structure, bonding and electron counts in cubane-type cluster having m4s4, m2m′2s4 and mm′3s4...

Po/yhedron Vol. 8, No. 24, pp. 2843-2882, I989 Printed in Great Britain

0277-5387/89 S3.00+.00 0 1989 Pergamon Press plc

POLYHEDRON REPORT NUMBER 29

STRUCTURE, BONDING AND ELECTRON COUNTS IN CUBANE-TYPE CLUSTERS HAVING M& M2M;S4 AND

MM;& CORES

SUZANNE HARRIS

Corporate Research Laboratory, Exxon Research and Engineering Company, Route 22 East, Annandale, NJ 08801, U.S.A.

CONTENTS

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 2843

2. HOMOMETALLIC CLUSTERS HAVING AN M4S4 CORE 2.1. All four metals octahedrally coordinated . . . . . . 2.2. All four metals tetrahedrally coordinated . . . . . .

2.2.1. n-Acceptor ligands . . . . . . . . . . 2.2.2. n-Donor ligands . . . . . . . . . . . .

2.3. All four metals five-coordinate . . . . . . . . . . 2.4. Two tetrahedral metals-two five-coordinate metals . . . 2.5. Three tetrahedral metals-one five-coordinate metal . .

......

......

......

......

......

......

......

2845 2845 2851 2852 2854 2856 2860 2863

3. HETEROMETALLIC CLUSTERS HAVING AN M,M;S, CORE ......... 2866 3.1. All four metals octahedrally coordinated ................ 2866 3.2. Two octahedral metals-two tetrahedral metals .............. 2866 3.3. Two octahedral metals--two five-coordinate metals ............. 2869

4. HETEROMETALLIC CLUSTERS HAVING AN MM;S, CORE ......... 2871 4.1. All four metals octahedrally coordinated ................ 2871 4.2. Three octahedral metals-one tetrahedral metal .............. 2872 4.3. One octahedral metal-three tetrahedral metals .............. 2874 4.4. Two octahedral metals---two five-coordinate metals ............. 2876

5. SUMMARY . . . . . . . . . : . . . . . . . . . . . . . . . . . 2879

1. INTRODUCTION

Homometallic M4S4 cubane-type clusters have been known for some 20 years. They all contain the core 1, which is characterized by two interpenetrating tetrahedra made up of four metal atoms and four triply-bridging sulphur atoms, respectively. (Although the core in 1 is drawn as a cube to

emphasize the cubane-type structure, the M4 tetrahedron is usually smaller than the surrounding S, tetrahedron.) Each metal atom is also coordinated by one to three other ligands (L). Although this general structure is observed in all the cubanes, various distortions are observed in the two

2843

2844 S. HARRIS

tetrahedra. The number and type of distortions are determined both by the direct metal-metal bonding and by the metal-sulphur and metal-ligand bonding. These in turn are influenced by several factors, two of the most important being the number of metal d-electrons and the coordination geometry around each metal atom. The M& clusters not only form an intriguing class of inorganic and organometallic clusters, but also, in the case of many of the Fe,& clusters, have served as important synthetic analogues for the redox sites of iron-sulphur proteins. l-3 The theoretical attempts to understand the electronic structure and properties of these clusters have ranged from qualitative and approximate molecular orbital (MO) treatments”‘* to more exact spin- and space- unrestricted X, calculations. ’ 3-16 Notable among the theoretical treatments of these clusters is the development of qualitative MO bonding schemes by Dahl and co-workers.4,8,17,‘8 Based initially upon the Td symmetry of the clusters, and later augmented by approximate MO calculations, these schemes make it possible to understand the metal-metal bonding and to predict the structures of many of the M4S4 clusters.

Within the last 10 years a number of heterometallic M,M;S, and MMjS, clusters containing the cores 2 and 3, respectively, have been synthesized and characterized. The motivation for the

(3) (3)

synthesis and study of the clusters having an MoFe,S, core has come primarily from their relation to a mixed-metal-sulphide cluster present in nitrogenase, 19*20 but the combinations of metals, ligands and ligand coordination geometry observed in the heterometallic clusters extend far beyond those found in the MoFe,S4 clusters. In spite of the proliferation of these heterometallic clusters, the theoretical treatments of these systems have been few. i***‘,** Unfortunately, the qualitative MO schemes of Dahl and co-workers are not easily extended to these lower symmetry heterometallic clusters. A recent set of calculations on several M,M&S, clusters showed that it was useful to view the metal-metal bonding in these clusters in terms of available orbitals on the MS3L, (x = 1, 2, 3) fragments within the clusters. ** An examination of the structures, electron counts and available MO calculations for a wide range of both homo- and heterometallic cubane-type clusters suggests that this same approach can be used to derive qualitative cluster MO bonding schemes for a large number of both homo- and heterometallic cubanes.

The cubane-type clusters can be divided into various groups based upon the coordination geometry around each metal atom in the cluster. Many of the homometallic clusters fall into the classification where all of the metals in the cluster lie in a pseudo-octahedral environment. In a number of other clusters the coordination around the metal atoms may be pseudo-tetrahedral, square pyramidal, or trigonal bipyramidal. In most of the homometallic clusters, the coordination geometry around each metal is identical, and there are only a few clusters in which the metal atoms exhibit two different coordination geometries. In the heterometallic M,M;S, and MM’$,, clusters, on the other hand, the different metals usually exhibit different coordination geometries, and only a few heterometallic clusters are known in which the coordination geometry around all the metals is the same.

This report groups the clusters into classes according to metal coordination geometry and considers the relation between structure, bonding and electron counts in each group. A qualitative metal cluster bonding scheme is presented for each class. In several of the homometallic groups the metal cluster bonding is described in terms of both the qualitative Dahl model, which is most applicable to homometallic clusters in which the ligand coordination around all four metals is the same, and a “metal fragment orbital” model, which becomes particularly useful for clusters having two different kinds of metal coordination and/or two different metals. It is important to recognize that in the systems where both of these models can be applied, the Dahl model and the fragment model provide consistent pictures of the metal cluster bonding. It should be pointed out that the bonding schemes described in this report are qualitative and are subject to the limitations inherent in such schemes. In several cases these limitations are pointed out and the need for further electronic structure calculations is discussed. Electronic structure calculations have already provided a more

Cubane-type clusters 2845

detailed picture of the bonding in some of these clusters, and the results of these calculations provide both a basis and a check for the qualitative schemes.

The discussion in this report is limited to clusters having metal-sulphur cores of structures type 1, 2 or 3. A number of clusters incorporating other cubane-type cores are known,23 and the metal cluster bonding schemes described in this report should be useful in describing the cluster bonding in many of these other cubane-type clusters. Since the discussion is also limited to “single” cubane clusters, the “double” cubane clusters containing two MFe3S4 cores are not explicitly considered. The bonding schemes described here should also be applicable to the individual cubane units within these larger clusters.

2. HOMOMETALLIC CLUSTERS HAVING AN M.,S, CORE

2.1. All four metals octahedrally coordinated

The clusters in this class are characterized by the general formula M&LIZ (4) or M&Cp, (5). If the metal-metal bonds are ignored, each M atom is six-coordinate (Cp is considered to occupy

three coordination sites) and can be viewed as part of a pseudo-octahedral fragment within the cluster. A number of the clusters making up this group are listed in Table 1. Also included in the table are the number of “metal” electrons (this number is calculated from the formal oxidation states of the four metals in the clusters) and the metal-metal distances found in each cluster. It should be noted that all 12 of the ligands in the M4S4L,* clusters are not always identical. In [Mo4S4(NO),(CN),]*-, for example, each molybdenum atom is coordinated by two cyanide ligands and one nitrosyl ligand. 24 In some clusters multidentate ligands occupy more than one coordination site and may actually span two metal atoms. The structure of Mo4S4(S2CNEt2)6 is shown in Fig. 1. Here, four of the bidentate Et,dtc ligands each bind to a single molybdenum atom, while each of

Fig. 1. Structure of Mo.,S&CNEt& (refs 25 and 26). Only the first C in each Et group is shown. One bidentate Et,dtc ligand is bound to each MO, and the remaining two Etzdtc ligands each span two MO atoms. Neglecting the Mo-MO bonds, each MO is bound to six S atoms and is approximately

octahedral.

2846 S. HARRIS

Table 1. Homometallic clusters having structure type 4 or 5 : all four metals octahedrally coordinated

Cluster Number of

metal electrons M-M distances Reference

MoqSXNCgH,Me),(S,CN(i-Bu),), 4

MoGUNGH~Me)&P(OW& 4

[V4S4WeCP)41+ 7

V4S4WeCPI4 8

Mo4S4W’EtJ, 10 [Mo,S,(edta),]‘- 10

Mo&(SKNW, 10

[Mo4S4WS),,16- 10 [Mo,S,(&P~C~),]~+ 10

Mo&(HBW,).&z) 11 [Mo,S,(edta)2]3~ 11 [Mo4S4(i-PrCp)$ 11

Cr&(MeCp), 12

[Mo.&(NH3),J4+ 12 [Mo4S4(edta),14- 12 Mo4S4R4 (R = Cp, MeCp, Me,Cp) 12

[Re4S4(S3)d4- 12

[Mo4S4Wh18- 12

Fe4S4CP41zc 18

W4S4CP41+ 19

W4S4(NQ4(CNh18- 20

Fe4S4CP4 20

Ru4S4WCP)4 20

[co4s4cP41+ 23

CO4S4CP4 24

Fe4S4(W 1 2 24

4 2.927, 2.932 3.006(2), 3008(2) 2.881(2), 3.66(4) 2.862(2), 3.69(4) 2.852(2), 2.855(4) 2.868(4), 2.884(2)

2.79(2), 2.88(4) 2.74-2.87

2.732(2), 2.86(4) 2.791(3), 2.869(3)

2.79-2.90 2.659, 2.92(5)

2.762.88 2.86-2.92 2.82-2.85 2.78-2.80 2.77-2.79 2.89-2.91

2.76(6) 2.85(6)

2.834(4), 3.254(2) 2.652(2), 3.188(2), 3.319(2)

2.99(2), 3.67(4) 2.65(2), 3.365(4) 2.77(2), > 3.5(4)

3.172(4), 3.330(2) 3.236-3.343 3.443-3.477

16

27 28 16

16,29 30 31

25,26 32 33 34 35 33 36 37 31

11,33 38 39 4

40 24

41,42 43 17 17 18

a Numbers in parentheses indicate number of averaged distances.

the two remaining Et,dtc ligands span two molybdenum atoms.25~26 The M4S4Lr2 and M4S4Cp4 designations are meant to indicate that in these clusters six coordination sites are occupied around each metal atom resulting in approximately octahedral coordination of all four metals.

In all the cubane-type clusters there are three sets of bonds which have to be considered when describing the electronic structure. These are the metal-metal bonds, the metal-ligand bonds, and the bonds between the metals and the sulphurs which are part of the M4S4 core. The metal- ligand and metal-sulphur interactions are both stronger than the metal-metal interactions, and the qualitative bonding schemes described here assume that the stronger metal-ligand and metal- sulphur interactions can be separated from the weaker metal-metal interactions. (From now on the stronger M-L and M-S interactions will be grouped together and described collectively as “metal- ligand interactions”.)

The Dahl group synthesized and characterized several M4S4Cp4 c1usters.4,17*40*42 The structure of Co,S,Cp, is illustrated in Fig. 2. In this cluster the long non-bonding cobalt-cobalt distances result in a Co,S, core which closely resembles a true cube. Making use of the Td symmetry of the clusters, the Dahl group developed a qualitative cluster bonding scheme that makes it possible to understand and predict the changes in metal-metal bonding which accompany changes in the number of cluster electrons. Assuming that the metal-metal interactions can be separated from the metal-ligand interactions, the metal nd, (n + 1)s and (n + 1)~ orbitals of the four metals making up the metal tetrahedron can be combined to form 36 symmetry adapted combinations. The 20 symmetry combinations involving the 20 nd orbitals (five from each metal) prove to be most important to the description of the tetrametal cluster bonding, since it is these combinations which are bonding, non-bonding or antibonding with respect to metal-metal interactions. The ligand orbitals

&bane-type clusters 2847

Fig. 2. Structure of Co,S&!p, (ref. 17). Each octahedral Co is bound to three core S atoms and a Cp ring. Since there are no Co-Co bonds, the Co& core closely resembles a cube.

can also be combined into symmetry orbitals, their number and symmetry properties depending on the number and nature of the ligands. The metal and ligand symmetry orbitals can then be combined to form cluster molecular orbitals.

The qualitative MO scheme derived in this manner for the Td M&Cp, complexes4 is shown in Fig. 3. The M4 symmetry orbitals are shown on the left. The 20 orbitals resulting from the metal d orbitals are divided into three groups--six M4 bonding orbitals (a, +e+tJ, six M4 antibonding orbitals (tl+f2), and eight orbitals which are essentially non-bonding between the metal atoms (e+l,+t*). The symmetry orbitals resulting from combinations of the various S atomic and Cp molecular orbitals are indicated on the right side of the diagram. The cluster orbitals which arise from the interactions of the metal and ligand combinations are indicated in the centre. The lower

Cluster Molecular Orbit&

LQand

%:,“P

M4 ~4S&P, 4cp + 4s

Fig. 3. Qualitative MO energy level scheme derived by the Dahl group (ref. 4) for M,S,Cp, clusters. The scheme is based on cubic Td symmetry. The symmetry orbitals for the M4 tetrahedron are shown on the left, while the symmetry combinations of the S and Cp orbitals are shown on the right. The cluster orbitals resulting from interactions between the M4, S and Cp orbit& are shown in the

middle.

2848 S. HARRIS

energy cluster orbitals are centred primarily on the ligands and are either ligand or M-L bonding orbitals. These levels are completely occupied. The higher energy orbitals are primarily metal in character and are M-L antibonding. The number of electrons occupying these orbitals will depend on both the total electron count of the cluster and the relative energies of the three sets of levels. The relative energies of the metal based cluster orbitals-particularly those which are non- bonding between the metals-are influenced by the metal-ligand interactions. In the M&Cp, clusters the interaction between the M4 non-bonding combinations (e + t, + tz) and the ligand orbitals of appropriate symmetry are strong enough to destabilize the M., non-bonding combinations to energies above the M4 bonding and antibonding sets of orbitals.

