l e 2 :
Mo6+0.40Se6-0,73
(Mo 4s24p64d4"65sO'55pO.5 ;5e 4s1-94p4"65dO'2).
In conclusion, these Xa results on an Mo6Se62- cluster permit one to acces various metal-metal and metal-selenide interactions and to confirm and to explain experimental results at the Fermi level of this chains compounds. Calculations have been performed at the Centre Interuniversitaire de Calcul de Bretagne (C.I.C.B. - Rennes).
22
Vol. 43, No. 1
PSEUDO-ONE-DIMENSIONAL SUPERCONDUCTOR Tl2Mo6Se 6
..°"
j.'*
, z
~ !, \
,." ',. . . . . . . .
\ ,,,,' ";.',, .~.~"
•i< 4:. ....... ..,"'
i!, ::-d&-~f'-~ ..~,,(..,~..,:
......... ~ '-,..,?
t. . . . . . . . . . . .
'"
: t
",?..
;;;7
..? ;
/
.................... 2:..'""
.
2
i;!,. ::::
o,~,
, u )~ _. .._.4..!
Figure
:t
;'
i,.
.
.
.
.
.
~- .
,
_ ~_
.
...
_~)i!i~
,
~avefunctions contours of the 6alg and 5a2u H0 in the YZ(a,b) and XY (c,d) planes. The continous contour lines are r e l a t i v e to a p o s i t i v e wavefunctionsand the dotted contour lines to a negative ones. The total region p l o t t e d covers 19x19 bohrs 2.
A
I
¢-
B
O
4.e
/
Figure
I
5
3
I
I
I
4 3 2 ReLative binding energy,
I
I eV
c H
" o
X~ density of state of Mo6Se62I - t o t a l DOS, 2- Mo 4d LDOS, 3- Se 4p LDOS.
Vol. 43, No.
I
PSEUDO-ONE-DIMENSIONAL
SUPERCONDUCTOR Tl2Mo6Se 6
References
I. M. Potel, Th~se d'Etat - Universit~ de Rennes (1981) 2. M. Potel, R. Chevrel and M. Sergent, Act. Cryst., B36, 1545 (1980) 3. J.C. Armici, M. Decroux, O. Fischer, M. Potel, R. Chevrel and M. Sergent, Solid State Commun., 33, 607 (1980) 4. P. Monceau, CRTB - Grenoble, private communication 5. J.C. Slater, QuantumTheory of Molecules and Solids, vol. 4, Mc Graw-Hill, New-York (1974) 6. R.P. Messmer and D.R. Salahub, Phys. Rev., B16, 2526 (1977) 7. F.M. Michel-Calendini and K.A. MUller, Solid State Commun., 40, 225 (1981) 8. A. Le Beuze, M.A. Makhyoun, R. L i s s i l l o u r and H. Chermette, J. Chem. Phys. in press. 9. R.E. Watson, Phys. Rev., 111, 1108 (1958) 10. K. Schwartz, Phys. Rev., B5, 2466 (1972) 11. O.K. Andersen, W. Klose and N. Nohl, Phys. Rev., B17,1209 (1978)
23
1982.
0038-1098/82/250019-05503.00/0 Pergamon Press Ltd.
ELECTRONIC STRUCTUREOF THE PSEUDO-ONE-DIMENSIONALSUPERCONDUCTORTI2Mo6Se6 ACCORDINGTO SCF SCATTERED-WAVE Xa COMPUTATIONS A. Le Beuze and R. L i s s i l l o u r Laboratoire de Chimie Th~orique, L.A.C.N.R.S. n° 254, Universit~ de Rennes I - Beaulieu 35042 Rennes C~dex, FRANCE H. Chermette I n s t i t u t de Physique NuclQaire et (IN2P3), Universit~ de Lyon I , 43 Bd. du I I Novembre 1918 69622 Villeurbanne C~dex, FRANCE M. Potel, R. Chevrel and ~!. Sergent Laboratoire de Chimie Min~rale B, L.A.C.N.R.S. n° 254, Universit6 de Rennes I - Beaulieu 35042 Rennes C~dex, F~ANCE (Received 29 January 1982 by E.F. Bertaut) The e l e c t r o n i c structure of TI2Mo6Se6 has been investigated using the X~ c lus t e r approach. The ground-state eigenvalues show that the Fermi level l i e s in a single degenerated band which supports the experimental results. Contour maps show the anisotropic character of the wawe functions of this Fermi l e v e l . The metal-metal and metal-selenides i n t e r a c t i o n s have been discussed.
