Closo clusters with unusual electron numbers: Localized bond schemes for n-atom clusters with n, (n + 1) or (n + 2) skeletal electron pairs

Polyhedron Vol. 3, No. 2, pp. Printed in Great Britain.

199-212,

1984 0

0277-5387/84 1984 Pergamoo

$3.00 + .oO Press Ltd.

CLOSO CLUSTERS WITH UNUSUAL ELECTRON NUMBERS: LOCALIZED BOND SCHEMES FOR n-ATOM CLUSTERS WITH n, (n + 1) OR (n + 2) SKELETAL ELECTRON PAIRS MARION E. O’NEILL and KENNETH WADE* Chemistry Department, Durham University, South Road, Durham DHl 3LE, England (Received 1 June 1983; accepted 25 July 1983)

Abstract-This paper considers whether satisfactory localized 2- and 3-centre bond schemes may be devized for real or hypothetical clusters B,H,‘- (c = 0, 2 or 4; n = 4+ 12) or isoelectronic analogues thereof, with close deltahedral shapes. As expected, localized bond schemes can be devized for all the species that would be predicted, using MO approaches, to have closed shell electronic configurations: these include species B,H,*(n = 5-+ 12) and B,H,‘- (c = 0 or 4; n = 4, 8, 9 or 11). There is also generally good agreement with MO treatments as to which systems are not expected to be stable: these include B4H42- and B,H,‘- (c = 0 or 4; n = 5, 7 or 10). Localized bond treatments have value for estimating the bond orders of cluster bonds in species B,H, and B,Hn2-, though they overestimate the bond orders in species B,Hn4- (except when n = 4). They are misleading, when applied to octahedral and icosahedral systems, in indicating the former shape to be feasible for hypothetical species B,H, and B,H, 4-, and the latter shape to be feasible for hypothetical species B12HlZand B,,H,:-.

A striking feature of the structural chemistry of the higher boranes and related clusters is the link that exists between skeletal shapes and electron numbers.‘-* Closed cage (&so) deltahedral shapes are normally adopted when the number of skeletal electron pairs exceeds the number of skeletal atoms by one, as in the case of anions B,Hn2- and related neutral molecules C,B, _2Hn (n = 5+ 12). More open structures are adopted by species with more skeletal electrons, though even for these the normal pattern is for the structure to be based on a polyhedron with one vertex fewer than the number of skeletal electron pairs. There are, however, a few important systems that are our concern here, in which a close n-vertex deltahedral structure is found to be associated with n or (n + 2) skeletal electron pairs instead of the more usual (n + 1) pairs. Examples include the neutral chlorides B,C1,9 and B9Cl9’owhich, like the metallaborane (C,H,),Co,B,H,L’, are n-atom n-eleciron pair systems. Examples of n-atom (n + 2)-electron pair systems with close deltahedral structures include the metallabor?ne (C,H,)4Ni4B4H4’2 and the cat*Author to whom correspondence dressed. POLY

should

be ad-

ionic bismuth cluster Bi,‘+.13 It has been suggestedI that an explanation for the unusual numbers of electrons these clusters contain lies in the fact that localized 2- and 3-centre bond schemes using n, (n + 1) or (n + 2) bond pairs can be devized for the deltahedra in question (Q,, dodecahedron for the 8-atom clusters, D3h tricapped trigonal prism for the 9-atom clusters). We have elsewhere pointed out that a consideration of the degeneracies of the frontier orbitals of such clusters provides a better guide as to which shapes can tolerate other than the usual (n + 1) skeletal bond pairs, and that localized 2- and 3-centre bond schemes can be devized for such unlikely species as B,H, and B,H, 4- .I5 Here we elaborate and extend our earlier discussion of localized bonds and explore further merits and defects of 2- and 3-centre bond treatments of close borane-type clusters.