In the cluster valence electron (CVE) scheme of Lauher, 44 an electron count of 60 should result in a completely bonded (six M-M bonds) tetrahedron of metals. In the M4S4Cp4 clusters, the lower energy metal-ligand bonding orbitals are occupied by 48 of these electrons. (The four low energy MOs corresponding to the sulphur 3s orbitals are not involved in the M-L bonding and are not included in the cluster electron count.) A 60-electron cluster would therefore have 12 metal electrons available to occupy the M4 cluster orbitals, in this case the set of six M-M bonding orbitals. This should result in a completely bonding tetrahedron of metals, in accordance with the CVE scheme. The M4S4Cp4 clusters considered by the Dahl group (Co4S4Cp4, with a 72 CVE count and [Fe4S4Cp4]“*‘+‘*+, with 68, 67 and 66 CVE counts, respectively) all have electron counts in excess of 60 and thus have more than 12 metal electrons. These extra metal electrons will occupy M-M antibonding orbitals. In Co4S4Cp4, the 24 metal electrons should occupy all six M-M bonding orbitals and all six M-M antibonding orbitals, leading to a completely non-bonding tetrahedron of metals. This is consistent with the non-bonding M-M distance of 3.295 observed in Co4S4Cp4. In [Fe4S4Cp4]o~‘+.2+, where there are 20, 19 and 18 metals electrons, respectively, the M-M antibonding orbitals are partially occupied by 8, 7 and 6 electrons. This should lead to distortions of the M4 unit away from Td symmetry, and the Dahl group successfully correlated the experimentally observed differences in M-M bond lengths with the symmetry of the M4 antibonding orbitals expected to be occupied. They also noted that the larger changes in M-M distances in comparison to the relatively small changes in M-S and M-L distances tend to confirm that these orbitals are primarily metal in character.

This qualitative scheme can be applied to both the M4S4Cp4 and M$4Li2 clusters, and the M-M distances in the clusters listed in Table 1 are consistent with the bonding scheme. The 60- electron clusters, those having 12 metal electrons and a completely filled set of M-M bonding orbitals, all contain a completely bonding metal tetrahedron. The presence of more than 12 metal electrons results in the occupation of M-M antibonding orbitals and leads to a corresponding decrease in the degree of M-M bonding. The M-M non-bonding orbitals are sufhciently high in energy in these clusters that they are never occupied. Clusters containing less than 12 metal electrons will have an incompletely filled set of M-M bonding orbitals, and differences in the M-M distances are again expected. This is certainly true in the clusters containing four metal electrons, where only two short M-M distances, or two M-M bonds, are observed. Interestingly, the structures of clusters such as [Mo,S,(i-PrCp),]+ and [Mo4S4(i-PrCp)4]2+, which contain 11 and 10 metal electrons, respectively, show only small deviations from the structure of Mo4S4(i-PrCp)4, which contains 12 metal electrons. According to the bonding scheme in Fig. 3, the occupied M-M bonding orbitals have al, e and t2 symmetry. The relative peak intensities and energies in the valence photoelectron spectrum of Mo4S4(i-PrCp)4 indicate that the highest occupied set of orbitals has t2 symmetry and that the energy ordering of the three highest energy sets of orbitals is t2 > e > al.33 It was suggested by Bandy et al.33 and Davies et aL4’ that the highest energy t2 orbitals are only weakly M-M bonding or nearly non-bonding. This would explain the very small changes in structure in the series [Mo4S4(i-PrCp)4]0,‘+,2f, where the metal electron count goes from 12 to 11 to 10. Molec- ular orbital calculations for Mo,S,Cp, and Cr4S4Cp4,’ ’ V,S,(MeCp), and p,S,(MeCp),]+ I6 and [Mo,S,(CN) 1 *] ‘-,’ confirm that the t2 set of orbitals lies highest in energy and that, in general, the order of the levels is t2 > e > a,. (Results of an earlier calculation for Cr,O,Cp, indicated that a different ordering of levels was appropriate for the M4X4Cp4 clusters.7 This different ordering is inconsistent. however, with both the observed structures of many of the clusters and all other reported calculations.) In a recent study of the magnetic susceptibility of [Mo&(edta)2]*-, Shibahara and co-workers found that [Mo4S4(edta),12- (10 metal electrons) is diamagnetic.46 They concluded that the HOMO in [Mo4S4(edta),14- (12 metal electrons) must be the a, orbital, since removal of


two electrons from this singly degenerate orbital would lead to a diamagnetic cluster. They argued that if the electrons were initially removed from the set of t2 orbitals, the distortions from Td symmetry are not sufficient to ultimately yield a diamagnetic cluster. Once again, these conclusions are inconsistent with the numerous calculations which repeatedly find that the a, orbital is the most stable of the M4 cluster bonding orbitals. Since wo&(i-PrCp)4]2+ (10 metal electrons), where it seems certain that two electrons have been removed from the t2-orbitals, is also diamagnetic4’ it is more likely that the HOMO in [Mo4S4(edta)2]4- is also of t2 symmetry. Using overlap population analyses, Williams and Curtis found that for Mo4S4Cp4 and Cr,S,Cp, only the al orbital is strongly M-M bonding. ’ ’ The e orbitals are weakly M-M bonding, while the t2 orbitals are nearly M-M non-bonding in character. They commented that the number of clusters with fewer than 12 metal electrons but short M-M distances is, therefore, not surprising, since even in these clusters the more strongly M-M bonding orbitals are occupied, and partial occupation of the nearly non- bonding t2 orbitals should lead to only weak first-order Jahn-Teller distortions. It should be noted that a number of the clusters having fewer than 12 metal electrons contain several multidentate ligands which span two metals. Although distinct patterns of short and long M-M distances are more pronounced in these clusters, comparisons of the M-M distances in these clusters should be made with care, since the shorter M-M distances may be dictated by these spanning ligands.

The qualitative bonding scheme developed by the Dahl group is thus seen to be generally applicable to a large number of M,S,Cp, and M4S4L1 2 clusters. As discussed above, the development of this scheme depends on the separability of the stronger metal-ligand interactions from the weaker metal-metal interactions. The scheme drawn in Fig. 3 first considers the metal-metal interactions and then adds on the metal-ligand interactions. Alternatively, it is possible to first consider the metal-ligand interactions and then add on the metal-metal interactions. That is, we can first consider a fragment within the cluster composed of a metal and its surrounding ligands. We determine how the metal-ligand interactions within this fragment affect the energies of the metal-based orbitals and then combine the metal orbitals to form the tetrametal cluster orbitals. As will be seen below, treating the interactions in this order becomes extremely useful for the less symmetric clusters considered later in the report. We will call this a “metal fragment orbital” approach. Fragment orbital approaches have proved extremely useful in describing the bonding in many organometallic clusters (particularly metal carbonyl clusters)47s48 where the stronger metal-ligand interactions and the weaker metal-metal interactions can be viewed separately. In metal carbonyl clusters, for example, it is possible to separate a cluster into several M(CO), fragments. The M-M bonds in the cluster can then be described in terms of metal-based fragment orbitals. The number, nature and relative energy of these fragment orbitals is determined largely by the number and geometry of the ligands in the M(CO), fragment. Each fragment can often be viewed as some part of an octahedron, and the fragment metal orbitals which are available for cluster formation can be related to the tzs and es orbitals in an octahedral complex. Upon formation of the cluster, the lower energy t,-like orbitals remain non-bonding between the metals, while the high energy e,-like orbitals on each fragment are utilized for the formation of M-M bonds. The spatial orientation of the e,-like fragment orbitals is such that formation of the M-M bonds tends to complete the octahedral coordination about each metal.

When the M-M bonds are neglected, each of the metal atoms in an M4S4Cp4 or M&L12 cluster lies in a pseudo-octahedral environment and can be viewed as part of an MS&p or M&L3 fragment. From the point of view of the metals, there are four such fragments in each cluster. Since the strongest interactions in the cluster occur within these fragments, the numerous lower energy molecular orbitals in each fragment or in the overall cluster are associated with L and M-L bonds. Once these bonds have been separated off, the formation of M-M bonds can be considered. Within each fragment, the energies and orderings of the five metal-based d orbitals are determined by the metal-ligand interactions and the formation of M-L bonds. (These “metal-based” orbitals do contain some ligand character because they are in fact generally M-L antibonding in character. Since they are primarily metal d orbital in character, however, we will refer to them as metal-based.) The actual number of electrons occupying these d orbitals will be determined by the formal oxidation state of the metal.

In a cluster where each metal is approximately octahedrally coordinated, the d orbitals will be split into the familiar pattern for near octahedral coordination, i.e. a set of two es orbitals lying higher in energy than a set of three tzg orbitals. This is illustrated in the left side of Fig. 4. Although

2850 S. HARRIS

Octahedrel

MS3L3 of

MS3CP

w&L12 or

k%CP,

Fig. 4. Qualitative MO energy level scheme (based on the “fragment metal orbital” approach) for the metal-based cluster orbitals in an M4S4L12 or M4S4Cp4 cluster, where each metal is octahedrally coordinated. The splitting of the metal d orbitals in an octahedral environment is shown on the left and the resulting groups of cluster orbitals are shown on the right. The lower energy M-L and L

bonding orbitals are not shown.

these are not really degenerate sets of orbitals as they would be for perfect Oh symmetry, it is useful to designate them as “eg” and “fzg” because they are still distinguishable as sets of two and three orbitals. When the local coordinate system on each metal is defined as in 6, the two sets are (d,z, d,,)e,

and (d,,, u’,,, dX~_y~)f2g. These are the orbitals which are available for the formation of M-M bonds. The es orbitals, which point directly at the six ligands, are not oriented properly for M-M bonding and thus remain non-bonding between the metals. The t2, orbitals are oriented properly for M-M bonding and combine in the cluster to form sets of M-M bonding and M-M antibonding orbitals. (This is in contrast to the metal-carbonyl clusters discussed above, where the e, orbitals are oriented properly to form M-M bonds and the tg orbitals remain non-bonding between the metals in the cluster.) As illustrated schematically in Fig. 4, the t2, orbitals from the four metal atoms combine to form sets of six bonding and six antibonding levels. The splitting of the metal e, and t2, orbitals resulting from the metal-ligand interactions is sufficiently large, however, that both sets of cluster orbitals derived from the metal t5 orbitals lie below the set of non-bonding levels derived from the metal e, orbitals. These sets of bonding, antibonding and non-bonding levels are of course the same sets of levels illustrated in Fig. 3, although the symmetry labels have been omitted in Fig. 4. The main difference between the two approaches is that because the metal fragment orbital approach first takes the stronger metal-ligand interactions into account, it is possible to identify the sets of M4 cluster orbitals with specific sets of metal fragment orbitals. This approach also makes it clear that the energy of the non-bonding M4 cluster orbitals relative to the M4 cluster bonding and antibonding orbitals is determined by the relative energies of the e, and t2, sets of orbitals within each M&Cp or MS3L3 fragment. Although these non-bonding orbitals are high in energy and not occupied in this group of clusters, this is not the case for many of the other groups described below,


and it becomes useful to understand how and why the energy of the non-bonding levels changes in the different groups of clusters.

2.2. AI1 four metals tetrahedrally coordinated

The clusters in this class are characterized by the general formula M4S4L4 (7). Neglecting the M-M bonds, each M atom is four-coordinate and can be viewed as part of a pseudo-tetrahedral

M&L fragment within the cluster. A number of clusters which fall into this group are listed in Table 2. These clusters can be further divided into those where L is a x-acceptor ligand and those where L is a K-donor ligand. The acceptor or donor properties of the ligands have a significant impact on the energetic ordering of the M4 cluster orbitals.

Table 2. Homometallic clusters having structure type 7 : all four metals tetrahedrally coordinated

Cluster

Number of metal electrons M-M distances Reference

(L = n-acceptor ligand) bWW4 B&PJO)41-

(L = n-donor ligand) [Fe&(S-2,4,6-(i-Pr),C,H&J ~Fe&WH3h12- [Fe&C14]2- [Fe&,Br,]*- b&J412- W&CW412-

(R = CH,Ph) (R = H) (R = Ph) (R = p-&H.,NHJ (R = CH2CH20H) (R = t-Bu)

[Fe,S,(S(CH2)2COO),16- P+&WW2CL1*-

o( = 0) (X = S)

[Fe,S,(SPh),(O-p-C,H,CH,)$- [Fe.$,(L*S,)Cl]*-

28 2.64-2.66 8,49 29 2.688(4), 2.704(2) 8

21 22 22 22 22 22

22 22

22 22

(L-S3 = Cs(SC6H2-3-S-4,6-(CH3)&(SCaHs-4-CH&) PWWW413-

(R = Ph) 23 (R = CH,Ph) 23 (R = p-C,H,Br) 23 (R = t-Bu) 23 (R = Et) 23

2.74(av.) 50 2.739(2), 2.760(4) 51 2.755(2), 2.771(4) 52 2.747(2), 2.763(4) 53

2.720-2.762 54

2.776(2), 2.732(4) 55 2.738-2.770 56

2.730(2), 2.739(4) 57 2.767(2), 2.741(4) 58

2.700-2.752 59 2.749(2), 2.764(4) 60 2.788(2), 2.743(4) 61

2.781(2), 2.752(4) 62 2.760(2), 2.729(4) 62

2.784,2.730,2.733(2), 2.767(2) 62 2.742-2.778 63

2.730(2), 2.750(4) 64,65 2.719-2.782 66 2.720-2.814 67 2.736-2.794 68

2.760(2), 2.7700 68

a Et,N+ salt.

2852 S. HARRIS

Fig. 5. Structure of Fe,S,(NO), (ref. 8). Each Fe is bound to three core S atoms and a x-acceptor NO ligand. Neglecting the Fe-Fe bonds, the geometry around each Fe atom is approximately

tetrahedral.

2.2.1. a-Acceptor ligunds. The Dahl group synthesized and characterized both Fe,&(NO), and [Fe$4(NO),]-.“*49 (The structure of Fe4S4(N0)4 is illustrated in Fig. 5.) Using the same approach applied earlier to the M4S4Cp, clusters, they developed a qualitative bonding scheme appropriate for this type of cluster. Once again, making use of the Td symmetry of the cluster, the metal orbitals are tirst combined separately from the ligand orbitals, and the metal and ligand symmetry orbitals are then combined to form cluster molecular orbitals. This scheme is illustrated in Fig. 6. The M4 symmetry orbitals shown on the left are identical to those in Fig. 3. The symmetry orbitals arising from the S atomic and NO molecular orbitals are shown on the right. The cluster orbitals resulting from the mixing of the metal and ligand orbitals are indicated in the centre. Once again, the lower energy orbitals are either L or M-L bonding orbitals and are fully occupied. The higher energy orbitals are primarily metal centred and fall into the same M-M bonding, antibonding and non- bonding groups found in the clusters where all the metals are octahedrally coordinated. A comparison of the diagrams in Figs 3 and 6 shows, however, that the relative ordering of these groups

Cluster Molecular Orbital!,

Ligand

=&%2

M4 M&W)4 4N0+4S

Fig. 6. Qualitative MO energy level scheme derived by the Dahl group (ref. 8) for M,S,(NO), clusters. The scheme is based on cubic Td symmetry. The symmetry orbitals for the M., tetrahedron are shown on the left, while the symmetry combinations of the S and NO orbitals are shown on the right. The cluster orbitals resulting from interactions between the M,, S and NO orbitals are shown

in the middle.


is different in the two types of clusters. In the clusters containing all octahedral metals the non- bonding M4 cluster orbitals are destabilized by metal-ligand interactions and lie above the M-M bonding and antibonding orbitals. In Fe,S,(NO), the eight non-bonding cluster orbitals are strongly stabilized by interactions with the n-acceptor NO ligands and lie below the M-M bonding and antibonding levels.

