J. CHEM. SOC. FARADAY TRANS., 1990, 86(4), 697-702 697

Computer Modelling of a Molybdenum Disulphide Catalyst?

Michael G. B. Drew and Philip C. H. Mitchell Department of Chemistry, The University, Whiteknights , Reading RG6 2AD Slavik KasztelanS Laboratoire de Catalyse Heterogene et Homogene, U.A. CNRS 402, Universite des Sciences et Techniques de Lille Flandres-Artois , F-59655 Villeneuve d'Ascq, Cedex, France

Small MoS, slabs, which are the active component of hydrotreating catalysts, have been modelled by molecular graphics and molecular mechanics. Slabs of various sizes with various degrees of edge unsaturation, have been investigated.

As the slab size was increased the minimised energy decreased with no minima in the range investigated. Therefore, a free slab does not adopt any particular optimum size. The finite and apparently preferred slab sizes observed experimentally in supported catalysts must therefore be determined by constraints on slab growth imposed, for example, by the support.

The structures, including distortions, and energies of slabs with different degrees of edge saturation, and of active sites with different degrees of coordinative unsaturation of edge molybdenum atoms, have been investi- gated. The saturated slab has a high strain energy and would be expected to lose its terminal HS groups easily (as found experimentally).

Active sites at molybdenum are created by removing edge sulphur atoms. Structures where two molybdenum atoms are not linked by at least one sulphur atom are unstable, owing to the repulsion between the molybdenum atoms. They distort to increase the distance between the molybdenum atoms.

We are using computer modelling to investigate fundamental problems of heterogeneous catalysis. Recent work in our laboratory has been concerned with developing molecular graphics and molecular mechanics to investigate molybdenum-disulphide-based catalysts.' Such catalysts, consisting of molybdenum disulphide supported on alumina, are used for hydrotreating oil feedstocks.2 According to transmission electron microscopy and EXAFS studies, molybdenum disulphide in the supported catalysts is in the form of small, discrete molybdenum disulphide slab^.^*^ A slab model of the active phase, based on the well known layer structure of MoS, , has been devised.' The slab model allows us to regard one slab as representative of the catalytically active phase and is particularly suitable for computer model- ling.

In previous work we investigated the interaction of a simple molecule, isoprene, with catalytic sites on the edges of a MoS, slab by molecular graphics and molecular mecha- nics.' In the present work we investigate the slab size and the process of active site generation through introducing vacancies at slab edges.

Methods Computer Modelling

Computer modelling was carried out on an IBM PC-AT with the PC-CHEMMOD system.6 The atomic coordinates of MoS, were retrieved from the S.E.R.C. crystallographic database7 and converted, via our own programs, into a suitable form for CHEMMOD.

Molecular-mechanics Calculations

Molecular mechanics was used to calculate the energies of our structures. In molecular-mechanics calculations a mol-

t Presented in part at the International Conference on the Chem-

$ Present address: Institut Francais du Petrole, B.P. 311, 92506 istry of the Early Transition Metals, University of Sussex, July, 1989.

Rueil-Malmaison, France

ecule is treated as a collection of atoms held together by elastic or harmonic forces.8 These forces constitute the force field; they are described by potential-energy functions of structural parameters : bond lengths, bond angles, torsion angles, and non-bonded interactions. The energy of the mol- ecule in the force field is due to deviations of a structure from the ideal structure. It is approximated by a sum of energy contributions :

E = E , + E , + E, + En, + E , .

The total energy, E, measures the intramolecular strain rela- tive to a hypothetical structure; E , is the bond-stretching energy, E, the angle-bending energy, E, the torsional energy due to rotation about bonds, En, the energy of interactions between non-bonded atoms (van der Waals interactions), and E, the Coulombic energy. We start from a model structure, and optimise the geometry by minimising the total steric energy, E.