LOCALIZED BOND SCHEMES. ASSUMPTIONS AND GENERALISATIONS Our approach has been to explore whether the close deltahedral structures of anions B,Hn2- and carboranes C,B, _ 2Hnmight be compatible with the presence of n or (n + 2) skeletal electron pairs, as

Vol. 3, No. 2m-E

199

M. E. O’NEILL and K. WADE

200

well as the more usual (n + 1) bond pairs, by assigning these electrons to localized 2-centre B-B bonds along edges of the B, polyhedra, or to localized 3-centre BBB bonds in the polyhedral faces. To deduce how many of each bond type should be used, and how they should be distributed about the surfaces of the B, polyhedra, we have used Lipscomb’s topological treatment of borane bonding’6s’7 which has for long provided the standard treatment of the bonding in neutral nido or arachno boranes B,H, +4 or B,H, + 6, although it has found only occasional application to close species because these generally require large numbers of canonical forms to be considered. Computer programmes to search exhaustively for these canonical forms have been developed, and Epstein and Lipscomb” have listed the results of such searches for most known neutral nido and arachno boranes and for many close borane anions B,H,*-. Our intention here is to supplement their work by considering some systems they ignored, and by drawing attention to some general characteristics of localized bond schemes that have hitherto gone unremarked. To start with, it is necessary to consider the salient features of the topological approach to borane bonding, and to note the assumptions on which it is based. Neutral boranes B,H,+, are treated as aggregates of n BH units, held together by (2n + m) electrons-two provided by each BH unit, one by each of the extra m hydrogen atoms. These framework or skeletal electrons are allocated to s BHB bonds, t BBB bonds, y BB bonds and x extra terminal BH bonds. Eor ionic species B,H,‘- , with no additional hydrogen atoms to be accommodated in BHB bonds or in extra terminal BH bonds, the equations relating s, t, y and x to each other reduce to the unique solutions s =x = 0, t = n - c and y = 3~12.“S Values of t and y that

concern us here, i.e. for values of n ranging from 4 to 12 and values of c of 0, 2 or 4, are listed in Table 1. To allocate these bonds satisfactorily to polyhedral clusters like the close anions B,H,,- , one must take account of further basic assumptions of the topological approach. These are as follows. (1) Each skeletal atom is assumed to participate in three skeletal bonds (the other bond it can form, by use of the fourth of its valence shell orbitals, links it to the exo hydrogen atom). (2) Each point of contact between bonded atoms-each edge of the skeletal B, polyhedronmust be accounted for, either by a 2-centre bond along that edge, by two 3-centre bonds adjacent to that edge, or by one 3-centre bond adjacent to it (Fig. la). (3) Two boron atoms cannot simultaneously be bonded to each other by both a 2-centre BB bond and one or two 3-centre BBB bonds, as shown in Fig. l(b), as these arrangements would require too close an alignment of the atomic orbitals involved, and would imply a greater concentration of electronic charge near to one polyhedron edge than is reasonable in these systems, which generally contain far fewer skeletal electron pairs [(n + 1) pairs for systems B,Hn2-] than polyhedral edges [3(n - 2) for n-vertex deltahedra]. (4) Cross-polyhedral interactions, which are generally significantly longer than polyhedral edge interactions, are considered to be nonbonded. (5) Where individual bond networks do not match the symmetry of the polyhedron in question (as is generally the case), resonance between all plausible canonical forms needs to be invoked. Bearing in mind these assumptions, we can deduce what bond arrangements are possible for specific cluster systems. In doing so, it is helpful to take account of the skeletal coordination numbers

Table 1. Values of t (the number of 3-centre BBB bonds) and y (the number of 2-centre BB bonds) for clusters B,H,‘- (c = 0, 2 or 4)

2

4

5

6

7

6

9

10

11

12

c-0

1’0

4

4

5

6

7

6

9

10

11

12

1’2

r-3

&

2

3

4

5

6

7

0

9

10

5’4

2’6

4

0

1

2

3

4

5

6

7

8

201

Closo clusters with unusual electron numbers 6

fi=L

lb)

9

/c!B \

7

4x0

+4B bond types ‘-

10 2-centre

bond

3-centre

bond

Fig. 1. Localized bond arrangements by which points of contact (the point of contact under consideration is that between the shaded atoms) between skeletal atoms (polyhedral edges) can be accounted for: (a) plausible arrangements (b) arrangements excluded.