cluster is compensated by inclusion of a Watson sphere 9 with the same radius of the outer sphere (O.S.) and bearing a charge +2. The geometry used is an Mo6Se6 u n i t corresponding to the D3d point group symmetry with the z axis being in the c d i rection. Bond distances, atomic spheres r a d i i and atomic s t a t i s t i c a l exchange I0 ~ values are l i s t e d in table I. Extramolecular (O.S.) and in tersphere scaling parameters are obtained by averaging atomic ones. The basis of atomic o r b i tals includes spherical harmonics up to I=3 f o r Mo and O.S. and I=2 f o r Se. The achieved accuracy of s e l f consistency f o r the energies is no worse than ± 0.0001Ry.
TI2Mo6Se6, a new superconductor material hms been synthetised recently I and both i t s c r y s t a l l i n e structure 2 and i t s physical properties 3'4 show a speudo-one-dimensional character. Thus, the c r y s t a l l i n e structure is mainly characterised by the presence of one dimensional (Mo3Se3)~ chains formed by an i n f i n i t e stack of Mo3 and Se3 t r i a n g l e s in staggered positions and may be viewed as the result of a l i n e a r condensation of face sharing Mo6Se6 u n i t . The remarkable monodimensional character of the physical properties is e x h i b i t e d by the anisotro~y in normal state r e s i s t i v i t y ( o f the order of i0 J) and by the fact that the upper c r i t i c a l f i e l d is about 26 times higher than the perpendiculare ones3,4. The authors, therefore, conclude that this anisotropy is a r e s u l t of e l e c t r o n i c i n t r i n s i c e f f e c t s , probably related to the anisotropy of the Fermi surface and thus of the elect r o n i c i n t e r a c t i o n between the Mo3Se3 unit along the chain. So, i t is of i n t e r e s t to i n v e s ti g a te the e l e c t r o n i c structure of such m a t e r i a l . I t is the aim of this paper. For this purpose we have carried out computations using the Self-Consistent Field XmScattered Waves (SCF-Xm-SW)5 framework for an Mo6Se62- cluster. E f f e c t i v e l y , this method is a powerful and convenient approach f o r describing the e l e c t r o n i c structure of large inorganic molecules 6 and crystals 7. Moreower, we have recently shown that i t was s u i t a b l e f o r molybdenum chalcogenide c l u s t e r compounds8. The Xmmethod is used here in the standard " m u f f i n - t i n " approximation with s l i g h t overlapping atomic spheres. We merely considered the T1 ion as i o n i c charges i n t e r a c t i n g on the e l e c t r o nic levels by mean of the t o t a l charge assumed to be -2 in the p e r f e c t l y i o n i c case T I } Mo6Se62". The e f f e c t of the extranegative charge of the
Table 1
Geometric and X~ parameters.
Atomic distances d Mo.Mo i n t r a t r i a n g l e :
2.6630
d $e.Se
5.2310
intratriangle :
d intertriangle :
2.250
Sphere r a d i i and a parameters R Mo =
1.5261 ~
~ o = 0.70441
R Se =
1.6070 ~
aSe : 0.70638
R(OS)=R(WS)=4.8299 ~
19
~(0S)=~(IS)=0.70589
20
PSEUDO-ONE-DIMENSIONAL
We r e p o r t here some p r e l i m i n a r y r e s u l t s . X ~ ground s t a t e eingenvalues diagram o f an ~o~ ~Se2c l u s t e r is p i c t u r e d on the r i g h t p a r t o f f~gu L re I . In o r d e r to discuss the various metal-met a l and m e t a l - s e l e n i d e i n t e r a c t i o n s , r e s u l t s obt a i n e d f o r an Mo6 m e t a l l i c c l u s t e r (DRd symmetry) are also shown on the l e f t . Table I I presents an a n a l y s i s o f the charge d i s t r i b u t i o n o f the v a l e n ce l e v e l s in the various regions o f the Mo6Se6 u n i t ( a c c o r d i n g l y to the angular momentum c o n t r i bution to the t o t a l charge i n s i d e the atomic spher e s ) . The l e v e l s are l a b e l l e d according to the i r r e d u c i b l e r e p r e s e n t a t i o n s o f the D3d p o i n t group.
Mo6Se62-
Mo6 // 2a2g
,'
if
,/
~=mm
~l / Z
iI , II /
' . -" :/ " / .//'
-02-
/
/ i l~
/
3eg =::J
-a v
-O3.