Within the CVE counting scheme, the 60-electron Fe&(NO), should contain a completely bonding M4 tetrahedron. When the 16 lower energy L and M-L bonding orbitals have been occupied by 32 of these electrons, 28 excess metal electrons remain to occupy the M4 cluster orbitals. (These 28 electrons can also be associated with the presence in the cluster of four Fe+ (d7) centres.) These 28 metal electrons will occupy all eight of the non-bonding orbitals and all six of the M-M bonding orbitals. The occupation of the six M-M bonding orbitals is consistent with the six bonding M-M distances of 2.65 A found in Fe.&(NO),. Although a CVE count of 60 once again corresponds to a completely bonded M4 tetrahedron, the actual number of metal electrons and the ordering and occupations of the metal-based cluster orbitals are quite different in this M&L4 (L = n-acceptor) cluster than in the M,S,Cp, or M4S4LLZ clusters. In the clusters containing octahedral metals, 12 metal electrons are necessary to completely fill the M-M bonding orbitals, and electrons in excess of the required 12 will occupy M-M antibonding orbitals. In the clusters containing tetrahedral n-acceptor ligands, 28 metal electrons are necessary to completely fill the M-M bonding set of orbitals, and only electrons in excess of the required 28 will occupy M-M antibonding orbitals. This qualitative bonding model is confirmed by the fact that when Fe,S,(N0)4 is reduced to give [Fe,S4(N0)4]-, all of the M-M distances increase slightly, suggesting that the additional electron occupies an M-M antibonding orbital. Smaller changes in the M-S distances once again confirm that the antibonding cluster orbitals are primarily metal in character. Although no clusters with less than 28 metal electrons have been synthesized, a loss of one or two electrons from the M-M bonding orbitals is expected to have little effect on the M-M distances, since it is probable that just as in the M&Cp, or M4S4L,2 clusters the higher energy orbitals belonging to the M-M bonding set are quite delocalized and close to non-bonding. A recent Extended Hiickel calculation for Fe,S,(NO), confirms the occupation of both the non-bonding and bonding cluster orbitals and finds that the t2 HOMO is essentially non-bonding.”

The orbital scheme shown in Fig. 6 is once again derived by first considering the metal-metal interactions and then adding on the metal-ligand interactions. This orbital scheme can also be derived using the metal fragment orbital approach, that is by first considering the stronger metal- ligand interactions and then adding on the metal-metal interactions (Fig. 7). Each metal in the

All Tetrahedral Coordlnatlon PI Acceptor I.

Me [---_1- m- 11- E 1 MM --- .a”-- -l-“.-* (4 nonbonding *ll*l...“.“.

Fig. 7. Qualitative energy level scheme (based on the “metal fragment orbital” approach) for the metal-based cluster orbitals in an M&L_, cluster, where each metal is tetrahedrally coordinated and L is a n-acceptor ligand. The splitting of the metal d orbitals in a tetrahedral environment is shown on the left and the resulting cluster orbitals are shown on the right. The relatively large separation between the “e” and “t ” 2 orbitals in the tetrahedral M!&L fragment is expected when L is a n-

acceptor ligand.

2854 S. HARRIS

M4S4L4 cluster is first viewed as a part of a tetrahedral M&L fragment. Within each fragment, the metal d-orbitals are split by the metal-ligand interactions into two sets of levels, e and tz. In the tetrahedral environment the e orbitals now lie at lower energies than the tZ orbitals. This is shown on the left side of Fig. 7. Once again, because the M&L fragment does not actually have Td symmetry, these groups of two and three orbitals are not degenerate but do lie close enough in energy to be grouped together. When the local metal coordinate system is defined as in 8 these

groups of orbitals correspond to (&,d,Je, and (dX,,,dXz_,,~,dZ2)tZ. (Because the M&L fragment actually has near Cfv symmetry, groupings of two, two and one metal orbitals will be apparent. Under CsO symmetry these correspond to e, e and al sets, where the higher energy a, orbital is & For consistency, however, it is useful to view these as tetrahedral fragments and to classify the two sets of metal orbitals as tz and e.) In clusters containing octahedrally-coordinated metals the tz9 orbitals are used to form M-M bonds while the es orbitals remain non-bonding. In clusters containing tetrahedral metals the tz orbitals are used for the formation of M-M bonds, while the e orbitals can be viewed as non-bonding. The resulting cluster bonding scheme is shown on the right side of Fig. 7. The t, orbitals from the four metal “fragments” combine as before to form six bonding and six antibonding cluster orbitals. The bonding orbitals are not the lowest energy M, cluster orbitals, however, because the metal e levels are sufficiently stabilized by the presence of the x-acceptor ligands that even though they remain non-bonding in the cluster they lie below the bonding levels. The qualitative cluster bonding scheme is entirely equivalent to the scheme in Fig. 6, except that it makes clear why the non-bonding levels lie below the M4 cluster bonding orbitals. It should be noted that although the non-bonding and bonding orbitals are shown as derived exclusively from the e and t2 metal fragment orbitals this separation is not as clean cut as in the clusters with octahedrally coordinated metals. In those clusters the separation is exact. Here, because the M&L fragment is closer to CJo than to Td symmetry, there will be some mixing of the two sets of metal fragment e orbitals upon formation of the cluster orbitals. This does not change the fact, however, that in general the energetic ordering of the M, cluster orbitals is non- bonding < bonding < antibonding.

2.2.2. x-Donor ligands. All of the known M&L4 clusters containing n-donor ligands have Fe& cores and generally have metal electron counts of 22 or 23. The structure of one of these clusters, [Fe,S,(SPh),]*-, is shown in Fig. 8. While a qualitative cluster bonding scheme can be derived for these clusters, an accurate description of the electronic structure becomes more complicated. Although the Dahl group did not characterize any clusters of this class, they did discuss how the qualitative bonding picture would be altered by the presence of n-donor ligands.’ They noted that the cluster non-bonding orbitals (e + t , + t2) are now expected to be energetically situated between the M 4 bonding orbitals (a, + e + tz) and the M4 antibonding orbitals (t 1 + t2). This ordering comes about because the cluster non-bonding orbitals are somewhat destabilized (relative to the corresponding non-bonding orbitals in the clusters containing n-acceptor ligands) by the presence of R-donor ligands.

A qualitative energy level diagram for an M4S4L4 cluster where L is a n-donor ligand can be derived via the metal fragment orbital approach. This diagram is shown in Fig. 9. Once again, the metal d orbitals within each M&L fragment are split by the metal-ligand interactions into t2 and e sets. In the presence of n-donor ligands the e orbitals are destabilized by metal-ligand interactions (or conversely, they are not stabilized as they are in the presence of x-acceptor ligands), so that the separation between the e and t2 orbitals is smaller than in the presence of n-acceptor ligands. As a result, when the r2 orbitals combine to form bonding and antibonding combinations the energy of the non-bonding cluster orbitals (the metal e orbitals) is intermediate between the energies of the bonding and antibonding orbitals.


Fig. 8. Structure of [Fe&(SPh),]*- (ref. 57). Each Fe atom is bound to three core S atoms and the S atom of a n-donor thiolate ligand. Neglecting the F+Fe bonds, the geometry around each Fe

atom is approximately tetrahedral.

All Tetmhadml Coordination PiDonor I.

Tetmhedml MSIL

c+

M944

Fig. 9. Qualitative energy level scheme for the metal-based cluster orbitals in an M&L, cluster, where each metal is tetrahedrally coordinated and L is a s-donor ligand. The splitting of the metal d orbitals in a tetrahedral environment is shown on the left and the resulting cluster orbitals are shown on the right. The relatively small separation between the “e” and “f*” orbitals in the tetrahedral

M&L fragment reflects the presence of the z-donor ligand.

Using the CVE counting scheme, any of the [Fe,S,(SR),]2- clusters is a 54-electron cluster. When 32 electrons are used for M-L bonding, 22 metal electrons remain to occupy the M4 cluster orbitals. Alternatively, the 22 “metal” electrons can be associated with two Fe’+ (&) and two Fe3+ (d’) centres. After 12 of these metal electrons occupy the bonding levels, the 10 remaining metal electrons partially occupy the eight non-bonding levels. The complete occupation of the M4 bonding levels is consistent with the completely bonded tetrahedron of metals observed in the clusters having 22 metal electrons. That this simple description gives a generally correct picture of the bonding is conhrmed by the structural changes which accompany the addition of a metal electron to the core. The most significant changes occur in the M-S bond distances, while the M-M distances remain essentially constant. This suggests that the extra electron enters an orbital which is non-bonding between the metals but is M-S antibonding. Similar changes in the core structure are observed when one electron is removed from the core, also suggesting that the electron is removed from a non-bonding cluster orbital. The similarities and differences in the structures of many of the Fe4S4L4 clusters have been discussed in detail in a number of the references in Table 2.

2856 S. HARRIS

It is interesting to note that a cluster having anywhere from 44 to 60 cluster valence electrons is expected to contain a completely bonded M4 tetrahedron, since any of the 16 electrons in excess of 44 should occupy a non-bonding cluster orbital. Only an electron count in excess of 60 will result in the occupation of M-M antibonding orbitals. (This assumes that the non-bonding orbitals all lie between the bonding and antibonding levels. In fact the energy ranges of the groups of orbitals may well overlap, so that an electron could occupy an antibonding level before all the non-bonding levels were occupied.) This apparent inconsistency with the general rule that a 60-electron count is required for a completely bonding tetrahedron appears to arise from the fact that the original CVE scheme was derived for metal-carbonyl clusters where the bonding schemes are somewhat different.44 It is not really surprising that the rules derived for those clusters are not always obeyed here.

The bonding scheme in Fig. 9 makes it possible to determine the number of bonding and non- bonding electrons and is consistent with the observed molecular structures for these clusters. It does not, however, provide a description of the various spin states which can occur in these clusters. Eight closely spaced non-bonding metal orbitals are partially occupied by a large number of electrons (in the [Fe4S4(SR)4]2- clusters, 10 electrons occupy eight closely spaced non-bonding levels). Various spin configurations lie close in energy, and it is difficult to calculate an accurate description of the ground-state spin configuration. From a simple viewpoint, we can think of such a cluster as containing four high-spin irons. The t2 orbitals combine to form completely filled bonding molecular orbitals, leaving a number of electrons in non-bonding orbitals on each iron centre. The spins of these electrons can be weakly coupled together, and a complete description of the electronic structure of these systems requires a calculational technique which can treat this coupling. The [Fe4S4(SR),12- clusters have been the subject of several sets of calculations,5~6~13-‘5~6g many of which have been aimed at understanding the spin interactions. These calculations confirm that the delocalized MO bonding scheme illustrated in Fig. 9 presents a bonding picture which is qualitatively correct. It is also clear, however, particularly from the work of Aizman and CaseI and Noodleman et al.” that an accurate description of the electronic structure of these clusters requires a computational technique which can take into account both the delocalized nature of the interactions and the weak coupling of the spins on the four metal centres.

2.3. Allfour metals five-coordinate

A cluster in this class is characterized by the general formula M4S4LB and ideally may exhibit either of two structures, 9 or 10. In 9, each metal atom is five-coordinate (neglecting M-M bonds)

and can be viewed as part of a nearly square pyramidal M&L2 fragment within the cluster. In 10, each metal is again five-coordinate but can be viewed as part of a trigonal bipyramidal M&L2 fragment. Clusters having these structures are listed in Table 3. As will become apparent, both in this discussion of clusters in which all of the metals are five-coordinate and in the later discussions

Table 3. Homometallic clusters having structure type 9 or 10: all metals five- coordinate

Cluster Number of


[Fe4S4(S2C2(CF~)2)412- 18 2.730(4), 3.224(2) 70,71

[Fe4S4@&NEbW 21 2.845(4), 3.070(2) 72


Fig. 10. Structure of [Fe,S,(S,C,(CF,),),]*- (refs 70 and 71). The F atoms are not shown. Each five-coordinate Fe is bound to three core S atoms and two S atoms of a bidentate dithiolene ligand. Neglecting the Fe-Fe bonds, the geometry around each Fe atom is approximately square pyramidal.

Two long F+Fe distances indicate that there are only four Fe-Fe bonds in the cluster.

of clusters in which only one or two of the metals are five-coordinate, the distinction between square pyramidal and trigonal bipyramidal coordination is not always clear cut.

The structure of [Fe4S4(S2C2(CF3)3)4]*- is illustrated in Fig. 10. One bidentate dithiolene ligand is bound to each iron atom. Since the coordination geometry around each metal is clearly square pyramidal, the cluster corresponds to structure 9. When the Dahl group structurally characterized this cluster,71 they noted that the pattern of M-M distances (four shorter plus two long) combined with the presence of 18 “metal” electrons (corresponding formally to four Fe3.‘+ atoms) suggests that the cluster bonding scheme in [Fe4S4(S2C2(CF3)&]*- is probably similar to the scheme in

PWWP412+. In that cluster, which contains octahedrally-coordinated metals and 18 metal electrons, 12 metal electrons completely occupy the M-M cluster bonding orbitals and the remaining six metal electrons partially occupy the M-M antibonding orbitals.

A qualitative orbital scheme for a cluster in which each metal is square pyramidal is shown in Fig. 11. The splitting of the metal orbitals brought about by the metal-ligand interactions in each of the square pyramidal MS3L2 fragments is illustrated on the left hand side of the figure. A square pyramid is easily derived from an octahedron by removing one of the six ligands surrounding the

All Square Pynmidal Coordination

M dr, __-[&El (4) MMnb

Md.2 --

[ 1 = (6) MM b

Fig. 11. Qualitative energy level scheme for the metal-based cluster orbitals in an M&LB cluster, where each metal is square pyramidal. The splitting of the metal d orbitals in a square pyramidal

environment is shown on the left and the resulting cluster orbitals are shown on the right.