Molecular mechanics calculations were performed on the Amdahl V7 computer at the University of Reading with the CHEMMIN program' which uses the block-diagonal Newton- Raphson method for energy minimisation. We added our own parameters to the program: for the bond-stretching term, 0.5 k,(r - r,),, we set r , , the ideal Mo-S distance, equal to 2.41 A, a value found in the crystal structure of bulk MoS,; for the bond-bending term, kb(8 - O,),, O , , the ideal angle, was set to 80 or 135" at molybdenum and 85" at sulphur atoms. In the CHEMMIN force field k, values are inversely proportional to r,; k, values are constant. However, we found in other work that force constants obtained in this way for bonds involving metal atoms were overestimated and so we used values for k, equal to half the calculated values. Thereby, we accommodated the proportionally greater flex- ibility around metal, compared with non-metal, atoms. Force constants for torsion angles S-Mo-S-Mo were set to zero. For non-bonded interactions, the sum of the attractive and repulsive interactions was calculated with the Lennard- Jones equation :

(2) V = - A/r6 + B/r12.

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698 J. CHEM. SOC. FARADAY TRANS., 1990, VOL. 86

Values of the parameters A and B were the averages of the values given to interacting atoms: for Mo, A = 1.37 x lo5 kcal mo1-' A6 and B = 2.35 x lo9 kcal mol-' Note that parameters were not changed for edge atoms for which the coordination number is lower than for the bulk atoms (vide supra). These parameters, when used to minimise a very large slab (approximating to the infinite solid) led to a mini- mised slab structure very similar to that found in the crystal structure. Because of this good agreement we considered that it was not necessary to include Coulombic terms in the energy summation.

Results and Discussion Molybdenum Disulphide Slabs

The active phase of an alumina-supported molybdenum di- sulphide catalyst comprises small isolated slabs of MoS, . In our computer graphics modelling we made a regular MoS, single slab by cutting an MoS, layer along two different crys-

tallographic edge planes, (lOi0) and (iOIO).'o.'l Slabs con- taining 7, 19, 37 and 61 molybdenum atoms, which are regular hexagons, and slabs with 12, 27 and 48 atoms, which are irregular hexagons, were modelled. The 6 1-atom hexagon is shown in fig. 1. Note that in our computer graphics repre- sentation, the relative atomic sizes are according to their atomic, not ionic, radii (i.e. Mo bigger than S).

Both the number of sulphur atoms and the number of Mo-S bonds in a slab can be counted according to formulae previously r e p ~ r t e d . ~ Their values for the slabs used in this work are given in table 1.

The 61-molybdenum-atom slab of fig. 1 illustrates a number of structural features. The slab is viewed with the basal plane in the plane of the diagram. The edges are ter- minated by HS-groups. In fig. l(a) we see a fully saturated slab such as we would expect after complete sulphiding of a molybdenum/alumina catalyst in an H,/H,S mixture. The terminal sulphur atoms are located at trigonal prismatic coordination positions of the molybdenum atoms; the Mo-S-H groups are bent (anale at subhur. 104"). In fig.

Fig. 1. Computer-drawn representations of hexagonal 61-Mo-atom slabs, viewed with their basal plane in the plane of the diagram. (a) Fully saturated slab terminated by HS groups; (b) partly unsaturated slab, singly bound HS groups removed from (1010); (c) fully unsaturated slab, bridging S removed from (1010). The edge planes are labelled. Note that in our computer graphics representation, the relative atomic sizes are according to their atomic radii: bigger spheres are Mo, smaller spheres are S atoms. The very small spheres in (a) are H atoms.

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J. CHEM. SOC. FARADAY TRANS., 1990, VOL. 86 699

Table 1. Numbers of atoms and bonds in hexagonal MoS, slabs

atoms bondsa

Mo basal S S, S,, (Mo-S)~ (Mo-S)' (Mo-S)~

7 6 6 12 42 30 18 12 14 12 12 72 60 36 19 24 12 18 114 84 72 27 38 18 18 162 132 108 37 54 18 24 222 174 162 48 74 24 24 288 240 216 61 96 24 30 366 300 288

a Mo-S bonds in slabs shown in fig. 1 ; sulphur, fully edge unsaturated.

saturated, no terminal

l(b) we see a partly unsaturated slab form_ed by removing singly bound HS groups [those along (lolo), i.e. terminal sulphur atoms]. These are the least strongly bound sulphur atoms; experimentally, they are those which are removed when the sulphided catalyst is reduced in hydrogen at below 473 K." In fig. l(c) the slab is fully unsaturated, bridging sulphur atoms having been removed from (1010) (experimentally, by reduction in hydrogen at 473-973 K).