>-.
lalU
2eu
2~
leu 2~cJ
-
-
,' /"
5c~u
,~' .." ."_,J'~,,_.... . . _"_ _
~ .11,u" "" / -~-
8eu 6cmu 7e 9 7eu
,/
/iI / t i "
/
/
--"
";~-
"- - - "/"-
2e9
-0.4-
8e9
./
"~f i i i~ / / # # i/
m~ i,i Z w
/
,I~ ,' :~-':;k" . . . . : / ,', 5" . . . .
2CAJ 4eu
3eU 302u
t
It" ,'
5e 9 la~J__ 4a'~ - 4e9
4a~g
3~u 3a2q i~u
,/
,l
-0.1_
/
//.,
6o~ ,'
~--
6e~
__2~u 6eu 5e~ j'
,/ / .+ . / "
5eu I~
,,~.."
/ ./ ...-y
k,'," . - ; - "
__4eu 4e~
~ 3eu 3cr-..u 14C~c~
-05-
Ia9
......
3~ ' 3e~
~'7- --
\ __
-0.5.
Fi gure I
2eu 2ecj 2~ 9 2~J
Valence e l e c t r o n i ~ energy l e v e l s o f Mo6 and Mo6Se6~- c l u s t e r s .
At view o f these datas we see t h a t the top o f the valence band corresponds t o s t a t e s o f predom i n a n t l y 4d c h a r a c t e r and s p a t i a l l y l o c a l i s e d on
SUPERCONDUCTOR T12Mo6Se 6
Vol. 43, No. I
Mo whereas the l o w e r p a r t is mainly dominate by Se-4p s t a t e s . The highest occupied l e v e l c o r r e s ponds to a f u l l occupation of the 6alg MO o f mainly Mo-4d c h a r a c t e r i n v o l v i n g p r i m a r l y dz 2 o r b i t a l s o r i e n t e d in the c d i r e c t i o n w i t h a few c o n t r i b u t i o n o f 4dxz,yz and 5s Mo o r b i t a l s . These m e t a l l i c o r b i t a l s i n t e r a c t weakly w i t h Se-ap ones (5 % Se-4p c h a r a c t e r ) . At 0.02 Ry above, l i e s the 5a2u level which i s , s t i l l , mainly l o c a l i s e d a t the Mo s i t e s ( d x z , d y z o r b i t a l s ) but shows a s t r o n g e r a n t i b o n d i n g h y b r i d i z a t i o n w i t h Se-4p o r b i t a l s (16 % Se-4p c h a r a c t e r ) . This strong a n t i b o n d i n g e f f e c t e x p l a i n s the i n v e r t e d o r d e r o f these two l e v e l s in the m e t a l l i c Mo6 cluster. In f a c t , in terms o f band s t r u c t u r e the Fermi l e v e l , corresponding to 26 e l e c t r o n s per Mo.6 u n i t , which would a r i s e from l i n e a r combinat l o n s o f Bloch sums o f the two s i n g l e degenerated MO s t a t e s 5a2u and 6alg o f an Mo6Se6 u n i t , would have a broad low d e n s i t y o f s t a t e s . The l a r g e d i s p e r s i o n o f t h i s band along the chain r e s u l t s from the high c o n t r i b u t i o n o f Mo-4d o r b i t a l s having l a r g e components in the c d i r e c t i o n ( i . e . 4dz 2 f o r 6alg and 4dxz, yz f o r 5a2u MO). Contour maps o f these two MO are p i c t u r e d on f i g u r e 2. Curves 2a and 2b concern r e s p e c t i v e l y the 6alg and 5a2u MO drawn in the yz plane. The former e x h i b i t s the weak i n t r a t r i a n g l e (MoRSe3) h y b r i d i z a t i o n o f Ho-4dz 2 o r b i t a l s w i t h [he-Se-4pz ones, when the second shows the c h a r a c t e r i s t i c behavior o f an a n t i bonding d~-p~ ( d y z , p z ) i n t r a - t r i a n g l e i n t e r a c t i o n ; l i k e w i s e , we can also note the a n t i b o n ding i n t e r - t r i a n g l e i n t e r a c t i o n . On the o t h e r hand, f i g u r e s 2c and 2d show the 6alg MO drawn in two p e r p e n d i c u l a r planes to the z d i r e c t i o n a t z:O. and z = l . l a.u. r e s p e c t i v e l y . These l a s t curves suggest a t u b u l a r e l e c t r o n i c d i s t r i b u t i o n a l l