2858 S. HARRIS

metal. The removal of this ligand (here it is assumed to be a ligand lying on the z-axis in the local coordinate system illustrated in 6) affects primarily the energy of the metal d,z orbital, so the degeneracy of the “eg” orbitals is lost in square pyramidal coordination. Although the dx. orbital remains high in energy, the dzz orbital is stabilized by the loss of the sixth ligand. The size of this stabilization will depend on the nature of the ligands and the actual geometry of the fragment, but it is clear that the energy of the dzz orbital will be well separated from the energy of the dxy orbital. Three orbitals corresponding to the tzs orbitals in an octahedral environment lie close together and lowest in energy. (As indicated in Fig. 6, these orbitals actually break up into two sets, because in most examples of square pyramidal coordination, the metal atom lies above the plane defined by the four basal plane ligands. In this geometry, the metal d,, and dYL orbitals he somewhat higher in energy than the dxz_yz orbital.) In the cluster, the tzg orbitals combine to form sets of six bonding and six antibonding M4 cluster orbitals. The dx,, and dzz orbitals remain M-M non-bonding, but now they will occur as two separate groups of non-bonding cluster orbitals. The non-bonding orbitals derived from the metal dry orbitals lie highest in energy, while those derived from the metal d,z orbitals lie lower in energy. As indicated by the qualitative scheme in Fig. 11, non-bonding orbitals derived from these d,z orbitals are expected to lie within the same energy range as the M-M antibonding orbitals. In the l&electron [Fe,S4(S2C2(CF3)2)4]2- complex, 12 of the metal electrons occupy the M-M bonding orbitals, leaving six electrons to occupy the higher energy cluster orbitals. As discussed above, the similarities in the structures of [Fe4S4(S2C2(CF3)2),]2- and [Fe4S.&p4]2+ suggest that in [Fe,S,(S2C2(CF,)2)4]2- these six electrons occupy M-M antibonding orbitals very similar in character to those occupied by six electrons in [Fe,S,CpJ2+. That is, in [Fe&S4 (S,C,(CF,),),]‘- the non-bonding metal d,z orbitals do not lie low enough in energy to be occupied. (This analysis .is based on the presence of 18 metal electrons in [Fe4S4(S2C2(CF3)2)4]2-. Due to the presence of the dithiolene ligands the actual number of “metal” electrons may be somewhat uncer- tain. If there are actually more than 18 “metal” electrons present in the cluster, then the structure of the cluster suggests that the non-bonding cluster orbitals derived from the metal dzz orbitals lie at low enough energies to be at least partially occupied.)

The main difference between the bonding schemes for a cluster containing all octahedral or all square pyramidal metals is seen to occur in the relative energies of the non-bonding cluster orbitals. For all octahedral coordination, the non-bonding cluster orbitals lie at sufficiently high energies to always remain unoccupied. For all square pyramidal coordination, the set of non-bonding cluster orbitals derived from the metal d,z orbitals lie at lower energies and may become occupied in clusters having higher metal electron counts.

The other idealized metal coordination geometry in an M&L8 cluster is trigonal bipyramidal. As seen in 10, each metal can be viewed as part of a trigonal bipyramidal M&L2 fragment. In comparison to a square pyramid this coordination geometry alters the energy ordering of the d orbitals within the M&L2 fragment and will therefore also have an effect on the energies of the cluster orbitals. A qualitative energy level scheme for a cluster in which all the metals are trigonal bipyramidal is shown in Fig. 12. The splitting of the metal orbitals within the M&L2 fragment is illustrated on the left. Under the Dsh symmetry of a trigonal bipyramid the metal d orbitals are split into three sets-e”, e’ and a;. When the local coordinate system on each metal in the cluster is defined as shown in 11, the three sets are (d,,, dJe”, (dxz_yz, d&e’ and (d&z’,. The d,, and dyz orbitals

lie lowest in energy, while the dzz orbital is most destabilized by the metal-ligand interactions and lies highest in energy. The d,z_,,z and dxy orbitals lie at intermediate energies. Although the orbital splittings are different in a trigonal bipyramid than in a square pyramid, the same metal orbitals (the “t2g”dXz_y2, d,, and dyz) are used to form M-M bonds. The qualitative cluster orbital scheme


All Trigonol Bipymmidal Coordlnstion

Md,z - -------[El (4) Wnb

Trigonal Bipyramida

MWz

Fig. 12. Qualitative energy level scheme for the metal-based cluster orbitals in an M.&LB cluster, where each metal is trigonal bipyramidal. The splitting of the metal dorbitals in a trigonal bipyramidal

environment is shown on the left and the resulting cluster orbitals are shown on the right.

is shown on the right hand side of Fig. 12. The d,,, dYZ and d,z_,,z orbitals from each metal centre, combine to form sets of six bonding and six antibonding cluster orbitals. The metal dzz and dx, orbitals form two groups of non-bonding cluster orbitals, but the relative energies of these groups are different here than in a cluster where the metals are square pyramidal. Now the non-bonding cluster orbitals derived from the metal dzz orbitals lie highest in energy, while the non-bonding cluster orbitals derived from the metal dxy orbital lie lower in energy. Once again, the lower energy non-bonding orbitals lie within the same energy range as the M-M antibonding orbitals. In general, simple bonding arguments4’ suggest that the metal dx,, orbital in a trigonal bipyramid lies lower in energy than the dzz orbital in a square pyramid. This suggests that in a cluster containing trigonal bipyramidal metals, the group of non-bonding cluster orbitals derived from the metal dx,, orbitals may lie lower in energy, relative to the M-M antibonding orbitals, than the corresponding set of cluster non-bonding orbitals derived from the metal dzz orbitals in a cluster containing square pyramidal metals. Such generalizations must be made with great caution, however, since the stabilization of the dz2 orbital in a square pyramid is extremely sensitive to both the geometry of the pyramid and the nature of the ligands.

The diagrams in Figs 11 and 12 show that in a cluster with either of the five-coordinate geometries a count of 12 metal electrons will result in the occupation of all six M-M bonding orbitals. Electrons in excess of 12 will first occupy M-M antibonding orbitals, and then at higher electron counts will occupy cluster non-bonding orbitals. It is not clear what forces favour square pyramidal or trigonal bipyramidal coordination in these clusters. This is not surprising, since even in mononuclear complexes the forces favouring one or the other of these coordination geometries are not completely understood.73 Since the energy barriers to interconversion tend to be small, many complexes are known whose coordination geometries lies somewhere between square pyramidal and trigonal bipyramidal. 74 This “intermediate” coordinate geometry, which can be described either as a distorted square pyramid or as a distorted trigonal bipyramid, is also found in several of the cubane-type clusters containing five-coordinate metals. Although this will further complicate the cluster bonding, the qualitative bonding schemes outlined here for the idealized geometries enable us to recognize that when a cluster contains five-coordinate metals an important feature of the cluster bonding scheme is the presence of a group of cluster non-bonding orbitals at relatively low energies. These orbitals may be occupied before all of the M-M antibonding orbitals are occupied, so that in comparison to a cluster with all octahedral metals, a cluster with all five-coordinate metals should be able to accommodate a relatively high metal electron count without as substantial a loss of M-M bonding.

2860 S. HARRIS

(a) f 4

Fig. 13. Two views of the structure of [Fe,S4(S,CNEt,),]- (ref. 72). Only the first C in each Et group is shown. One Etzdtc l&and is bound to each Fe atom and, neglecting the Fe-Fe bonds, each Fe is five-coordinate. The view in (a) shows that the geometry around each Fe can be described as distorted square pyramidal, while the view in (b) shows that the geometry around each Fe can also

be described as distorted trigonal bipyramidal.

The structure of [Fe$.,&CNEtJJ- illustrates several of these points. In this cluster one bidentate Et,dtc ligand is coordinated to each metal. Although Liu et al. describe the coordination of the metals in this cluster as distorted trigonal bipyramidal,72 the two views of this cluster shown in Fig. 13 demonstrate that the local coordination about each metal might also be described as distorted square pyramidal. Clearly, the actual coordination geometry lies somewhere in between. Although the cluster contains 21 metal electrons, the M-M distances (four shorter plus two long) are similar to those found in [Fe&Cp4]2+ and [Fe~S~(S~C*(CF~)~)~]*-, which contain only 18 metal electrons. After 12 metal electrons occupy the six M-M bonding orbitals in [Fe,S,(S,CNEt&,]-, nine electrons remain to occupy higher energy orbitals. If all nine of these electrons occupied M-M antibonding orbitals, we would expect to see longer M-M distances (cf. clusters in Table 1 with metal electron counts of 19 and 20). The similarities in structure with the IS-electron clusters suggest that in [Fe~S*(S*CNEt*)~]- some of these nine electrons occupy non-ending cluster orbitals. This in turn suggests that in this cluster the lower energy non-bonding orbitals shown in Fig. 11 or 12 lie low enough in energy to become at least partially occupied.

2.4. Two tet~a~edr~~ rnet~~~-two~ve-coordinate metals

Homometallic cubane-type clusters exhibiting two different metal coordination geometries are relatively rare. One type of cluster falling into this classification can be represented by the general formula M.&L& (12). Two of the metals are four-coordinate and can be viewed as part of a

tetrahedral MS&’ fragment, while the other two metals are five-coordinate and can be viewed as part of a square pyramidal M&L2 fragment. Clusters having this framework are listed in Table 4. The structure of [Fe&(Etzdtc),(SPh),j2- is shown in Fig. 14. In this cluster, the coordination geometry around each five-coordinate iron can be clearly identified as square pyramidal, In

Cubane-type clusters

Table 4. Homometallic clusters having structure type 12 : two tetrahedral metals- two five-coordinate metals

2861

Cluster

[Fe.,S&CNEt&X~“- (X = a-> (X = SPh-)

Number of metal electrons

22 22

M-M distances Reference

75 2.733,2.780(4), 3.053 2.766, 2.816(4), 3.045

Fig. 14. Structure of [Fe~S~(S~C~Et~)~(SPh)~]2- (ref. 75). Only the first C atom in each Et group is shown. Two of the Fe atoms are bound to three core S atoms and the S atom of a n-donor thiolate ligand. The geometry around these Fe atoms is approximately tetrahedral. Each of the other two Fe atoms is bound to three core S atoms and the two S atoms of a bidentate Et,dtc ligand. The

geometry around each of these five-coordinate Fe atoms is approximately square pyramidal.

[Fe&(Et2dtc)zC12]2-, on the other hand, the sulphurs in the dtc ligand are twisted somewhat so that the geometry around the five-coordinate iron is a distorted square pyramid.

A q~~tive energy level scheme for clusters having two ~trah~ral metals and two square pyramidal metals is derived in Fig. 15. Viewing the M4 cluster orbitals in terms of metal fragment orbitals becomes extremely useful when the metals in the cluster have different coordination geometries. The splittings of the metal d orbitals within the square pyramidal MS3L2 and tetrahedral MS&’ fragments are shown on the left and right of the figure, respectively. The orderings of the metal d orbitals are similar to those shown in Figs 11 and 9 for square pyramidal and tetrahedral metal fragments. Since the ligand L’ in the tetrahedral M&L fragment is a x-donor, the separation between the “tZ)’ and “e” orbitals of the tetrahedral metal is expected to be small. A qualitative scheme for the M., cluster orbitals is shown in the centre of Fig. 15. As in the clusters described previo~ly, the square pyramidal “tZg” and tetrahedral “tZ” srbitals are used for M-M bonding. These 12 orbitals from the four metal centres will combine to form sets of six bonding and six antibonding cluster orbitals. The major effect of the two different coordination geometries is the appearance of three sets of non-bonding cluster orbitals. These arise from the square pyramidal metal d,z and dv orbitals and the tetrahedral metal “e” orbitals. The highest energy set of two non- bonding orbitals is derived from the square pyramidal metal dx,, orbitals. Next highest in energy is the set of two non-bonding orbitals derived from the square pyramidal metal d,z orbitals. This set is expected to lie within the same energy range as the cluster antibonding orbitals. Finally, the lowest energy set of four non-bonding orbitals is derived from the tetrahedral metal “e” orbitals. The energy range of this set is expected to lie between the M-M bonding and ~tibonding sets. This orbital scheme is consistent both with the schemes appropriate for the clusters described earlier and with the established structures of the M4S4L2L4 clusters.

The scheme shown in Fig. 1.5 indicates that after 12 metal electrons occupy the six M-M

2862 S. HARRIS

TWO square PytYunMal M Two Tetrahedral Y ( L’ 01 PI Donor)

Md.z--

Square Pyramidal

MS3L2

Tetrahedral YSIL

Fig. 15. Qualitative energy level scheme for the metal-based cluster orbitals in an M&L& cluster con~ning two square p~a~dal metals and two tetrahedral metals. The splittings of the metal d orbitals in square pyramidal and tetrahedral environments are shown on the left and right sides of the diagram, respectively. The resulting cluster orbitals are shown in the middle. The relatively small separation between the “e” and “tZ” orbitals in the tetrahedral MS&’ fragment reflects the presence

of a n-donor ligand.

bonding orbitals, up to eight additional metal electrons could be added to the cluster before M-M antibonding orbitals have to be occupied. These eight additional electrons would occupy the cluster non-bonding orbitals derived from the tetrahedral metal “e” orbitals. Thus clusters, having anywhere from 12 to 20 metal electrons, are expected to have a fully bonded metal tetrahedron. Metal electron counts in excess of 20 will result in the occupation of M-M antibonding orbitals. (The upper limit of 20 is not really definite, because the energy range of this set of non-bonding orbitals may well overlap with the energy range of the M-M antibonding levels. If this occurs, antibonding orbitals will become occupied before all of the non-bonding orbitals are filled, i.e. at metal electron counts G 20.) Both [Fe.&(Etzdtc)2X,]Z- clusters contain 22 metal electrons and both have similar structures. The distinctive structural feature of each cluster is a long distance (> 3 A) between the two square pyramidal iron atoms. The other M-M distances are all within bonding range. The cluster bonding scheme in Fig. 15 provides a simpIe explanation for this structure. Of the 22 metal electrons, if 12 electrons occupy M-44 bonding orbitals and eight electrons occupy the lower energy set of non-bonding orbitals, two electrons will have to occupy an M-M antibonding orbital. The one long Fe-Fe distance is consistent with the occupation of an antibonding orbital localized between the two five-coordinate iron atoms.

Although it is satisfying to arrive at this simple description of the bonding in these clusters, further examination of both this bonding picture and the properties of these clusters suggests that this simple description is incorrect. First, although the two clusters are found to be paramagnetic,75 the orbital occupations just outlined would lead to a diamagnetic cluster. Second, the complete occupation of the “e” non-bonding orbitals would correspond to two tetrahedral Fe+ centres and two square pyramidal Fe4+ centres. This combination of oxidation states is highly unlikely; a combination of two Fe’+ and two Fe3+ centres is much more plausible. Oxidation states of 2+ or 3 + for the tetrahedral irons would result in only partial occupation of the “e” non-bonding orbitals. Since the structures of the clusters indicate that only one antibonding orbital is occupied, however, eight electrons must occupy non-bonding orbitals. If the “e” non-boning levels are not completely occupied, some of these eight electrons must therefore occupy the non-boning orbitals derived from the square pyramidal metal dzz orbitals. In terms of the diagram in Fig. 15, this means that several of the “e” non-bonding levels, the lower energy antibonding levels, and the “d$ non-bonding levels must lie very close in energy. Furthermore, the square pyramidal metal dzz orbital must be sufficiently


stabilized to become occupied after only one M-M antibonding orbital is occupied. This picture is consistent with high-spin square pyramidal and tetrahedral Fez+ and Fe3+ centres combining to form a paramagnetic cluster having one long Fe-Fe bond. Although a detailed description of the electronic structure of these clusters will require calculations capable of treating the spin couplings, the combination of the qualitative bonding scheme and the known properties and structure of the complexes make it possible to understand the general features of the cluster bonding.