In a saturated slab the molybdenum atoms are in a six- coordinate, trigonal prismatic environment. Removal of sulphur atoms exposes molybdenum atoms at edge and corner sites. The sulphur atoms may be replaced by hydrogen atoms or the molybdenum atoms may remain coordinately unsaturated. Certain of the exposed molybdenum atoms are catalytic sites. Sulphur atoms in the slab may be bound to one molybdenum atom (terminal sulphur) or shared between two or three molybdenum atoms. We refer to differently bound molybdenum or sulphur atoms as being of different types. Of particular interest in this work are two types of peripheral sulphur atoms which are shown in fig. 2, they are the terminal sulphur atoms in the (lOi0) edge plane, desig- nated SI, and the bridging sulphur atoms in the (iOl0) edge plane, S,,.

In recent work the catalytic chemistry of MoS, has been associated with the S,, edge plane.I2 Various structures can be generated on this plane by removing sulphur atoms from around a pair of adjacent molybdenum atoms. This pair of molybdenum atoms constitutes an elementary ensemble. 3*14 In order to study such ensembles a trapezoidal slab of 40 molybdenum atoms with a type I1 edge plane of 12 molyb- denum atoms was modelled (see fig. 3). The trapezoidal shape

Fig. 3. Trapezoidal 40-Mo-atom slab. The larger circles represent Mo atoms.

was used in this calculation because it provides a long edge which maximises the number of possible molybdenum atom ensembles.

Preferred Slab Size?

The experimental evidence is that the catalytic sites of a sul- phided Mo/alumina catalyst are molybdenum atoms in the edges of MoS, slabs dispersed over the support. The optimum size of slab for any particular shape is the slab with the maximum ratio of edge molybdenum atoms to total molybdenum atoms. For a hexagonal slab the optimum size is 27 molybdenum atoms with an edge/total ratio of 0.33.3 An increase of molybdenum loading on the support leads to an increase of mean slab size, the number of slabs remaining constant. For a typical catalyst containing 9 wt % Mo on alumina the expected hexagonal slab size is 61 molybdenum

In our computational study we address the ques- tion whether a slab of a certain size is energetically more stable than any other.

A series of hexagonal slabs was modelled, see fig. 1. The energies of the slabs were calculated as a function of the number of molybdenum atoms before and after minimisation by the CHEMMIN program. We show in fig. 4 the results for the unsaturated slab, fig. l(b). The energies are expressed per mole of MoS2 slab, which in effect is being considered as a molecule. This is reasonable as in the slab all molybdenum atoms are six-coordinate and sulphur atoms either two- or three-coordinate. During minimisation the energies decrease

Fig. 2. Edge planes of MoS, slabs ($ fig. 1). (a) (lOiO), singly bound or terminal sulphur, denoted S , ; (b) (lolo), bridging sulphur, S,, .

I I I I I I I

10 20 30 40 50 60 70

Mo atoms per MoS, slab Fig. 4. Energy of unsaturated slab, S, sulphur atoms removed [cf. fig. l(b)J us. number of Mo atoms in the slab (a) before and (b) after minimisation.

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700 J. CHEM. SOC. FARADAY TRANS., 1990, VOL. 86

considerably because the HS . * * SH repulsions are decreased by atomic displacements.

In fig. 5 we plot the minimised energies of the structures of fig. 1. The edge-saturated and fully unsaturated slabs [fig. l(a) and (c)] are clearly unstable. The higher energy of the satu- rated slab is due to the strong repulsions between the HS groups. The high energy of the unsaturated slab is due to repulsion between pairs of Mo - - . Mo atoms. In the minimum-energy slab the structure has distorted consider- ably from the ideal bulk structure. The energy of the dis- torted structure is less than the energy of the ideal structure but even so remains high.

We see also that the saturated slab has a high strain energy; we would therefore expect it to lose its terminal SH groups readily. This suggestion is consistent with the pre- sence of a type of easily removed sulphur in MoS, catalysts" now considered to be terminal sulphur in the (1010) edge plane.I2 The calculations also show that the regular hexago- nal slabs are more stable than the irregular slabs. This causes the oscillating form of the curves in fig. 5(a) and (c).

