Metal-metal bonding in La4Re6O19 and rutilerelated dioxides

Mat. Res. Bull. Vol. 3, pp. 437-444, 1968.

Pergamon Press, Inc.

Printed

in the United States.

METAL-METAL BONDING IN La4Re6019 and RUTILERELATED DIOXIDES T. P. Sleight and C. R. Hare Department of Chemistry State University of New York at Buffalo Buffalo, New York 14214 and A. W. Sleight Central Research Department* E. I. du Pont de Nemours and Company Wilmington, Delaware 19898

(Received March 22, 1968; Communicated by J. B. Goodenough) ABSTRACT Extended Huckel calculations have been used to rationalize the existence of a Re-Re double bond across the edge-shared octahedra in La4Re6019. By analogy, double bonds are probably also present in the distorted rutiles: MoO 2, NO 2, and a-ReO 2. Quantitative energy diagrams are not given, but it is shown qualitatively that the molecular levels of primarily metal-metal bonding character are very sensitive to the separation of the bridging oxygens, as well as to the metal-metal distance. Introduction The structure of La4Re6019 can be depicted as a network of dimerlc units, Re2010 -3 1/J,'A which are essentially two octahedra sharing an edge (1,2).

The Re-Re distance is 2.42 ~ which, accord-

ing to Cotton (3), corresponds to a bond order of two.

A valence

bond approach with d2sp 3 metal hybridization used for metal-ligand bonding allows the remaining three d orbitals to point toward the *Contribution No. 1416

437

438

METAL-METAL BONDING

edges of the octahedron.

Vol. S, No. 5

This approach readily suggests the poss-

ibility of a metal-metal single bond, but the possibility of a double bond is not so obvious.

It was thus decided to study this

unit to determine if seml-empirlcal molecular orbital calculations could reasonably rationalize a Re-Re double bond. Ex2erimental Extended Huckel calculations were carried out on the dimeric, Re2010-3, unit.

The rhenium Ions were given a formal oxi-

dation state of +4.5 while the bridging oxygens and terminal oxygens (actually shared with another unit) were given formal charges of -2 and -i, respectively.

This approximation for the

rhenium oxidation state was necessary because an integral number of electrons was required in these calculations.

Such an approxi-

mation Is valid for Re2010 -B I/3 because the molecular orbital levels are independent of the input oxidation state and number of electrons. A rlght-hand coordinate system was chosen with the x axis through both rhenium ions and the y axis through the bridging oxygens (Fig. 1).

According to the metal-metal interactions,

the

dx~ y2 orbital is ~, the dxz is ~, and the dy z is 8 bonding in symmetry.

The dxy and dz2 orbltals interact more strongly with

the oxygens, and the corresponding molecular orbitals are forced to higher energies (Fig. 2). The parameters

(Slater type orbital exponents and

Coulomb integrals, Hii's) were varied extensively while the resonance integrals (Hij) were calculated by the Cusachs (4) approximation with K set equal to 2.0.

This approximation has been shown

to be the most appropriate for the calculation of the properties of the dlatomic copper molecule

(5).

The rhenium parameters were

varied within reasonable limits of parameters use~ in other rhenium calculations

(6).

Parameters for oxygen are available

Vol. 3, No. 5

M E T A L - M E T A L BONDING

y

FIG. i The Re2010 -3 1/3 Unit with the Coordinate System Used

2~(w)(xy)

FIG. 2

2~, (~(~y) ...3o (~Xzt) \ 2bs (s)(z2)

Level Ordering of Moleaular Orbitals in Re2010 -3 1/3 J~(~)(~-F) / l ~ (r~(xz) --Ib,(8) (yz) ~2a (8*) (yz) %'Jbi(lr ) (xz) \ la (o')(xZ--yz)

439

440

METAL-METAL BONDING

from several sources

(7).

ground state be bonding;

It was required that the calculated that is, have a negative potential energy

with respect to the dissociated ions. parameters (6).

Vol. 3, No. 5

The most satisfactory

for rhenium were those used in calculations on ReC16 -2

The level ordering of the metal-llke molecular orbltals was

not changed significantly when a variety of oxygen parameters was used.

The separation of the metal-llke

orbitals was increased by

a decrease in the rhenium d-orbltal exponent, but the ordering of the levels remained unchanged. Results and Discussion A quantitative

energy level diagram for La4Re6019

(i.e.,

Re2010-3 l/B) is not appropriate because of a general lack of information necessary to validate the molecular orbital calculations. All reasonable parameter variations metal-metal bonding levels

indicate that the ~ and

are occupied and that the correspond-

ing o~ and w~ levels are empty.