along the z axis as a consequence o f the s t a k i n g up o f the F~o-4dz2 and Se-4pz orbitals. In f a c t , theses curves lay to emphasize on the e l e c t r o n i c monodimensional c h a r a c t e r o f the Fermi l e v e l o f t h i s chains compounds. This t h e o r e t i c a l r e s u l t supports the experiments conclusion o f a very l a r g e Fermi v e l o c i t y in the d i r e c t i o n o f the chain and the low d e n s i t y o f s t a t e s e s t i m a t e d to be equal to 0 . I s t a t e s / e V . atoms, spins. This contrasts with the result obtained8,11 f o r r e l a t e d compoundsPbMo6S 8 (Chevrel phases) where the Fermi l e v e l a t 22 electrons/Mo 6 corresponds to an h a l f occupation of a 2eg band which corresponds to the 6eg f o r an Mo6Se62cluster. Just below this l a s t , l i e the 2alu and 6eu MO states corresponding to the t2u one in Mo6X82- (Oh p o i n t group). Like in Chevrel phases, the s t r o n g e r upward s h i f t observed f o r the 6eg Mo-d s t a t e , when we compare Mo6 and Mo6Se62l e v e l s , is a consequence o f the l a r g e a n t i b o n ding i n t e r a c t i o n f o r the eg s t a t e o f Mo-4d o r b i t a l s w h i t h Se-4p ones (Selenide c o n t r i b u t i o n of 23 % f o r 6eg NO compared t o - 4 - 5 % f o r 2alu and 6eu MO's). The uppermost of the Se-4p band corresponds t o the la2g Se s t a t e and represents non bonding Se-4p e l e c t r o n s , l i k e w i s e f o r the 4eg MO, these two l e v e l s corresponding to the It2g o f the cub i c Mo6X8 u n i t in Chevrel phases. The remaining Se-4p s t a t e s h y b r i d i z e s t r o n g l y w i t h Mo s t a t e ; t h u s , i t may be seen t h a t the Se-p band have s i g n i f i c a n t l y Mo-s and d c h a r a c t e r . P a r t i c u l a r y ,
Vol. 43, No.
I
Table 2
Levels
PSEUDO-ONE-DIMENSIONAL
SUPERCONDUCTOR TI2Mo6Se 6
21
2Ground-state electronic structure (SCF SW Xa) of the Mo4Se5 cluster. The Fermi level is flagged by the arrow.
s
p
d
81 85 55 84 71 75 72 32 76 57 52
13 5 16 6 14 3 8 11 i 6 16
4 2 8 2 7 I 4 2 ] 5 2
0 7 8 7 7 15 12 38 16 25 22
3 4 3 2 I i I I 1 I
26 13 7 6 3 5 12 3 2 6 12 9 9 14 8
2 1 5 5
5 23 4 5 20 19 74 23 26 65 74 60 34 62 44 I 47 49 44 54 53
91 90 86 85
I i i 2
p
d
2 1 2 1 I 4 1 7 2 5 5 3 3
3alu 3a2g 9eg 2a2g 9eu 8eg 8eu 6a2u 7eg 7eu 5a2u
-0.0346 -0.0432 -0.0587 -0.0601 -0.0648 -0.0902 -0.1335 -0.1427 -0.1481 -0.1618 -0.2306
6alg 6eg 2alu 6eu 5eg 5eu la2g 4a2u 5alg 4eu 4eg 3eu 3a2u lalu 4alg 3alg 3eg 2eu 2eg 2alg 2a2u
-0.2510 -0.2638 -0.2925 -0.3051 -0.3243 -0.3508 -0.3677 -0.3316 -0.3355 -0.3994 -0.4010 -0.4598 -0.4737 -0.4781 -0.4780 -0.5238 -0.5262 -0.5664 -0.5720 -0.5887 -0.5912
2 23 5 16 3 18 5
14 5 7 4 3 2
56 56 86 86 74 70 8 66 59 21 5 23 37 14 44 62 35 22 45 17 34
leg leu la2u lalg
-1.1284 -i.1378 -1.1531 -1.1716
3 I 7
4 4 i I
4 I I0 5
1 1 4 I I 5
2 I I
17
INT
Se
Mo
Energy (Ry i
2 5 5 i0 4 6 5 2 8