The partly unsaturated slab, fig. l(b), has the lowest energy; its total energy decreases as the slab size increases. This means that the slab will always tend to grow. We reached the same conclusion in a thermochemical calculation of the free energy of formation of the slabs using the Gibbs- Curie-Wulff equation to calculate the surface tension of the slabs.16 The infinite slab was the most stable because of the loss of surface energy as the smaller slabs grew.

The molecular-mechanics calculation treats the molyb- denum disulphide as covalent since electrostatic forces were not included. We found that the inclusion of Coulombic terms did not improve the fit to the molybdenum disulphide structure and, moreover, introduced another uncertainty in the force-field parameterisation. Therefore, our calculations do not include Coulombic terms.

Note also that we used the same force-field parameters for edge and basal molybdenum and sulphur atoms. There is clearly more space around the edge atoms and it could be argued that the angle-bending term for the edge atoms should be revised either through reducing the force constant or changing the ideal angles. However, to refine the param- etrisation in this way would require experimental data on the edge geometry and no such data are available. The conse- quence of using the same set of parameters for all molyb- denum and sulphur atoms in our calculations is that on

l L o i

0

/

I I I I I I I 1

0 10 20 30 40 50 60 70 Mo atoms per MoS, slab

Fig. 5. Minimised energies of MoS, slabs: (a) fully saturated slab [fig. l(a)] ; (b) partly unsaturated slab [fig. l(b)] ; (c) fully unsaturated slab [fig. l(c)].

minimisation the slabs appear distorted, the edges appearing slightly concave towards the slab as the edge atoms are drawn inwards.

We see, then, that as the slab size is increased the mini- mised energy decreases with no minima in the range investi- gated: free slabs will grow to the stable, infinite slab. Therefore, a free slab does not adopt any particular optimum size. The finite and apparently preferred slab sizes observed experimentally in supported catalysts must therefore be determined by constraints on slab growth imposed in a sup- ported catalyst under experimental conditions. This problem will be studied in future work.

Distortions of the Slab due to Molybdenum Unsaturation in the (iOl0) Edge Plane

In view of the importance of the (1010) edge plane in the catalysis and the role of the number of vacancies, or coordi- native unsaturation of the molybdenum atoms, in defining the structures of the active sites, we report our calculations on the generation of unsaturated molybdenum atoms in the (1010) edge plane by the gradual removal of bridging sulphur atoms, designated S,,, from the hexagonal slab of 61 molyb- denum atoms. For this slab three sides terminate with S,, and contain eight S,, each; therefore, 24 S,, can be removed. Ener- gies after minimisation are plotted against the number of S,, atoms removed in fig. 6. We see that the energy of the slab hardly changes as we remove up to 12 SII, four from each S,,-type side, while keeping the molybdenum atoms linked by one sulphur. However, removal of the last 12 sulphur atoms leads to a large increase of energy because of the strong non- bonded repulsions which now arise between pairs of adjacent unsaturated molybdenum atoms.

Many structures with different numbers and arrangements of vacancies can be en~isaged. '~ The (iOl0) edge plane of a trapezoidal slab having various degrees of unsaturation is illustrated in fig. 7. Four cases have been selected: the struc- tures having (a) all molybdenum two-fold coordinately unsaturated (2-cus) and all molybdenum linked together, (b) all molybdenum atoms 2-cus but with some no longer linked to neighbouring molybdenum atoms, (c) all molybdenum

100 "4 6 701 60

0 2 4 6 8 10 12 14 16 18 S, , atoms removed

Fig. 6. Removal of bridging (S,,) sulphur from the (1010) edge of a 61-Mo-atom slab: minimised energy us. the number of S,, removed.

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Table 2. Energy-minimised slabs'

70 1

Fig. 7. Effect of creating vacancies of different types in the (1010) edge of a 40-Mo-atom trapezoidal slab (cf. fig. 3) showing structures of the edge before [(a)+)] and after [(e)-(h)] energy minimisation. (a), (e) all Mo two-fold coordinatively unsaturated (2-cus) and linked by S bridges (68.4, 10.2 kcal mol-'); (b), (f), Mo 2-cus, some not linked (90.7, 42.6 kcal mol-'); (c), (g), Mo 3-cus (690, 41.1 kcal mol-'); (d), (h), Mo Ccus, totally unsaturated (1530, 102.1 kcal mol - I).