The molecular orbltals given in

Figure 2 include only the metal-like orbitals because of the approximations

previously cited for the terminal oxygens.

In Fig.

2 the levels are labeled according to the point group D 2, the type of metal-metal

interaction,

and the predominate

d orbital involved.

The calculation was also made with the axes of the coordinate system nearly along metal-ligand bonds, the z axis. orbitals,

i.e., rotation of 45 ° around

In this case the ~ levels are formed from the d

xy and the lower ~ (and 8) levels result from a linear com-

bination of the d

and d orbltals. It might be expected that xz yz this dlmerlc unit would have bonding similar to that in diatomic

molecules

(5) except for the removal of the degeneracy of the

and 8 levels.

This is not true because all of the levels have a

significant mixture of oxygen antibondlng character.

For example,

the 2a(6") level is lower in energy than the Ib3(6 ) level because the latter contains antlbondlng character from the bridging

Vol. 3, No. 5

M E T A L - M E T A L BONDING

441

oxygens while the 2a(5") orbital contains n__oobridging oxygen character.

The bridging oxygens are also very important in determin-

ing the level ordering of the ~ and ~ orbltals. are particularly oxygen atoms.

These orbitals

sensitive to the distance between the bridging

As these oxygens are brought closer to the x axis,

the ~ and ~ bonding orbitals are destabilized. The simple filling of levels

( 2 ~

5" 1 1/3) implies

that both ~ and ~ metal-metal bonds are possible.

A representa-

tive Mulllken orbital population analysis (8) for the (~), -3 dx2-Y2 d (~), and d (8*) orbitals of Re2010 gives coefficients of xz yz 0.19, 0.17, and -O. O1, respectively. Therefore, the ~ or ~ metalmetal bonding is not effectively canceled by 5" contributions. Re-O overlap population metal bond (~, w a n d

A

(~ and ~) of 0.27 indicates that the metal-

5") is stronger than one metal oxygen bond.

The Mulliken population analysis is sensitive to the d-orbital exponent,

and for more extensive orbitals the metal-metal bond is

stronger than indicated above; however,

the qualitative conclusions

are the same. The partially filled 8" level is predominantly metal (dyz) in character,

but has sufficient oxygen character by inter-

action with the terminal oxygens so that the observed metallic conductivity is readily understood.

The metal-ligand interaction

of this level is antibonding in nature,

and the conduction mechan-

ism is thus similar to that which Goodenough

(9) has proposed for

other transition metal oxides. All the transition metal dioxides,

except ZrO 2 and HfO 2,

are known to exist in the rutile-type or closely related structures. In these structures there are infinite chains of edge-shared octahedra.

Frequently,

the metals in these octahedra are not regular-

ly spaced but are alternately displaced toward and away from each other forming reasonably discrete pairs. presumably

The metal-metal pairs

form homopolar bonds, and certain qualitative

features

442

M E T A L - M E T A L BONDING

Vol. 3, No. 5

of Fig. 2 might apply to such transition metal dioxides. Marinder and Magnell

(lO) have shown that for these

transition metal dioxides there is a very high correlation between the metal-metal

distance and the number of electrons available for

metal-metal bonding

(Table I).

In VO 2 (below 65°C) and Nb02, where

the cations are both d l, there are presumably metal-metal bonds between the metals. the metal-metal

single

For MoO 2 (d2), WO 2 (d2) and a-Re02

(d 3)

distances are considerably shorter than in V02 and

Nb02, and from Fig. 2 a metal-metal double bond is considered likely.

Table I also shows that there is a high correlation be-

tween the oxygen-oxygen

distances along the edges of an octahedron

and the bond order of the metal-metal bond across the octahedral edge.

Paullng (ll) has indicated that anions on a shared edge

will be displaced away from each other due to electrostatic siderations,

and this is found in the rutile structure when there

is no metal-metal bond (Table I). calculations

con-

indicate

However,

the molecular orbital

that displacing the bridging oxygens away

from each other is more favorable for a metal-metal bond. From Table I it appears that the electrostatic

and the metal-

metal bonding effects nearly cancel for a single bond, i.e. VO 2 and Nb02,

but the metal-metal bonding effect clearly dominates

in the case of a double bond. That a triple bond is not realized in a-ReO 2 is evident from a comparison of the distances in Table I.

Thus,

for a-Re02

two of the available electrons per cluster are apparently not used for metal-metal bonding.