the two lowest l y i n g 2alg and 2a2u Se-4p s t a t e s i n t e r a c t mainly w i t h the 3alg-5s and 2a2u-4dxy s t a t e s o f the m e t a l l i c Mo6 u n i t , the a n t i b o n ding c o u n t e r p a r t being pushed a t the top o f energy range o f the Mo6Se62- c l u s t e [ . . In o r d e r to improve the energy ~ i s ~ r i b u t i o n of Se-4p l i k e l e v e l s and Mo-4d ones i n s i d e the valence band we have p i c t u r e d in f i g u r e 3 t o t a l d e n s i t y o f s t a t e s (DOS-curve I) and l o c a l d e n s i ty of s t a t e s (LDOS-Mo-4d and Se-4p corresponding to curves 2 and 3 r e s p e c t i v e l y ) . T r a n s i t i o n p r o b a b i l i t i e s have not been considered. Two peaks (A) and (B) can been seen in t h e o r e t i c a l DOS. The a n a l y s i s of the LDOS curves 2 and 3 allows to conclude t h a t the peak (A), e s p e c i a l l y close to the Fermi l e v e l , is mainly dominated by Mo-4d l i k e s t a t e s , which would be emphasized by t a k i n g i n t o account the p h o t o i o n i s a t i o n cross s e c t i o n s . Moreover, as mentioned above, a strong
i
2 I I i 2 2 4 2 2
OUT
4
1
Se-4p, Mo-4d h y b r i d i z a t i o n occurs at higher energy and is at the o r i g i n o f the second peak (B). In f a c t , these curves show t h a t covalent bond plays an i m p o r t a n t r o l e in the s t a b i l i t y o f t h i s chains compounds as one can see on the t o t a l e l e c t r o n i c d i s t r i b u t i o n o b t a i n e d from t a b l e 2 :
Mo6+0.40Se6-0,73
(Mo 4s24p64d4"65sO'55pO.5 ;5e 4s1-94p4"65dO'2).
In conclusion, these Xa results on an Mo6Se62- cluster permit one to acces various metal-metal and metal-selenide interactions and to confirm and to explain experimental results at the Fermi level of this chains compounds. Calculations have been performed at the Centre Interuniversitaire de Calcul de Bretagne (C.I.C.B. - Rennes).
22
Vol. 43, No. 1
PSEUDO-ONE-DIMENSIONAL SUPERCONDUCTOR Tl2Mo6Se 6
..°"
j.'*
, z
~ !, \
,." ',. . . . . . . .
\ ,,,,' ";.',, .~.~"
•i< 4:. ....... ..,"'
i!, ::-d&-~f'-~ ..~,,(..,~..,:
......... ~ '-,..,?
t. . . . . . . . . . . .
'"
: t
",?..
;;;7
..? ;
/
.................... 2:..'""
.
2
i;!,. ::::
o,~,
, u )~ _. .._.4..!
Figure
:t
;'
i,.
.
.
.
.
.
~- .
,
_ ~_
.
...
_~)i!i~
,
~avefunctions contours of the 6alg and 5a2u H0 in the YZ(a,b) and XY (c,d) planes. The continous contour lines are r e l a t i v e to a p o s i t i v e wavefunctionsand the dotted contour lines to a negative ones. The total region p l o t t e d covers 19x19 bohrs 2.
A
I
¢-
B
O
4.e
/
Figure
I
5
3
I
I
I
4 3 2 ReLative binding energy,
I
I eV
c H
" o
X~ density of state of Mo6Se62I - t o t a l DOS, 2- Mo 4d LDOS, 3- Se 4p LDOS.
Vol. 43, No.
I
PSEUDO-ONE-DIMENSIONAL
SUPERCONDUCTOR Tl2Mo6Se 6
References
I. M. Potel, Th~se d'Etat - Universit~ de Rennes (1981) 2. M. Potel, R. Chevrel and M. Sergent, Act. Cryst., B36, 1545 (1980) 3. J.C. Armici, M. Decroux, O. Fischer, M. Potel, R. Chevrel and M. Sergent, Solid State Commun., 33, 607 (1980) 4. P. Monceau, CRTB - Grenoble, private communication 5. J.C. Slater, QuantumTheory of Molecules and Solids, vol. 4, Mc Graw-Hill, New-York (1974) 6. R.P. Messmer and D.R. Salahub, Phys. Rev., B16, 2526 (1977) 7. F.M. Michel-Calendini and K.A. MUller, Solid State Commun., 40, 225 (1981) 8. A. Le Beuze, M.A. Makhyoun, R. L i s s i l l o u r and H. Chermette, J. Chem. Phys. in press. 9. R.E. Watson, Phys. Rev., 111, 1108 (1958) 10. K. Schwartz, Phys. Rev., B5, 2466 (1972) 11. O.K. Andersen, W. Klose and N. Nohl, Phys. Rev., B17,1209 (1978)
23