This discussion introduces an important element which must be included in any description of the electronic structure of these cubane-type clusters-the electronic configurations of the individual metal centres. The descriptions in this report focus primarily on the total number of metal electrons occupying the M4 cluster orbitals and generally do not stress the electron configurations or formal oxidation states of the individual metals in the cluster. As we have just seen, however, concentration only on the total electron count can lead to incorrect descriptions of the electronic structure of the cluster. In order to correctly describe the electronic structure it is important to take into account both the total number of metal electrons and the number of electrons associated with each metal centre.

2.5. Three tetrahedral metals-one$ve-coordinate metal

Another type of cluster exhibiting two different metal coordination geometries has the general formula M4S4LJ.Y3. Three of the metals are four-coordinate and can be viewed as part of a tetrahedral MS3L’ fragment, while the fourth metal is five-coordinate and can be viewed as part of an MS3L2 fragment. This fragment may be either square pyramidal (13) or trigonal bipyramidal (14). Clusters having these structures are listed in Table 5. In [Fe&(Etzdtc)CIJZ-, illustrated in

Fig. 16(a), three irons are part of the tetrahedral FeS,Cl fragments while the third iron is bound to an Et,dtc ligand and is part of a square pyramidal fragment. In [Fe$4(SCsH4-o-OH)4]2-, [Fig. 16(b)] three irons are part of tetrahedral fragments, while the fourth iron is bound to both the sulphur and oxygen atoms in the (SC6H4-o-OH)- ligand and is best viewed as part of a trigonal bipyramidal fragment.

A qualitative bonding scheme for a cluster having structure 13 is illustrated in Fig. 17. The ordering of the metal orbitals within the square pyramidal and tetrahedral fragments are shown on the left and right hand side of the figure, respectively. These orderings are the same as the orderings shown in Fig. 15. The narrow separation of the tetrahedral “e” and “t2” orbitals reflects the R- donor ligands in the tetrahedral fragments. The cluster orbitals are shown in the centre of the figure, and the overall groupings of orbitals are similar to the groups shown in Fig. 15. The square pyramidal “ tzg” and tetrahedral “tZ” orbitals combine to form sets of M-M bonding and antibonding orbitals. The two different coordination geometries once again result in three sets of cluster non-bonding

Table 5. Homometallic clusters having structure type 13 or 14: three tetrahedral metals--one five-coordinate metal

Cluster Number of


[Fe,S,(SzCNEtJC13]2- 22 2.76(3), 2.850(2), 2.936 75 [Fe,S,(SC,H,-o-OH).,]*- 22 2.725(4), 2.839, 2.868 76

2864 S. HARRIS

G-4 04

Fig. 16. Structures of (a) [Fe,S,(S2CNEt2)C13]*- (ref. 75) and (b) [Fe,S,(SCgH4-o-OH)4]2- (ref. 76). In (a) only the first C atom in each Et group is shown, and in (b) only the S atoms of the three monodentate (SCsH,-o-OH)- ligands bound to the tetrahedral Fe atoms are shown. In both clusters the geometry around three of the Fe atoms is approximately tetrahedral, while the fourth Fe atom is five-coordinate. In [Fe4S4(S,CNEtz)C13]2- (a) the fourth Fe is bound to the two S atoms of the Et,dtc ligand, and the geometry around this five-coordinate Fe is approximately square pyramidal. In [Fe4S4(SC6H4-o-OH),]‘- (b) the fourth Fe is bound to both the S and 0 atoms of the (S&H,-o- OH)- ligand, and the geometry around this five-coordinate metal is better described as trigonal

bipyramidal.

One Squan, Pyramidal M Three Tetrahedral M ( C I Pi Donor)

Square Pyramidal

MS3L2

Tetrahedral MSIL

Fig. 17. Qualitative energy level scheme for the metal-based cluster orbitals in an M&L,L; cluster containing one square pyramidal metal and three tetrahedral metals. The splittings of the metal d orbitals in square pyramidal and tetrahedral environments are shown on the left and right sides of the diagram, respectively. The resulting cluster orbitals are shown in the middle. The relatively small separation between the “e” and “fZ” orbitals in the tetrahedral MS&’ fragment reflects the presence

of a n-donor ligand.


orbitals, but now the number of orbitals in each set is different from the number shown in Fig. 15. Because there is only one square pyramidal metal, there are only two non-bonding levels associated with the square pyramidal metal orbitals. One non-bonding orbital derived from the square pyramidal metal dX,, orbital lies at high energy, and one non-bonding level derived from the square pyramidal metal dzz orbital lies at lower energy. Since there are now three tetrahedral metals, a group of six non-bonding orbitals derived from the tetrahedral metal “e” orbitals falls between the M-M bonding and antibonding sets of orbitals. Although the bonding scheme indicates that all six of these non-bonding orbitals lie between the bonding and antibonding levels, it is very likely that the energy ranges of the non-bonding and antibonding orbitals overlap. If this overlap actually occurs, some of the antibonding orbitals could become occupied before all six of the non-bonding orbitals are occupied. The scheme shown in Fig. 17 indicates that after 12 metal electrons occupy the six M-M bonding orbitals, 12 more metal electrons can be added to the cluster without occupying antibonding orbitals. Thus clusters having anywhere from 12 to 24 metal electrons are expected to have a fully bonded metal tetrahedron. It is only when the electron count exceeds 24 that M-M antibonding orbitals must be occupied. As noted above, however, some of the six non- bonding orbitals may actually lie above the lower energy antibonding orbitals, and if this is the case antibonding orbitals could become occupied at metal electron counts < 24.

The bonding scheme in Fig. 17 can be used to describe the bonding in [Fe,S,(Etdtc)C1,]2- [Fig. 16(a)]. This cluster has 22 metal electrons, so after 12 metal electrons occupy the six M-M bonding orbitals, the 10 remaining metal electrons could occupy non-bonding orbitals. Based on this analysis, [Fe&(Etdtc)C1,]2- should contain a completely bonded tetrahedron of metal atoms. The actual structure of [Fe&,(Etdtc)C13]2- suggests, however, that an antibonding orbital is occupied, since at least one Fe-Fe distance is somewhat longer than might be expected for Fe-Fe bonding. This indicates that the energy ranges of the group of six non-bonding “e” orbitals and the group of six M-M antibonding orbitals do overlap, resulting in the occupation of an antibonding orbital before all of the non-bonding orbitals are occupied. An orbital occupation scheme where only eight electrons occupy the “e” cluster non-bonding orbitals and two electrons occupy an antibonding orbital is consistent with the molecular structure of the cluster and also corresponds to reasonable oxidation states for all of the metals (three high-spin tetrahedral iron centres, two Fe2- and one Fe3+, and one square pyramidal Fe3+ centre). Alternatively, an orbital occupation scheme in which only seven electrons occupy the “e” cluster non-bonding orbitals, two electrons occupy an antibonding orbital, and one electron occupies the non-bonding orbital derived from the square pyramidal metal d,z orbital is also possible. This scheme is also consistent with the structure of the cluster and corresponds to three high-spin tetrahedral iron centres, one Fe*+ and two Fe3+, and one high-spin square pyramidal Fe2+ centre. Either one of these descriptions is reasonable.

The other cluster which fits into this class is [Fe&(SC6H4-o-OH)4]2- [Fig. 16(b)], where the five-coordinate iron atom is best viewed as trigonal bipyramidal. 76 This cluster also contains 22 electrons, and the qualitative scheme in Fig. 17 can also be used to describe the cluster bonding in the cluster, since the major effect of a change from square pyramidal to trigonal bipyramidal geometry is the interchange of the non-bonding orbitals associated with the five-coordinate metal (cf. Figs 11 and 12). The bonding scheme in Fig. 17 indicates that [Fe&(SC6H@-OH),]2- should also have a completely bonded metal tetrahedron, but once again a relatively long Fe-Fe distance suggests that an antibonding orbital is occupied. This would again indicate an overlap in the energies of the “e” non-bonding and M-M antibonding cluster orbitals. An orbital occupation scheme in which eight electrons partially occupy the “e” non-bonding orbitals and two electrons occupy an antibonding orbital once again is consistent with the structure of the cluster and corresponds to reasonable oxidation states for all of the iron centres. The bonding picture will be further complicated if the dxy non-bonding orbital associated with the five-coordinate iron is sufficiently stabilized to be occupied. Several occupation schemes are possible, depending on how the electrons are apportioned to the different metal centres. It is important to recognize, however, that a bonding scheme which assigns more than eight electrons to the non-bonding “e” orbitals is unlikely, since it leads to an unreasonable combination of metal oxidation states. It is also quite clear that a better understanding of the electronic structure of these clusters incorporating five-coordinate metals will require detailed calculations.

One important outcome of an overview of the bonding schemes expected for the different types of M4S4 clusters is the observation that although the same metal electron counts may be found in

2866 S. HARRIS

a number of clusters, the actual electronic structure of the M4S4 cores may differ. For example, the relation between clusters having 22 metal electron [Fe.&J2+ cores and the iron-sulphur proteins makes this group of clusters especially interesting. Although most of the interest has concentrated on clusters listed in Table 2, the mixed coordination clusters listed in Tables 4 and 5 also have 22- electron [Fe&S,]‘+ cores. Comparison of the bonding schemes in Figs 9, 16 and 17 makes it clear, however, that even though these clusters all contain 22-electron {Fe$I.,]2+ cores, the cores are not equivalent electronically.

3. HE~ROMETALLIC CLUSTERS HAVING AN MZM;S, CORE

3.1. All four metals octuhedrally coordinated

Unlike the homometallic clusters, heterometallic clusters in which all four metals have the same coordination geometry are relatively rare. The clusters listed in Table 6 are the only examples of M2M;S4 clusters in which all four metals have similar coordination geometries-in this case octahedral. Although the M2M~S~~e~~p)~(~p)~ clusters listed in Table 6 have not been st~ct~ally characterized, spectroscopic evidence indicates that they have the cubane-type structure M2M&Cp4 (15). These clusters are therefore expected to be similar to the homometallic M,S,Cp,, clusters 5,

both in molecular and electronic structure. Since all four of the metals are octahedrally coordinated, the cluster bonding orbital scheme should be very similar to the scheme in Fig. 4. The d orbitals on each metal will split into “tzg” and “eg” groups, and although larger splittings are expected for the 4d orbitals, the 3d and 4d orbitals will combine to form the same groups of bonding, antibonding and non-bonding cluster orbitals shown in Fig. 4. Since both of these clusters have metal electron counts of 12, the cluster bonding orbit&s should be completely occupied and a fully bonding metal tetrahedron is expected. Because of the two different metals, the metal “tetrahedron” will of course be less symmetric than the metal tetrahedron observed in an M_,S,Cp, cluster.

3.2. Two octahedral metalstwo tetrahedral metals

A cluster in this class is characterized by the general formula M2MfZS4L& (16) or MzM;S&p2L; (17). A number of clusters belonging to this class are listed in Table 7. In each cluster, two of the

metals are six-coordinate and can be viewed as part of an octahedral M&L3 or MS&p fragment, while the other two metals are four-coordinate and can be viewed as part of a tetrahedral M’$L fragment. The structure of Mo2C02Sa(Et2dtc)2(CH&N)z(C0)2 is shown in Fig. 18. In this cluster, each octahedral molybdenum atom is bound to an acetonitrile ligand and an Et2dtc ligand, while each tetrahedral cobalt atom is bound to one x-acceptor CO ligand.

2868 S. HARRIS

Two Octehedml M Two Tetrahedral M’ ( L’ E Pi Acceptor)

M e, [=I- [I~EzE~] (4) n b

Me

Octahedral o

MSILI M&t’&L~L12

hlSo3:p or

MZM’2SlCP2~2

Tetrahedral

M’S,L

Fig. 19. Qualitative energy level scheme for the metal-based cluster orbitals in a heterometallic M2M$34L&‘z or M2M’&Cp,Lz cluster containing two octahedral metals and two tetrahedral metals. The splittings of the metal d orbitals in octahedral and tetrahedral environments are shown on the left and right sides of the diagram, respectively. The resulting cluster orbitals are shown in the middle. The relatively large separation between the “e” and “t 2” orbitals in the tetrahedral M’S&’ fragment

reflects the presence of a z-acceptor ligand.

A qualitative bonding scheme for these clusters is shown in Fig. 19. The ordering of the metal d orbitals within each octahedral fragment is shown on the left hand side of the diagram, while the order of the metal d orbitals within each tetrahedral fragment is shown on the right. These fragment diagrams take into account two features of the clusters listed in Table 7. First, since the tetrahedral metal generally lies to the right of the octahedral metal in the periodic table, the tetrahedral metal d orbitals are expected to lie lower in energy than the octahedral metal d orbitals. Also, since in each cluster the ligand L’ associated with the tetrahedral metal is a n-acceptor, the tetrahedral “e” orbitals will be stabilized and the separation between the tetrahedral “e” and “fa” orbitals will be relatively large. In the cluster, the “t2S” and “t2” orbitals combine to form sets of six bonding and six antibonding orbitals, while the metal “eg” and “e” orbitals remain non-bonding. These non- bonding orbitals will occur in two groups, the octahedral “eg” orbitals at high energy and the tetrahedral “e” orbitals at low energy. The stabilization of the tetrahedral metal “e” orbitals by the n-acceptor ligands is expected to result in the set of four cluster non-bonding orbitals lying below the cluster bonding orbitals.

A cluster metal electron count of 20 is expected to be necessary for a completely bonding metal tetrahedron. Of these 20 electrons, eight will occupy the low energy non-bonding orbitals, leaving 12 to occupy the M-M bonding orbitals. Metal electrons in excess of 20 are expected to occupy antibonding orbitals. This scheme is consistent with the structures of MozCozS4(Etzdtc)z (CH3CN)2,7g (20 metal electrons) and MozNi,S4(MeCp)2(CO)z80Y81 (22 metal electrons). All of the M-M distances in the 20-electron cluster correspond to M-M bonds, while in the 22- electron MotNizS4(MeCp)z(CO)z cluster the two nickel atoms are separated by a long non- bonding distance, indicating the occupation of an antibonding orbital. Recent molecular orbital calculations for Mo~CO&(~~C)~(CH~CN)~(CO)~ and Mo~N~&(C~)~(CO)~ confirm the qualitative energy level scheme shown in Fig. 19. ” The four distinct groups of non-bonding, bonding, antibonding, and non-bonding cluster orbitals are all observed in the calculated energy levels of these


clusters, confirming that 20 metal electrons should result in a completely bonded metal tetrahedron. These calculations also show that just as in the homometallic clusters only the lower energy M-M bonding cluster orbitals are strongly bonding. The higher energy “bonding” orbitals are quite delocalized and nearly non-bonding, suggesting that clusters with electron counts short of 20 can be expected to have relatively short M-M distances. The lowest energy antibonding orbital, however, is localized between the two tetrahedral metals. It is this orbital which is occupied by the two extra electrons in MoZNiPS4(MeCp)z(CO)2, resulting in the long Ni-Ni distance. The strongest M-M interactions in these clusters occur between the two 4d metals, and the M-M bonding interactions decrease in the order 4d-4d > 4d-3d > 3&3d. The weaker overlap between the smaller 3d orbitals results in relatively weak M-M bonding interactions between the 3d metals. Several other M2Co&Cp,L; (M = Cr, MO) clusters78*82 are also assumed to have cubane-type structures, and the bonding scheme in Fig. 19 should also apply to these clusters. The 20-electron clusters are expected to contain a completely bonding metal tetrahedron, while a long Co-Co distance is expected in the clusters containing 22 metal electrons.