or skeletal connectivities, k, of individual skeletal atoms-the numbers of neighbouring skeletal atoms to which particular atoms are directly linked by polyhedral edges. Figure 2 shows the series of polyhedra known for boron halide clusters B,X, (n = 4, 8 or 9) or for borane anions B,H,*(n = 6+12) or carboranes C2Bn_*Hn (n = 5+12). In these, k ranges from 3 to 6. The localized bonding arrangements that are compatible with these connectivities, and with the assumptions listed above, are shown in Fig. 3. From this, we see that a skeletal atom with only three skeletal neighbours can bond to these either by using three 2-ccntre bonds along the polyhedral edges or by using three 3-centre bonds in the polyhedral faces that meet at that atom. Combinations of two 2-centre bonds and one 3-centre bond, or of one 2-centre bond and two 3-centre bonds, are excluded by assumption 3 above. An atom with four skeletal neighbours cannot bond exclusively to them by means of 2-centre bonds, since that would require it to participate in four skeletal bonds, contravening assumption 1 above. It can, however, use exclusively 3-centre bonds, or combinations of one 2-centre bond and two 3-centre bonds, or one 3-centre bond and two 2-centre bonds. An atom with five skeletal neighbours can use three 3-centre bonds, or two 3-centre bonds and one 2-centre bond, while an atom with six skeletal neighbours

k=3

8

k=4.

k=5o

k=663

Fig. 2. The polyhedral skeletons of boron halide clusters B,X, (n = 4,8 or 9), borane anions B,Hn2- (n = 6-12) or carboranes C2B,_2H, (n = 5+ 12) showing skeletal connectivities k.

k=3

A

A

-k=l

J_=S

X

k-6 X

X

@ Fig. 3. The bonding networks by which atoms of particular connectivities k can bond to their skeletal neigh-

bours.

202

M. E. O’NEILL and K. WADE expected is the trend in ke, the total order of the k skeletal bonds formed by a particular atom, which also decreases as k increases, provided that all the bonding options shown in Fig. 3 can be utilised, and are given equal weight. The implication of this trend is that atoms of low coordination number in clusters require a greater share of the skeletal bonding electrons than their more highly coordinated neighbours, and so are expected to be the more negatively charged, a conclusion consistent with the results of MO calculations and also with studies of the spectra and reactions of specific clusters.lG2’ In ‘the following section, we illustrate the localized bond networks with which the skeletal bonding in some specific systems can be described, and draw attention to respects in which these networks appear either particularly apt or particularly misleading.

has only one bonding option open to it, which is to use three 3-centre bonds. Before exploring the compatibility of these localized bond arrangements with the connectivity requirements of all the atoms of complete polyhedra, it is worth noting how strongly the bond arrangements shown in Fig. 3 connect the central atoms to their neighbours. As we shall be trying to rationalise the lengths of the edges in specific polyedra, it is convenient to regard the bonding power of the skeletal bond pairs as channelled along the polyhedral edges, whether the bond pairs occupy 2-centre edge bonds or 3-centre face bonds, and to estimate the edge bond order, e, of each polyhedral edge (which will generally prove to be < 1). An edge to which a 2-centre edge bond is assigned is assumed to have e = 1.0. Each of the three edges surrounding a 3-centre face bond is assumed to have a bond order of l/3 (0.33’). Edges between two 3-centre face bonds are assumed to have a bond order of 2/3 (0.66’). Intermediate values of the edge bond order, e, are possible for edges to which two or more different bond arrangements contribute as resonance canonical forms. The two bonding possibilities (Fig. 3) open to an atom of skeletal connectivity k = 3, for example, generate edge bond orders e of 1.0 and 2/3 (0.66’) respectively. If both bond arrangements are equally possible, resonance between the two will lead to an average edge bond order e, of 5/6 (0.83’), and a total bond order, ke, of 2.5 for the three skeletal bonds formed by such an atom. The edge bond orders corresponding to the other possible values of k illustrated in Fig. 3 are given in Table 2, which reveals some interesting trends. Not surprisingly, the mean bond order of the edge bonds formed by a particular atom decreases as the skeletal connectivity, k, of that atom increases, since a higher proportion of 3-centre bonds needs to be used as k increases. Perhaps less obviously

APPLICATIONS TO SPECIFIC POLYHEDRAL SYSTEMS B,H,’ (c = 0, 2 OR 4) Tetrahedral B,H, systems

It has long been recognized that tetrahedral clusters in which each skeletal atom is capable of forming 3 skeletal bonds can be held together either by six 2-centre edge bonds (as exemplified by tetrahedrane, C4H4, the carbon counterpart of B,HJ4-) or by four 3-centre face bonds (as exemplified by B,Cl,). In MO terms, these correspond to occupancy of the A, T and E-symmetry bonding MO’s, or of only the A and T-symmetry bonding MO’s, respectively. What is less generally recognized is that a localized bond treatment of a hypothetical species B,H,*-, which on the arguments outlined above would require the use of three 2-centre BB bonds and two 3-centre BBB bonds, cannot be devized without recourse to