atoms 3-cus, (d) all molybdenum atoms, 4-cus, i.e. fully unsaturated. The energies and structures before and after minimisation are shown in fig. 7. Our calculations clearly show that structures where the two molybdenum are not linked by at least one sulphur atom have much higher energy and are deformed relative to the normal structure. The repul- sion between molybdenum atoms is the dominant effect.

no. of (Mo ... M o ) ~

slab type Mo S /kcal mol-' 1010 lOi0

atoms minimised /A energy

fully saturated 48 120 62.9 3.24 3.48 partly unsaturated 61 120 3.55 3.28 3.48

61 108 - 2.90 3.35 3.23 61 105 22.4 4.31 3.10

fully unsaturated 61 96 116 4.42 2.96

a Slabs as fig. 1 ; shortest Mo * * Mo distances along two slab edges.

Calculations on a 61-Mo-atom slab are summarised in table 2, where, starting with the fully saturated slab [fig. l(a)], we see how the slab energies and Mo Mo distances change as we remove sulphur atoms. Note how the repul- sions open up the Mo - - - Mo distance in the hole created by the sulphur removal and how the difference between the Mo Mo distances in the two edges increases. (This differ- ence is a measure of the slab distortion.) The distortions are illustrated in fig. 8 for the 61-Mo-atom slab. We see that after minimisation the distance between the molybdenum atoms has increased; the cavity has opened up. We should not, of course, attach too much weight to the precise numerical values of the Mo . . . Mo distances since they depend on the parametrisation of the molecular-mechanics calculation. However, we consider that the general effect, distortion of the slab as edge atoms are removed, is real. Therefore, in dis- cussing substrate binding at an active site created in the way we have described we need to consider the final, distorted site. For example, we have found in modelling isoprene hydrogenation that the undistorted cavity is too small to accommodate isoprene, whereas the distorted cavity, obtained after minimisation of the structure, is of sufficient size.

The active site cavity shown in fig. 8 is reminiscent of the active centre of an enzyme; moreover, the coordination centre is strained analogously to the entatic-state description of a metalloenzyme." In future work we shall investigate geometric factors in the accommodation and exclusion of a substrate molecule at the site and electronic factors in binding and activation of the molecule. We shall also be con- cerned with how the strained site may be stabilised, for example by adsorption of sulphur or a reactant species such as hydrogen or a substrate molecule. Experimentally, we may

Fig. 8. Vacancies (labelled v) along (i010). Four-fold unsaturated Mo atoms, (a) before and (b) after energy minimisation showing the expansion of the cavity due to M o - . M o repulsion. The larger circles represent Mo atoms.

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702 J. CHEM. SOC. FARADAY TRANS., 1990, VOL. 86

relate the slab deformation to the curved structure of the MoS, layers in bulk molybdenum disulphide which may explain the rag structure of MoS, .lS

Conclusions We have used computer graphics and molecular-mechanics calculations to model molybdenum-disulphide-based cata- lysts.' We have investigated the structures and strain energies of molybdenum disulphide slabs as we vary their sizes and create active sites through introducing vacancies at slab edges. Our main conclusions are:

(a) There was no optimum slab size, the small slabs tending to grow to the stable infinite slab. It appears, therefore, that the small slabs observed experimentally on, for example, sul- phided Mo/alumina catalysts, are stabilised by binding to the carrier.

(b) A saturated slab, i.e. one in which the edges are ter- minated by HS groups, has a high strain energy because of repulsions between the HS groups. This result is consistent with the experimental observation that saturated slabs tend to lose sulphur readily.

(c) Active sites at molybdenum are created by removing edge sulphur atoms. The preferred structures are those in which edge molybdenum atoms remain linked by one sulphur atom. Structures where two molybdenum atoms are not so linked are unstable owing to repulsion between the molybdenum atoms. (d) The calculations reveal that the molybdenum disulphide

slabs distort in various ways: (i) Because the forces acting on edge atoms are different from the forces on basal atoms the small slabs distort in comparison with an infinite slab, the edge atoms being drawn inwards. (ii) At an ensemble site con- taining two or more unsaturated molybdenum atoms, the Mo - - * Mo separation is increased compared with the satu- rated slab. This distortion needs to be taken into account in discussions of substrate binding at the active site.