Another series of clusters, V1M&(MeCp)a(N0)2 (M = Fe, Co, Ni),83,84 provides a further test of the qualitative scheme in Fig. 19. Based on this scheme and the previous discussion, the 20 metal electrons in VzCo,S4(MeCp),(N0)2 would occupy both the low energy non-bonding orbitals and the six M-M bonding orbitals, resulting in a completely bonded metal tetrahedron. The structure of the l&electron V2Fe2S4(MeCp)2(N0)2 cluster should be similar to the structure of V2C02S4 (MeCp),(NO)z, since any unoccupied high energy bonding orbital is expected to be at most weakly M-M bonding. The extra two electrons in the 22-electron V2NizS4(MeCp),(N0)2 cluster would occupy an antibonding orbital-probably one localized between the two tetrahedral nickel atoms, leading to a long Ni-Ni distance. The structure of the 22-electron VzNi2S4(MeCp)2(N0)2 cluster is consistent with this description of the bonding, since the long Ni-Ni distance can be considered non-bonding. An examination of the M-M distances in the three clusters, however, shows that in the set of three clusters, the M’-M’ distances increase in the order Fe-Fe < Co-Co < Ni-Ni. As Racuchfuss and co-workers have noted, the Co-Co distance in VzCo2S4(MeCp)2(N0)2 is longer than expected for a Co-Co bond, suggesting that the 20-electron VzCo2S.,(MeCp)2(N0)2 cluster is not “electron precise”.84 (In the CVE counting scheme this is a 60-electron cluster and is also expected to contain a completely bonding metal tetrahedron.) This relatively long Co-Co distance, as well as the paramagnetism of the cluster, implies that in V2C02S4(MeCp),(NO), the antibonding Co-Co orbital is occupied by one electron. An orbital occupation scheme for the three clusters which is consistent with their structures is V2Fe2S4 (nb)“(b)“(ab)“, V2C02S4 (rib)*(()’ ‘(ab)‘, VzNizS4 (rib)*(()’ ‘(ab)‘, where nb = non-bonding orbitals, b = bonding orbitals and ab = antibonding orbitals. Such a scheme would require the bonding and antibonding orbitals to be separated by only a small gap. In these clusters the relatively large energy separation between the V and M’ 3d orbitals and the weak bonding interactions between the small 3d orbitals could well result in the bonding orbitals spanning a large energy range, thus leading to such a narrow separation of the bonding and antibonding orbitals. Clearly, a more complete description of the electronic structure of these clusters is highly desirable. The apparent antiferromagnetic character of VzFezS4(MeCp),(NO)z and the paramagnetism of V2C02S4(MeCp),(N0)2 indicate that such a description will require spin unrestricted calculations.

3.3. Two octahedral metals-two five-coordinate metals

Another combination of coordination geometries occurs in a cluster which has the general formula M2M’$4(Cp)zL4 (18). Here, two metals are six-coordinate and can be viewed as part of an

2870 S. HARRIS

Table 8. Heterometallic clusters having structure type 18 : two octahedral metals--two square pyramidal metals

Cluster Number of M-M distances

metal electrons M-M” M’_M’” M-M’ Reference

Mo,Fe2S,(Me,Cp)z(C0)4

a M = octahedral metal. b M’ = tetrahedral metal.

18 2.761 3.334 2.813(4) 85

octahedral MS&p fragment, while the other two metals are five-coordinate and can be viewed as part of a square pyramidal M’S3L; fragment. The one cluster having this geometry, Mo2Fe2S4 (Me,Cp)z(CO),, is listed in Table 8 and illustrated in Fig. 20. In this cluster there is no ambiguity concerning the square pyramidal configuration about the five-coordinate metals. Two C and two S atoms lie in the same plane to form the base of the pyramid, and the Fe atom lies about 0.5 A above this plane.

A qualitative energy level scheme for this cluster is shown in Fig. 21. The octahedral metal d orbitals shown on the left are divided into the familiar “tZg” and “eg” groups. The square pyramidal metal d orbitals are shown on the right. As in the previous diagrams involving square pyramidal metals, the lowest energy orbitals are the “tZ9 ” set, while the highest energy orbital is dxy. Intermediate in energy is the d,z orbital. In Fig. 21, the dzz orbital is shown to be at lower energy than in the previous diagrams for square pyramidal metals. This large stabilization of the dzz orbital is expected for a square pyramidal M’S& fragment only when (1) L’ is a x-acceptor ligand, and (2) the metal atom lies well out of the plane of the base of the pyramid. Under these conditions the dzz orbital is further stabilized by interactions with the ligand x-acceptor orbitals. In the cluster orbital scheme shown in the centre of Fig. 21 the metal “fZg” orbitals combine to form sets of six bonding and six antibonding orbitals, while three sets of cluster non-bonding orbitals occur. These are derived from the octahedral metal “eg” orbitals and the square pyramidal metal dxy and dzz orbitals. The non- bonding “eg” and dx, orbitals lie above the antibonding orbitals, while the non-bonding set derived from the square pyramidal dzz orbitals lies between the bonding and antibonding orbitals. This ordering of both the metal fragment orbitals and the cluster orbitals is confirmed by a recent set of MO calculations on Mo2Fe&(Cp),(C0)4.22

Using the bonding scheme in Fig. 21, we would expect that a cluster metal electron count anywhere between 12 and 16 should lead to a completely bonding metal tetrahedron, since after 12 electrons occupy the bonding orbitals up to four more electrons can be added to the cluster before an antibonding orbital must be occupied. Since Mo,Fe$,(Me,Cp),(CO), contains 18 metal electrons, two electrons will occupy an antibonding orbital. The long Fe-Fe distance indicates that

Fig. 20. Structure of MozFe,S,(Me,Cp),(CO), (ref. 85). The Me groups on the Cp ligands are not shown. Each octahedral MO is bound to three core S atoms and a Cp ligand, while each five- coordinate Fe is bound to three core S atoms and two n-acceptor CO ligands. The geometry around

each five-coordinate Fe atom is approximately square pyramidal.


Two Octahedral M Two Square Pyramidal M ( C E PI Acceptor)

M ep [=]- [B] (4) nb i, d.l

[=zz3~-

Octahedral MS&p MzM’zS&p,L’4

Fig. 21. Qualitative energy level scheme for the metal-based cluster orbitals in a heterometallic M,M;S.,Cp& cluster containing two octahedral metals and two square pyramidal metals. The splittings of the metal d orbitals in octahedral and square pyramidal environments are shown on the left and right sides of the diagram, respectively. The resulting cluster orbitals are shown in the middle. The relatively large stabilization of the d,z orbital in the square pyramidal MS& fragment reflects

the presence of two x-acceptor ligands.

these electrons occupy a localized Fe-Fe antibonding orbital, and the MO calculations confirm the occupation of six bonding, two non-bonding and one antibonding orbital localized between the two Fe atoms. It is important to recognize that the very low energy non-bonding orbitals are a consequence of the n-acceptor ligands coordinated to the square pyramidal metal. In the presence of n-donor ligands the metal dzz orbitals would lie at higher energies, antibonding orbitals would be occupied before non-bonding orbitals, and a smaller metal electron count would lead to a decrease in the degree of M-M bonding. The consequences of n-donor vs n-acceptor ligands on the ordering of the cluster orbitals was apparent in the earlier discussions of the M&L4 clusters incorporating four-coordinate tetrahedral metals. The bonding scheme in Fig. 21 makes it clear that the presence of x-donor vs a-acceptor ligands will also have an effect on the ordering of the cluster orbitals in clusters incorporating five-coordinate square pyramidal metals.

4. HETEROMETALLIC CLUSTERS HAVING AN lWM;$ CORE

4.1. AN four metals octahedrally coordinated

The clusters listed in Table 9 are the only examples of MM& clusters in which all four metal atoms have similar coordination geometries. Although the clusters CrsM$(Cp), (M = V, Nb)86

Table 9. I-Ieterometallic clusters having structure type 19: all metals octahedrally coordinated

Cluster

Number of metal electrons Reference

Cr,MS.,(Cp), (M = V, Nb) 11 86

a Spectroscopic evidence suggests a cubane-type structure.

2872 S. HARRIS

have not been structurally characterized, spectroscopic evidence indicates that they have the cubane- type structure MM’&Cp, (19). Each metal can be viewed as part of an octahedral MS&p or

M’S&p fragment, and the clusters are expected to be similar in both molecular and electronic structure to the homometallic M,&Cp, clusters (5). Making use of the cluster bonding scheme in Fig. 4, a cluster metal electron count of 12 is expected to lead to a fully bonding metal tetrahedron. Both Cr3MS4(Cp), clusters are paramagnetic with a metal electron count of 11, and the M-M distances are expected to be within the range expected for M-M bonds.

4.2. Three octahedral metals---one tetrahedral metal

A number of clusters characterized by the general formula MM;S,LL’, (29) or MM’&LCp, (21) are listed in Table 10. In each case three metals can be viewed as part of an octahedral M’S&

or M’S&!p fragment and one metal can be viewed as part of a tetrahedral M&L fragment. The structure of one of these clusters, [Mo,FeS,(NH,),(H,0)]4+, is shown in Fig. 22. Here, each MO is coordinated by three NH3 ligands, while the Fe atom is bound to the 0 of the single Hz0 molecule. In several of the clusters, such as Mo~CuS4(S,P(OCH,),),(CL_00CCCl~)(CH,N)(I),87 the octahedral metals are coordinated to monodentate, bidentate and spanning bidentate ligands. The metal electron counts in the clusters range from 14 to 16, and in all cases the M-M distances are indicative of M-M bonds.

A qualitative bonding scheme for these clusters is shown in Fig. 23. The groups of metal d orbitals within the tetrahedral and octahedral fragments are shown on the left and right side of the

Table 10. Heterometallic clusters having structure type 20 or 21: three octahedral metals-one tetrahedral metal

Cluster

Number of metal electrons

M-M distance M’-M” MI-M’ Reference

Cr,FeS,(Cp),(OOCCMe,) 14 2.721-2.787 2.828-2.848 88

[Mo3FeS4(NHs),(H20)14+ 14 2.675-2.691 2.7662.830 89

Cr3CoSdW3W) 16 2.649-2.666 2.810-2.824 90 Mo,CuS,(S,P(OCH,)&u-OOCCH,)(HCON(CH,),)(I) 16 2.807-2.856 2.679-2.770 91 WSC~S,(S,P(OCH,),),~~-OOCCH3)(GH5NXI) 16 2.841-2.960 2.687-2.767 92 Mo~CUS~(S~P(OCH~)~)~~-OOCCC~~)(CH~N)(I) 16 2.792-2.875 2.701-2.761 87

u M’ = octahedral metal, M = tetrahedral metal.


Fig. 22. Structure of [MoJFeSq(NH,),(H,0)]4C (ref. 89). All of the H atoms have been omitted. Each octahedral MO is bound to three core S atoms and three NH3 ligands, while the tetrahedral Fe is

bound to three core S atoms and an H,O molecule.

One Tetrahedral M ( L = Pi Donor) Three Octehedrel M

~EZZC.

[ 1 (6) nb -- -[z ]M’%

Tetmhedml MSJL MM’&LL’@

or

Octehedml

M’SJL’3 MM’3S4LCp, or

M’S3Cp

Fig. 23. Qualitative energy level scheme for the metal-based cluster orbitals in a heterometallic MM;S,LL, or MM’$,LCp, cluster containing one tetrahedral metal and three octahedral metals. The splittings of the metal d orbitals in tetrahedral and octahedral environments are shown on the left and right sides of the diagram, respectively. The resulting cluster orbitals are shown in the middle. The relatively small separation between the “e” and “t 2” orbitals in the M&L fragment reflects the

presence of a a-donor ligand.

diagram, respectively. Because the octabedrally coordinated metals he to the left of the periodic table, the energy of the octahedral metal orbitals is expected to be higher than the energy of the tetrahedral metal orbitals. Also, because in most of the clusters the ligand L coordinated to the tetrahedral metal is a n-donor, the separation between the tetrahedral “e” and “fZ” orbitals is expected to be small. The cluster orbitals are shown in the centre of the diagram. The octahedral

2874 S. HARRIS

“ tzg” and tetrahedral “t*” orbitals combine to form six bonding and six antibonding cluster orbitals. Six non-bonding orbitals derived from the octahedral “eg” orbitals should lie high in energy, while two cluster non-bonding orbitals derived from tetrahedral “e” orbitals are expected to lie between the sets of cluster bonding and antibonding orbitals. Although no calculations have been carried out which can confirm this cluster bonding scheme, the scheme is consistent with the observed structures of the clusters, since occupation of antibonding orbitals would require metal electron counts greater than 16. In the clusters having electron counts of 14 and 16, 12 metal electrons will occupy the cluster bonding orbitals and two or four electrons will partially or fully occupy the low energy non-bonding orbitals. The presence of two unpaired electrons in Cr3FeS4(Cp),(OOCCMe3)88 (14 metal electrons) suggests that in this cluster one electron occupies each of the non-bonding orbitals derived from the Fe “e” orbitals. In Cr,CoS,(Cp),(CO) the non-bonding cluster orbitals derived from the Co “e” orbitals will be stabilized by the rc-acceptor CO ligand and are expected to lie below the cluster bonding orbitals. The 16 metal electrons will still fully occupy the non-bonding and bonding orbitals.

4.3. One octahedral metal-three tetrahedral metals

Structurally characterized clusters belonging to this class are listed in Table 11. They can all be represented by the general formula MM&L,L; (22). One metal can be viewed as part of an

octahedral MS3L3 fragment, while the other three metals can be viewed as parts of tetrahedral M’S&’ fragments. Except for [MoFe,S,(SEt),(C0,]3-,g3 all of the clusters listed in Table 11 contain 19-electron [MoFe3S,13+ or [VFe,S,]+ cores. The structural, chemical and electronic properties of the MoFe3S4 clusters have been studied extensively by the Holm group.20,g4*g5 (See also the references in Table 11. These studies have been motivated primarily by the similarities between these clusters and the MO cofactor in nitrogenase. The structure of one of these clusters, [MoFe,S, (SEt)3(C14cat)(CN)]3-, is illustrated in Fig. 24. The octahedral MO atom is coordinated by the two 0 atoms of the cathecholate ligand and by the cyanide ligand, while each tetrahedral Fe atom is bound to one thiolate ligand. Recently a series of VFe3S4 clusters has also been studied by the Holm

Table 11. Heterometallic clusters having structure type 22 : one octahedral metal-three tetrahedral metals

Cluster Number of

metal electrons M-M distances M-M’ a M’-M’ Reference

19 2.736-2.789 2.660-2.711 99, 100 19 2.765-2.794 2.725-2.733 101 19 2.727-2.737 2.690-2.720 102 19 2.735-2.751 2.690-2.699 102 19 2.718-2.775 2.706-2.726 103 19 2.703-2.732 2.724-2.767 103 19 2.771-2.781 2.691-2.738 96,98 19 2.760-2.792 2.704-2.738 98 19 2.6992.745 2.749-2.760 98 22 3.225-3.272 2.739-2.742 93

’ M = octahedral metal, M’ = tetrahedral metal.