Table 2. Dependence of edge bond orders, e, on skeletal atom connectivities, k Connectfvity,1

3

3

4

4

4

5

5

6

Number of P-centre bonds 3

0

2

1

0

1

0

0

Number of 3-centre bonds 0

3

1

2

3

2

3

3

Mean edge bond order. 0

2/3

2/3

?/I2

l/2

7/15

2/5

l/3

2.0

2.6'

2.3'

2.0

2.3'

2.0

2.0

3.0

k Average &*

lAssumfng all

1

2.5

2.3'

2.16'

of the bond arrangements listed for a particular value of&

equally possfble.

2.0

are

Closo clusters with unusual electron numbers

(cl

Id1

Fig. 4. (a) Skeletal structure of 1,5-CzB,H,; (b) Classically bonded network of six 2-centre EC bonds; (c) Alternative bond network, using three 2-centre and three 3-centre bonds; (d) Inappropriate network of one 3-centre and six 2-centre bonds for a hypothetical D,, species B,Hs4-.

unsatisfactory bond arrangements of the type shown in Fig. l(b). Molecular orbital considerations would lead to the conclusion that a tetrahedral species B,H,*- would be paramagnetic and susceptible to Jahn-Teller distortion.*’ For the series B&l,, B,H,*- and C,H,, localized bond and MO treatments are thus in accord, in showing the tetrahedral arrangement of four BH or similar isolobal units to be compatible with four or six bond pairs, but not five pairs. D,, B,H, systems Although B,H,2 - is unknown, it would be expected to have a structure like that of its carborane counterpart, 1,5-C,B,H,, which is familiar as the smallest close carborane known. This has a trigonal bipyramidal structure23 (Fig. 4a) with axial carbon and equatorial boron atoms. The equatorial bonds are relatively long (1.85 A) for a carborane. Their length is usually dismissed as implying a nonbonding interaction between the equatorial boron atoms, as might be expected for a classically bonded structure (Fig. 4b) in which the six skeletal bond pairs are assigned to the six polyhedral edges linking axial atoms to equatorial atoms, i.e. to the six C-B links. This description involves each boron atom in only two skeletal bonds. A much better description, that is fully compatible with all the requirements of the topological treatment of borane bonding, including the assumption that each atom forms three skeletal bonds, involves use of the required three 2-centre skeletal bonds and three 3-centre skeletal bonds

203

(Table 1 and Fig. 4c). The low coordination numbers of the axial atoms require these sets of bonds to occupy opposite hemispheres Af the pseudospherical structure, though resonance between the two possible canonical forms leads to edge bond orders e of 5/6 (0.83’) and l/3 (0.33’) for the axial and equatorial bonds respectively. Although the disparity between these bond orders is likely to be even greater in C,B,H, than in B,H,*- , since the more electro-negative axial carbon atoms in the carborane will drain electron density away from the equatorial boron atoms, these bond orders are more in line with the observed bond lengths23 (EC 1.56 A, B-B 1.85 A) and with the results of MO calculations24 than the description in terms of six 2-centre B-C bonds. The equations of balance, applied to a hypothetical neutral species B,H,, require its skeletal bonding to be described in terms of five 3-centre bonds. The connectivities required for a trigonal bipyramid, however, are incompatible with the use of five 3-centre bonds, so this species appears unlikely on the basis of localized bond arguments. It appears equally unlikely on the basis of MO treatments, which in view of the degeneracy of the HOMO of B,H, *- require D3h B,H, to be a paramagnetic species susceptible to Jahn-Teller distortion.‘5,22 A trigonal bipyramidal structure is also incompatible with a bonding rationale involving seven skeletal bond pairs in six 2-centre bonds and one 3-centre bond as would be required for a species B,H,4-. Allocation of six 2-centre bonds to the axial edges and one cross-polyhedral 3-centre bond to the equatorial triangle as in Fig. 4(d) would conflict with assumption 4 above, and can be eliminated on the grounds that the four bonds formed by each of the equatorial atoms, including the exo B-H bond, would then all be coplanar. MO argumentP also lead to the conclusion that a D,, structure for a hypothetical species B,H, 4would be unsatisfactory since the doubly degenerate HOMO would then be only half full. Thus, both localized bond and MO treatments lead to the same conclusion: that the close trigonal bipyramidal structure adopted by C,B,H,, and expected for B,H, *-, is not expected to be retained by species with two electrons more or fewer. B,H, systems MO treatments of octahedral arrangements of six BH units indicate a closed shell electronic configuration for the species B,H, * - which contains the seven skeletal bond pairs needed to fill all seven of the A, T,, and T,, bonding MO’S.“~,~~ Octahedral