In this paper we have used a molecular-mechanics approach to provide insights into structural aspects of molybdenum disulphide catalysts. There is currently growing interest in computational studies of catalytic problems.' Molecular mechanics is a useful computational technique for investigating real catalysts especially where steric, or non- bonded, interactions are present. Molecular-mechanics calcu- lations have the advantage of being conceptually simple, economical with computer time (the calculations reported here required only a few minutes of our main-frame computer), and capable of handling many hundreds of atoms (unlike quantum mechanics). The procedure suffers, of course, in the same way as all empirical procedures from the need to parametrise (we are working on this problem for inorganic systems of interest). Our approach provides a good deal of

insight into structural features of catalysts which are difficult to study experimentally and the calculations are a useful pre- liminary to detailed quantum-mechanical calculations on particular electronic effects. Finally, we should note that molecular mechanics implies a covalent-type force field. This seems more acceptable for a solid like MoS,, where we expect a degree of covalency, than the ionic-type force fields developed for oxidic solids like zeolites.

S.K. thanks the University of Lille for financial support; M.G.B.D. and P.C.H.M. thank the S.E.R.C. for funds for the purchase of the computer equipment.

References 1

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M. G. B. Drew, S. J. Edmondson, G. A. Forsyth, R. J. Hobson and P. C. H. Mitchell, Catal. Today, 1988,2, 633. P. C. H. Mitchell, in Catalysis (Specialist Periodical Report), ed. C. Kemball (The Chemical Society, London, 1977), vol. 1, p. 204; P. C. H. Mitchell, in Catalysis (Specialist Periodical Report) ed. C. Kemball and D. A. Dowden (The Chemical Society, London, 1982), vol. 4, p. 175. S. Kasztelan, H. Toulhoat, J. Grimblot and J. P. Bonnelle, Appl. Catal., 1984, 13, 127. See also R. Candia, 0. Sorensen, J. Villadsen, N. Y. Topsoe, B. S. Clausen and H. Topsoe, Bull. Soc. Chim. Belg., 1984,93, 783. J. V. Sanders, Chem. Sci., 1979, 14, 141. S. Kasztelan, H. Toulhoat, J. Grimblot and J. P. Bonnelle, Bull. Soc. Chim. Belg., 1984,93,807. PC-CHEMMOD system, U-Micro Computers, Warrington, U.K. S.E.R.C. Chemical Databank System, ICSD component, Dare- sbury Laboratory, S.E.R.C. Daresbury, Warrington, U.K. U. Burkert and N. L. Allinger, Molecular Mechanics, ACS monograph 177,1982. D. N. J. White, CHEMMIN Program, University of Glasgow, per- sonal communication. K. Tanaka and T. Okuhara, J. Catal., 1982,78, 155. P. Ratnasamy and S. Sivasanker, Catal. Rev. Sci. Eng., 1980, 22, 401. A. Wambeke, L. Jalowiecki, S. Kasztelan, J. Grimblot and J. P. Bonnelle, J. Catal., 1988, 109, 320. R. R. Chianelli, A. F. Ruppert, S. K. Behal, B. H. Kear, A. Wold and R. Kershaw, J. Catal., 1985,92,56. S . Kasztelan, C.R. Acad. Sci. Paris Ser. Z I , 1988,307, 727. D. G. Kalthod and S. W. Weller, J. Catal., 1985,95,455. H. Toulhoat and S. Kasztelan, in Proc. 9th Int. Congr. Catal., ed. M. J. Phillips and M. Ternan (The Chemical Institute of Canada, Calgary, 1988), vol. 1, p. 152. R. J. P. Williams, J. Mol. Catal., 1985, 30, 1. R. R. Chianelli, T. B. Prestridge, T. A. Pecoraro and J. P. de Neufville, Science, 1979, 203, 1107. See for example, A. K. Cheetham, J. D. Gale, A. K. Nowak, B. K. Peterson, S. D. Pickett and J. M. Thomas, Farday Discuss. Chem. Soc., 1989, 87, 79; J. M. Thomas and C. R. A. Catlow, Progr. Inorg. Chem., 1988,35, 1.

Paper 9/02946J; Received 1 l t h July, 1989

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