However,

in B-ReO 2, where the In-

finite chains of edge-shared octahedra are zlg-zagged

(12), all

three electrons per Re are presumably used in metal-metal bonding. A more complete discussion of the bonding and properties of rutilerelated dioxides will be presented elsewhere

(13).

It is important to remember that the metal-metal bonds in La4Re6019 and the transition dioxides are not necessary for the

Vol. 3, No..5

METAL-METAL BONDING

443

TABLE I Bond Order ~ d

Compound

Metal-Metal Distance

Interatomic Distances

Oxygen Ratio a

d eleatrons per cation

Bond Order

Reference for Positional Parameters

Ti02

2.96

.89

3d 0

0

c

CrO 2

2.92

.91

3d 2

0

d

GeO 2

2.86

.89

3d l0

0

c

RuO 2

3.11

.89

4d 4

0

e

SnO 2

3.19

.87

4d I0

0

c

VO 2

2.62

.97

3d I

1

f

NbO 2

2.80

1.03

~d I

1

g

MoO 2

2.51

l.n

4d 2

2

h

WO 2

(2.49) b

--

5d 2

2

12

ReO 2

(2.~9) b

--

5d 3

2

12

542 2/3

2

1,2

La4Re6019

2.42

1.13

a.

Ratio of the oxygen-oxygen bridging distance to the average of the oxygen-oxygen distances of the remainder of the octahedral edges. This ratio would be one for regular octahedra.

b.

These distances are not accurately known.

c.

W. H. Baur, Acta Cryst. ~, 515 (1956).

d.

W. H. Cloud, D. S. Schrelber, and K. R. Babcock, J. Appl.

3_/3, 1193 (1962). e.

F. A. Cotton and J. T. Mague, Inorg. Chem. ~, 317 (1966).

f.

J. Longo and P. Kierkegaard, to be published.

g.

B. Marinder, Arklv Kemi 19, 435 (1962).

h.

B. Brandt and A. Skapski, Acta Chem. 21, 661 (1967).

stability of their structure type.

It is known that KSbO 3 (14)

and KBiO 3 (15) are isotypic with La4Re6019, and metal-metal bonding would seem impossible for these d lO cations.

Furthermore,

many rutile-type oxides are known where there is clearly no metalmetal bonding.

444

METAL-METAL B O N D I N G

Vol. S, No. 5

Acknc~!ed~ments The Computing Center at the State University of New York at Buffalo is partially supported by NIH grant FR-00126 and NSF grant GP-7318. We are grateful to D. B. Rogers and to W. Cooper for discussion. References i.

J. M. Longo and A. W. Sleight, Inorg. Chem. ~, 108 (1968).

2.

N. Morrow ahd L. Katz, American Crystallographic Association Meeting, 1967, Paper R-6.

3.

F.A.

Cotton, Quart. Rev. (London), 20, 389 (1966).

4.

L. C. Cusachs, J. Chem. Phys., 45, S157 (1965).

5.

C. R. Hare, T. P. Sleight, W. Cooper and G. A. Clarke, Inorg. Chem., in press.

6.

F. A. Cotton and C. B. Harris, Inorg. Chem., ~, 376 (1967); ~, 924 (1967).

7.

E. Clementi, Tables of Atomic Functions, International Business Machines, New York, 1965; R. Rain, N. Fukuda, H. Win, G. A. Clarke, and F. E. Harris, J. Chem. Phys., 45, 4743 (1966); E. B. Moore and C. M. Carlson, private communication.

Also the parameters computed here which reproduce the

potential surface and ionization potential of 02 . -22.0 eV, .

9. I0.

~(2s) = 2.50; HLi (2p) = 14.24 eV,

[Hil (2s) =

~(2p) = 2.44].

R. W. Mulliken, J. Chem. Phys. 23, 1833 (1955). J. B. Goodenough, Bull. Soc. Chim. France (1965) 1200. B. Marinder and A. Magneli, Acta. Chem. Scand., ii, 1635

(1957). ll.

L. Pauling, The Nature of the Chemical Bond, p. 561, Cornell University Press, Ithaca (1960).

12.

A. Magneli, Acta. Chem. Scand. ll, 28 (1957).

13.

D. B. Rogers, R. D. Shannon, A. W. Sleight and J. L. Gillson, to be published.

14.

P. Spiegelberg, Arkiv Kemi, 14A, No. 5 (1940).

15.

J. Zemann, Mineral. Petrog. Mitt., ~, 361 (1950).