Cubane-type clusters

n

2875

Fig. 24. Structure of MoFe,S,(SEt),(Clpat)(CN)]3- (ref. 102). The Et groups in the three @Et)- ligands are not shown. The tetrahedral Fe atoms are bound to three core S atoms and the S atom of a thiolate ligand. The octahedral MO atom is bound to three core S atoms, a cyanide hgand, and the

two 0 atoms of the bidentate catecholate ligand.

group,g5g8 and the electronic and structural properties of these ciusters are found to be very similar to the properties of the MoFe& clusters. As in the [Fe,S,(SR)4]2- clusters, a detailed understanding of the electronic structure of these heterometallic clusters is complicated by the weak coupling between high-spin transition metal ions. The results of spin-unrestricted Xa calculations on the model cluster, [MoFe,S,(SH),]3-, provide an analysis of the electronic structure which is consistent with the experimentally observed electronic properties of the clusters having [MoFe3SJ3+ cores.21

A qualitative cluster bonding scheme for this class of clusters can be derived from the metal fragment orbitals. This scheme is shown in Fig. 25. The groups of metal d orbitals within the octahedral and tetrahedral fragments are shown on the left and right of the diagram, respectively.

One Ocbhedral M

Three Tetrahedral M’ ( C = PI Donor )

Octahadml ” Tebmhedral MS&J MW&L3L)$ Y’SJL

Fig. 25. Qualitative energy level scheme for the metal-based cluster orbitals in a heterometallic MM;S,L,L; cluster containing one octahedral metal and three tetrahedral metals. The splittings of the metal d orbitals in octahedral and tetrahedral environments are shown on the left and right sides of the diagram, respectively. The-resulting cluster orbitals are shown in the middle. The relatively small separation between the “6 and “1 2” orbitals in the M’S,L’ fragment reflects the presence of a

n-donor ligand.

2876 S. HARRIS

Because the L’ ligand associated with each tetrahedral metal is a n-donor, the separation between the tetrahedral metal “e” and “tZ” orbitals is expected to be small. The cluster orbitals are shown in the centre of the diagram. Once again, the metal “tZg” and “tZ” orbitals combine to form six bonding and six antibonding cluster orbitals. Two non-bonding cluster orbitals derived from the octahedral metal “eg” orbitals lie high in energy, while six non-bonding cluster orbitals derived from the tetrahedral metal “e” orbitals are expected to lie between the sets of cluster bonding and antibonding orbitals. The intermediate energy of these six non-bonding orbitals is a result of the R- donor ligands. Based upon this simple bonding scheme, metal electron counts between 12 and 24 should result in a completely bonding metal tetrahedron, since after the bonding orbitals are occupied by 12 electrons, the six-nonbonding orbitals can accommodate up to 12 additional electrons before an antibonding orbital must be occupied. (As in several of the previously described classes of clusters, the energy ranges of the non-bonding and antibonding orbitals probably overlap. If they do, antibonding orbitals will be occupied for electron counts < 24.) The M-M distances (Table 11) in all of the clusters which have lIvloFe,S,13+ and pFe3S4]‘+ cores are indicative of M-M bonds. Since all of these clusters have 19 metal electrons, the bonding scheme in Fig. 25 indicates that in each cluster seven electrons will occupy non-bonding orbitals. Just as in the Fe& clusters, it is the presence of these seven non-bonding electrons associated with the Fe atoms which leads to the observed complex electron-spin couplings.

The structure of the remaining cluster in Table 11, [MoFe3S,(SEt),(CO)3]3-, is markedly different from the structure of the other MoFe,S, and VFe3S4 clusters in this class. This cluster, which contains 22 metal electrons, is characterized by long non-bonding Mo-Fe distances (cu 3.25 A), as well as relatively long Mo-S distances (ca 2.63 A compared to Mo-S distances of cu 2.35-2.40 A in the other clusters listed in Table 1 l), and Coucouvanis et al. suggested that this cluster is best described as a weak complex of the MOM unit and the [Fe3S,(SR),]3- cluster.93 The different structure of this cluster once again calls attention to the need for considering the individual oxidation states of the metals in the cluster as well as the total metal electron count. For example, the MoFe,S, clusters discussed in the preceding paragraph have a total of 19 metal electrons. This results in 12 metal electrons occupying the cluster M-M bonding orbitals and seven electrons occupying cluster non-bonding orbitals associated only with the Fe atoms. These cluster orbital occupations can be associated with one Mo3+, one Fe2+ and two Fe3+ centres. In contrast, [MoFe,S,(SEt)3(CO),]3- has three extra metal electrons, or a total of 22 metal electrons. Although the bonding scheme in Fig. 25 indicates that the cubane structure should be able to accommodate these three additional electrons, it also suggests that at least some of these extra electrons would have to occupy non- bonding orbitals associated with the Fe atoms. That is, even though the extra three electrons are introduced by the MOM unit, formation of a true cubane-type cluster would require formal oxidation of the MO and reduction of one or more of the three Fe atoms. The exact degree of oxidation and reduction would depend on the relative energies of the non-bonding “e” orbitals and the M-M antibonding orbitals. The fact that a true cubane-type cluster is not formed suggests that the required oxidation and reduction is unfavourable. We should recognize that even though the cluster bonding diagrams described in this report indicate that a range of total metal electron counts is possible for a cluster having a particular structure, there may not be any reasonable combinations of individual metal oxidation states which lead to some of these total metal electron counts.

4.4. Two octahedral metals-two jive-coordinate metals

The last group of heterometallic clusters can be characterized by the general formula MM;S,L,L;, where two metals, one M and one M’, can be viewed as part of octahedral MS3L3 and M’S3L; fragments and two metals are part of five-coordinate M’S3L$ fragments. Several clusters having this structure are listed in Table 12. These clusters can be viewed as having one of the ideal structures 23 or 24. In 23, each five-coordinate metal is square pyramidal, whereas in 24 each five- coordinate metal is trigonal pyramidal. In the [MoFe3S.,(S2CNR2)5]0*-’ clusters listed in Table 12, each metal is coordinated by a bidentate dtc ligand, while the fifth dtc ligand spans an Fe and MO atom. As in many of the homometallic clusters containing five-coordinate metals, the actual geometry about the five-coordinate metals lies somewhere in between the two geometries shown in 23 or 24 and can be described as either distorted square pyramidal or distorted trigonal bipyramidal. The two views of MoFe3S4(S2CNEt2)5 shown in Fig. 26 demonstrate that either description might apply,


Table 12. Heterometallic clusters having structure type 23 or 24 : two octahedral metals-two five-coordinate metals

Cluster

Number of metal electrons M-M“

M-M distances M-M’ b MI-M’ Reference

[MoFGL&CNEbW 18 2.624 2.841-2.895 2.736 104 MoFe$,(S2CNR2), 17

(R = Et) 2.705 2.739, 2.790 2.296 105 2.861, 3.057

(R = Bu) 2.683 2.80(2), 2.91(2) 2.701 106 (R = CsH,o) 2.696 2.78(2), 2.93(2) 2.701 107

“M = octahedral metal. bMf = five-coordinate metal.

Fig. 26. Two views of the structure of MoFe&(SzCNEt2)5 (ref. 105). Only the first C in each Et group is shown. Four of the bidentate Et,dtc ligands each bind to a single metal atom, while the fifth Etzdtc ligand spans an MO atom and an Fe atom. The MO atom and one of the Fe atoms are therefore six-coordinate and have approximately octahedral coordination geometry, while the two remaining Fe atoms are five-coordinate. The two views of the structure show that the geometry around the five- coordinate Fe atoms can be viewed as either (a) distorted square pyramidal or (b) distorted trigonal

bipyramidal.

2878 S. HARRIS

although in this cluster a designation of distorted square pyramidal may be more appropriate. The distortions are not the same in all of the clusters listed in Table 12, however, so as a group the five- coordinate metals are best described as having a geometry intermediate between that shown in 23 or 24.

A qualitative energy scheme for a cluster having geometry 23 (two five-coordinate square pyramidal metals) is shown in Fig. 27. The ordering of the metal d orbitals within the octahedral and square pyramidal fragments are shown on the left and right side, respectively, of the diagram. The diagram has been simplified somewhat in that only one set of metal octahedral orbitals are shown. Because two different metals, in this case Fe and MO, are octahedrally coordinated, there are actually two different sets of octahedral metal orbitals. Since the presence of these two sets should not greatly alter the general scheme derived in the centre of Fig. 16, the second set has been omitted. The “t%” sets of orbitals from all four metal atoms combine to form the sets of cluster bonding and antibonding orbitals. Three groups of cluster non-bonding orbitals are expected, four high energy orbitals derived from the octahedral metal “eg” orbitals, two high energy orbitals derived from the square pyramidal metal dx, orbitals and two lower energy orbitals derived from the square pyramidal metal dz2 orbitals. The lower energy non-bonding orbitals are.expected to lie within the same energy range as the antibonding orbitals. Just as in the homometallic clusters containing five-coordinate metals, the bonding in the MM’&L& clusters considered here is expected to be similar to the bonding in clusters containing all octahedral metals-except for higher electron counts.

All of the clusters in Table 12 contain 17 or 18 electrons. Using the diagram in Fig. 27, 12 of these electrons should fully occupy the cluster bonding orbitals, while the remaining five or six electrons are expected to occupy cluster antibonding orbitals. An examination of the M-M distances listed in Table 11 shows that in general the distances between the octahedral MO and Fe atoms (the two atoms spanned by the dtc ligand) and between the two five-coordinate Fe atoms are indicative of MO-Fe and Fe-Fe bonds. The other four M-M distances are less regular and are generally longer (in some cases long enough to be non-bonding). These distances are consistent with partial occupation of the cluster antibonding orbitals. An understanding of the actual deformations of the

One Octahedral M, One Octahedral M Two Squam PyramIdal M’

Octahedral MS3L3

or

Fig. 27. Qualitative energy level scheme for the metal-based cluster orbitals in a heterometallic MM’&L,L; cluster containing two octahedral metals and two square pyramidal metals. The splittings of the metal d orbitals in octahedral and square pyramidal environments are shown on the left and right sides of the diagram, respectively. The resulting cluster orbitals are shown in the middle.


M-M bonds would require an understanding of the character of the antibonding orbitals, but the M-M distances do suggest that antibonding orbitals localized between either the two octahedral metals or the two five-coordinate metals lie high enough in energy to remain unoccupied, while the lower energy occupied antibonding orbitals involve interactions between the octahedral and five- coordinate metals. The lower energy non-bonding orbitals may be sufhciently stabilized to be at least partially occupied, but the long distances between the five- and six-coordinate metals indicate that these non-bonding orbitals are high enough in energy that at least the majority of the extra five or six electrons occupy antibonding orbitals.

A comparison of the energy level diagrams in Figs 25 and 27 shows that the bonding schemes are markedly different in the MoFe&, clusters having the two different structure types 22 and 23. The tetrahedral coordination of the three Fe atoms in the MM’$,L,L; (22) clusters introduces a large number of low energy non-bonding cluster orbitals. In the MM$&,L,L’, clusters (23), on the other hand, the non-bonding cluster orbitals are destabilized by the octahedral and square pyramidal or trigonal bipyramidal coordination of the Fe atoms. Even with equivalent metal electron counts the electronic structures of these two types of clusters would not be equivalent.

5. SUMMARY

When the cubane-type clusters are grouped into classes based on metal coordination geometry it is possible to develop a qualitative M4 cluster bonding scheme for each class. These schemes make it possible to understand, at least qualitatively, the M-M bonding in a large number of both homo- and heterometallic clusters. The M-M bonding in these clusters is strongly influenced by the ligand environment of each metal in the cluster. When we view each metal as part of an M&L, fragment within the cluster, we can see that M-M bonds are formed between fZg(t2) type orbitals, while e&) type orbitals do not take part in the M-M bonding. Since the ligand environment (both the ligand geometry and the nature of the ligands) of each metal has a strong effect on the relative energies of these “tzg” and “Q” orbitals, it ultimately has an effect on the energies of the bonding, antibonding and non-bonding M4 cluster orbitals. Specifically, changing the ligand geometry around the metals and/or the type of ligands bound to the metals changes the relative energy of the non-bonding cluster orbitals. This effect is closely related to the structure of a cluster, since the position of the non-bonding cluster orbitals determines how many “metal” electrons the cluster can accommodate without the loss of M-M bonding.

The Dahl group recognized the importance of these non-bonding cluster orbitals when they developed qualitative bonding schemes which could be applied to a number of the homometallic clusters. Their schemes assumed that the stronger metal-ligand (or metal-sulphur) interactions could be separated from the weaker metal-metal interactions, and in deriving these schemes they first considered the metal-metal interactions and then added on the metal-ligand interactions. Although these schemes are extremely useful for many of the homometallic clusters, this approach is not easily extended to the lower symmetry heterometallic clusters having more than one kind of coordination geometry. Alternatively, it is possible to first consider the stronger metal-ligand interactions and then add on the weaker metal-metal interactions. Using this approach each metal is viewed as part of an M&L, fragment, and the cluster bonding, antibonding and most importantly non-bonding orbitals can be associated with specific sets of metal orbitals within these fragments. This approach makes it possible to derive qualitative cluster bonding schemes for even the low symmetry heterometallic clusters. Detailed descriptions of the electronic structure of many of these clusters must await accurate electronic structure calculations, but it is useful in the meantime to have these qualitative bonding descriptions.

REFERENCES

1. J. A. Ibers and R. H. Holm, Science 1980,209,223. 2. J. M. Berg and R. H. Holm, in Iron-S&r Proteins (Edited by T. G. Spiro), Chap. 1. Wiley-Interscience,

New York (1982). 3. B. A. Averill, Struct. Bond. (Berlin) 1982,53, 59. 4. Trinh-Toan, B. K. Teo, J. A. Ferguson, T. J. Meyer and L. F. Dahl, J. Am. Chem. Sot. 1977,99,408.

2880 S. HARRIS

5. P. J. M: Guerts, J. W. Gosselink, A. Van der Avoird, E. J. Baerends and J. G. Snijders, Chem. Phys. 1980,46, 133.

6. A. J. Thompson, J. Chem. Sot., Dalton Trans. 1981, 1180. 7. F. Bottomley and F. Grein, Znorg. Chem. 1982,21,4170. 8. C. T.-W. Chu, F. Y.-K. Lo and L. F. Dahl, J. Am. Chem. Sot. 1982,104,3409. 9. A. Mtiller, R. Jostes, W. Eltzner, C.-S, Nie, E. Diemann, H. BBgge, M. Zimmerman, M. Dartmann, U.

Reinsch-Vogel& S. Che, S. J. Cyvin and B. N. Cyvin, Znorg. Chem. 1985,24, 2872.

10. S.-S. Sung, C. Glidewell, A. R. Butler and R. Hoffmann, Znorg. Chem. 1985,24,3856. 11. P. D. Williams and M. D. Curtis, Znorg. Chem. 1986,25,4562. 12. C. Liu, J. Hua, Z. Chen, Z. Lin and J. Lu, Znt. J. &ant. Chem. 1986,29,701. 13. C. Y. Yang, K. H. Johnson, R. H. Holm and J. G. Norman Jr, J. Am. Chem. Sec. 1975,97,6596. 14. A. Airman and D. A. Case, J. Am. Chem. Sot. 1982,104,3269. 15. L. Noodleman, J. G. Norman Jr., J. H. Osborne, A. Airman and D. A. Case, J. Am. Chem. Sot. 1985,

107,3418. 16. J. Darkwa, J. R. Lockemeyer, P. D. W. Boyd, T. B. Rauchfuss and A. L. Rheingold, J. Am. Chem. Sot.

1988,110, 141. 17. G. L. Simon and L. F. Dahl, J. Am. Chem. Sot. 1973,95,2164. 18. L. L. Nelson, F. Y.-K. Lo, A. D. Rae and L. F. Dahl, J. Organomet. Chem. 1982,225,309. 19. R. H. Holm, Chem. Sot. Rev. 1981,10,455. 20. R. H. Holm and E. D. Simhon, in Molybdenum Enzymes (Edited by T. G. Spiro), Chap. 1. Wiley-

Interscience, New York (1985). 21. M. Cook and M. Karplus, J. Am. Chem. Sot. 1985,107,257. 22. S. Harris, Znorg. Chem. 1987,26,4278. 23. C. D. Garner, in Transition Metal Clusters (Edited by B. F. G. Johnson), Chap. 4. John Wiley, New

York (1980). 24. A. Miiller, W. Eltzner, W. Clegg and G. M. Sheldrick, Angew. Chem. Znt. Edn Engl. 1982,21,536. 25. T. C. W. Mak, K. S. Jasim and C. Chieh, Angew. Chem. Znt. Edn Engl. 1984,23,391. 26. T. C. W. Mak, K. S. Jasim and C. Chieh, Znorg. Chem. 1985,24, 1587. 27. K. L. Wall, K. Folting, J. C. Huffman and R. A. D. Wentworth, Znorg. Chem. 1983,22,2366. 28. A. W. Edelblut, K. Folting, J. C. Huffman and R. A. D. Wentworth, J. Am. Chem. Sot. 1981,103,1927. 29. I. L. Eremenko, A. A. Pasynskii, A. S. Katugin, 0. G. Ellert, V. E. Shklover and Yu. T. Struchkov, BUN.

Acad. Sci. USSR Div. Chem. Sci. 1984, 1531. 30. H. Keck, A. Kruse, W. Kuchen, J. Mathow and H. Wunderlich, 2. Nuturfor. 1987,42b, 1373. 31. T. Shibahara, H. Kuroya, K. Matsumoto and S. Ooi, Znorg. Chim. Acta 1986,116, L25. 32. F. A. Cotton, M. P. Diebold, Z. Diri, R. Llusar and W. Schwotzer, J. Am. Chem. Sot. 1985,107,6735. 33. J. A. Bandy, C. E. Davies, J. C. Green, M. L. H. Green, K. Prout and D. P. S. Rodgers, J. Chem. Sot.,

Chem. Commun. 1983,1395. 34. F. A. Cotton, Z. Dori, R. Llusar and W. Schwotzer, Znorg. Chem. 1986,25,3529. 35. T. Shibahara, H. Kuroya, K. Matsumoto and S. Ooi, J. Am. Chem. Sot. 1984,106,789. 36. A. A. Pasynskii, I. L. Eremenko, Yu. V. Rakitin, V. M. Novotortsev, 0. G. Ellert, V. T. Kalinnikov,

V. E. Shklover, Yu. T. Struchkov, S. V. Lindeman, T. K. Kurbanov and G. S. Gasanov, J. Organomet.

Chem. 1983,248,309. 37. T. Shibahara, E. Kawano, M. Okano, M. Nishi and H. Kuroya, Chem. Z&t. 1986,827. 38. A. Miiller, E. Krickemeyer and H. Biigge, Angew. Chem. Znt. Edn Engl. 1986,25,272. 39. A. Miiller, W. Eltner, H. Biigge and R. Jostes, Angew. Chem. Znt. Edn Engl. 1982,21,795. 40. Trinh-Toan, W. P. Fehlhammer and L. F. Dahl, J. Am. Chem. Sot. 1977,99,402. 41. R. A. Schunn, C. J. Fritchie Jr and C. T. Prewitt, Znorg. Chem. 1966,5,892. 42. C. H. Wei, G. R. Wilkes, P. M. Treichel and L. F. Dahl, Znorg. Chem. 1966,5,900. 43. J. Amarasekera, T. B. Rauchfuss and S. R. Wilson, J. Chem. Sot., Chem. Commun. 1989; 14. 44. J. W. Lauher, J. Am. Chem. Sot. 1978,11,5305. 45. C. E. Davies, J. C. Green and G. H. Stringer, NATO ASZSer., Ser. C 1986,176,413. 46. T. Sugano, T. Shibahara, H. Kobayashi, N. UryQ and M. Kinoshita, Bull. Chem. Sot. Jpn 1988, 61,

1785. 47. M. Elian and R. Hoffmann, Znorg. Chem. 1975,14, 1058. 48. T. A. Albright, J. K. Burdett and M. H. Whangbo, Orbital Interactions in Chemistry, Chap. 17. Wiley-

Interscience, New York (1985). 49. R. S. Gall, C. T.-W. Chu and L. F. Dahl, J. Am. Chem. Sot. 1974, %, 4019. 50. T. O’Sullivan and M. M. Millar, J. Am. Chem. Sot. 1985,107,4096. 51. W. E. Cleland, D. A. Holtman, M. Sabat, J. A. Ibers, G. C. DeFotis and B. A. Averill, J. Am. Chem.

Sot. 1983,105,6021. 52. M. A. Bobrik, K. 0. Hodgson and R. H. Holm, Znorg. Chem. 1977,16,1851.

89. T. Shibahara, H. Akashi and H. Kuroya, J. Am. Chem. Sot. 1986,108, 1342. 90. A. A. Pasynskii, I. L. Eremenko, B. Orazsakhatov, V. T. Kalinnikov, G. G. Aleksandraov and Yu. T.

Struchkov, J. Organomet. Chem. 1981,214,367. 91. 92. 93.

94.

95.

X. Wu, S. Lu, L..Zu, Q. Wu and J. Lu, Z&g. Chim. Acta 1987, 133, 39. H. Zhan, Y. Aheng, X. Wu and J. Lu, Jiegou Huaxue (J. Struct. Chem.) 1988,7,157. D. Coucouvanis, S. Al-Ahmad, A. Salifoglou, W. R. Dunham and R. H. Sands, Angew. Chem. Znt. Edn Engl. 1988,27, 1353. P. K. Mascharak, G. C. Papaefthymiou, W. H. Armstrong, S. Foner, R. B. Frankel and R H. Hahn, Znorg. Chek. 1983, 22,2851. M. J. Camey, J. A. Kovacs, Y.-P. Zhang, G. C. Papaefthymiou, K. Spartalian, R. B. Frankel and R. H. Holm, Znorg. Chem. 1987,26,719.

96. J. A. Kovacs and R. H. Holm, J. Am. Chem. Sot. 1986,108,340. 97. J. A. Kovacs and R. H. Holm, Znorg. Chem. 1987,X, 702. 98. J. A. Kovacs and R. H. Holm, Znorg. Chem. 1987,26,711.


53. A. Miiller, N. Schladerbeck and H. Biigge, Chimiu 1985,39,24. 54. W. Saak and S. Pohl, Z. Naturfor. 1985,4Ob, 1105. 55. B. A. Averill, T. Herskovitz, R. H. Holm and J. A. Ibers, J. Am. Chem. Sot. 1973,%, 3523. 56. A. Miiller, N. H. Schladerbeck and H. Biigge, J. Chem. Sot., Chem. Commun. 1987,35. 57. L. Que Jr, M. A. Bobrik, J. A. Ibers and R. H. Holm, J. Am. Chem. Sot. 1974, %, 4168. 58. T. J. Ollerenshaw, C. D. Gamer, B. Ode11 and W. Clegg, J. Chem. Sot., Dalton Trans. 1985,216l. 59. G. Christou, C. D. Gamer, M. G. B. Drew and R. Cammack, J. Chem. Sot., D&on Trans. 1981, 1550. 60. P. K. Mascharak, K. S. Hagen, J. T. Spence and R. H. Holm, Znorg. Chim. Acta 1983,80, 157. 61. H. L. Car&l, J. P. Glusker, R. Hob and T. C. Bruice, J. Am. Chem. Sot. 1977,99,3683. 62. M. G. Kanatzidis, N. C. Baenziger, D. Coucouvanis, A. Simopoulos and A. Kostikas, J. Am. Chem.

Sot. 1984,106,4500. 63. T. D. P. Stack and R. H. Holm, J. Am. Chem. Sot. 1988,110,2484. 64. E. J. Laskowski, R. B. Frankel, W. 0. Gillum, G. C. Papaefthymiou, J. Renaud, J. A. Ibers and R. H.

Holm, J. Am. Chem. Sot. 1978,100,5322. 65. M. 3. Camey, G. C. Papaefthymiou, M. A. Whitener, K. Spartalian, R. B. Frankel and R. H. Holm,

Znorg. Chem. 1988, 27, 346. 66. J. M. Berg, K. 0. Hodgson and R. H. Holm, J. Am. Chem. Sot. 1979,101,4586. 67. D. W. Stephan, G. C. Papaefthymiou, R. B. Frankel and R. H. Holm, Znorg. Chem. 1983,22,1550. 68. K. S. Hagen, A. D. Watson and R. H. Holm, Znorg. Chem. 1984,23,2984. 69. G. C. Papaefthymiou, E. J. Laskowski, S. Frota-Pessoa, R. B. Frankel and R. H. Holm, Znorg. Chem.

1982,21, 1723. 70. A. L. Balch, J. Am. Chem. Sot. 1969,91,6962. 71. T. H. Lemmen, J. A. Kocal, F. Y.-K. Lo, M. W. Chen and L. F. Dahl, J. Am. Chem. Sot. 1981, 103,

1932. 72. Q. Liu, L. Huang, Y. Yang and J. Lu, Jiegou Huaxue 1987,6, 135. 73. J. E. Huheey, Inorganic Chemistry, 3rd edn, Chap. 10. Harper & Row, New York (1983). 74. E. L. Muetterties and L. J. Guggenberger, J. Am. Chem. Sot. 1974,%, 1748. 75. M. G. Kanatzidis, D. Coucouvanis, A. Simopoulos, A. Kostikas and V. Papaefthymiou, J. Am. Chem.

Sot. 1985,107,4925. 76. R. E. Johnson, G. C. Papaefthymiou, R. B. Frankel and R. H. Holm, J. Am. Chem. Sot. 1983, 105,

7280. 77. H. Brunner, H. Kauermann and J. Wachter, J. Organomet. Chem. 1984,265,189. 78. H. Brunner and J. Wachter, J. Organomet. Chem. 1982,240, C41. 79. T. R. Halbert, S. A. Cohen and E. I. Stiefel, Orgunometullics 1985, 4, 1689. 80. M. D. Curtis and P. D. Williams, Znorg. Chem. 1983, 22, 2661. 81. M. D. Curtis, P. D. Williams and W. M. Butler, Znorg. Chem. 1988,27, 2853. 82. H. Brunner, H. Kauermann and J. Wachter, Angew. Chem. Znt Edn Engl. 1983,22,549. 83. T. B. Rauchfuss, T. D. Weatherill, S. R. Wilson and J. P. Zebrowski, J. Am. Chem. Sot. 1983,105,6508. 84. T. B. Rauchfuss, S. D. Gammon, T. D. Weatherill and S. R. Wilson, New J. Chem. 1988,12,373. 85. H. Brunner, N. Janietz, J. Wachter, T. Zahn and M. L. Ziegler, Angew. Chem. Znt. E&I Engl. 1985, 24,

133. 86. A. A. Pasynskii, I. L. Eremenko, B. Orazsakhatov, V. T. Kalinnikov, G. G. Aleksandrov and Yu. T.

Struchkov, J. Organomet. Chem. 1981,216,211. 87. X. Wu, Y. Zheng, N. Zhu and J. Lu, Jiegou Huuxue (J. Struct. Chem.) 1988,7,137. 88. I. L. Eremenko, A. A. Pasynskii, B. Orazsakhatov, 0. G. Ellert, V. M. Novotortsev, V. T. Kalinnikov,

M. A. Porai-Koshits, A. S. Antsyshkina, L. M. Dikareva and V. N. Ostrikova, Znorg. Chim. Acta 1983, 73, 225.

S. HARRIS

99. W. H. Armstrong, P. K. Mascharak and R. H. Holm, Znorg. Chem. 1982,21, 1699. 100. P. K. Mascharak, W. H. Armstrong, Y. Mizobe and R. H. Helm, J. Am. Chem. Sec. 1983,105,475. 101. R. E. Palermo and R. H. Holm, J. Am. Chem. Sot. 1983,105,4310. 102. R. E. Palermo, R. Singh, J. K. Bashkin and R. H. Hahn, .Z. Am. Chem. Sot. 1984,106,2600. 103. Y.-P. Zhang, J. K. Bashkin and R. H. Hohn, Znorg. Chem. 1987,26,694. 104. Q. Liu, L. Huang, B. Kang, C. Liu, L. Wang and J. Lu, Huaxue Xuebuo 1986,44, 343. 105. L. Huang, Y. Yang, Q. Liu and J. Lu, Jiegou Huaxue 1986,5,61. 106. B. Kang, Q. Liu, L. Huang, D. Wu, J. Cai, L. He, H. Liu and J. Lu, Jiegou Huuxue 1987,6,8. 107. Q. Liu, L. Huang, B. Kang, Y. Yang and J. Lu, Kexue Tongbao (Foreign Lung. Edn) 1987,32,898.

structure, bonding and electron counts in cubane-type cluster having m4s4, m2m′2s4 and mm′3s4...

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