204

M. E. O’NEILL and K. WADE

lb) B&-I;-

(c)

B&

Fig. 5. Apparently satisfactory bond networks for octahedral species B,H, (six 3-centre bonds), B,Hh2- (three 2-centre and four 3-centre bonds) and B,Ht(six 2-centre and two 3-centre bonds).

However, localized bond treatments (Fig. 5), whether using six 3-centre bonds for a hypothetical species B,H,, or three 2-centre and four 3-centre bonds for B,H,2 -, or six 2-centre and two 3-centre bonds for a hypothetical octahedral species B,He4-, appear to indicate that an octahedral structure is compatible with six, seven or eight skeletal bond pairs, and that the bond orders of the octahedral edges would be expected to increase with the number of electrons available for skeletal bonding. The localized bond treatment thus has no predictive value for these systems’ likely existence, and gives no clear indication of why seven skeletal bond pairs are needed. D,, pentagonal bipyramidal B,H, systems Although the structure of B,H$- has not been confirmed by X-ray crystallographic studies, a D,, pentagonal bipyramidal structure like that established for the carborane 2,4-C,B,H,26 is indicated by NMR studies” and by MO treatmentP which, moreover, show both HOMO and LUMO to be doubly degenerate. Hypothetical pentagonal bipyramidal species B,H, or B7H74- would therefore be expected to be paramagnetic and so highly reactive species, susceptible to distortion to relieve the degeneracy of their highest occupied molecular orbitals. Interestingly, localized bond treatments also indicate that eight skeletal bond pairs, but not seven or nine pairs, are appropriate for a pentagonal bipyramidal arrangement of seven BH units. The three 2-centre bonds and five 3-centre bonds required by the equations of balance for B,H,*- can be allocated as shown in Fig. 6, using the two

Fig. 6. The localised bond network of three 2-centre and five 3-centre bonds compatible with the D,, pentagonal bipyramidal

structure of B,HT2-.

bonding networks possible for an atom of skeletal connectivity k = 5 (Fig. 3). Two 3-centre bonds must be allocated to one pentagonal pyramid, three 3-centre bonds to the’other, and so only one of the 2-centre bonds can be used for edges connecting axial to equatorial atoms. All three of the bonding schemes shown in Fig. 3 as possible for an atom of connectivity k = 4 must therefore be used. Allowing for resonance, this bond scheme corresponds to edge bond orders e of 0.43’ for the edges linking axial atoms to equatorial atoms, and 0.583’ for the equatorial edges. These values in turn correspond to total bond orders ke of 2.16’ for the axial atoms, and 2.3’ for the equatorial atoms, implying that the latter, which have the lower coordination number, are the more negatively charged, as indicated also by MO treatmentsI Hypothetical D,, species B,H, and B7H74would need the following localized bond networks. For B,H,, seven 3-centre BBB bonds would need to be allocated to seven of the ten pentagonal bipyramidal faces, while for B7H,4-, six 2-centre BB bonds and three 3-centre BBB bonds would have to be used. From Fig. 3 it is apparent that neither bond arrangement is compatible with the presence of two non-adjacent atoms with k = 5, which between them would require a minimum of four and a maximum of six 3-centre bonds to be used. DZd dodecahedral B,H,-systems Molecular orbital treatments of B,H,*- have identified the HOMO and LUMO as having 6, and is respectively.‘6,28 Neither a2 symmetry degenerate-degeneracies could of course only be

205

Close clusters with unusual electron numbers accidental in a system with 2-fold symmetry. In contrast to the situation that obtains for the deltahedra of B,H, ’ -, B,H, ’ - and B,H: - (which are

n-vertex shapes compatible only with (n + 1) skeletal bond pairs), the Du dodecahedral cluster shape of B,Hs2- is therefore compatible with n, (n + 1) or (n + 2) (i.e. 8, 9 or 10) skeletal bond pairs, 3s illustrated by the chloride B,Cls9 (8 pairs), the cobaltaborane (C,H, ),Co4B4H411(8 pairs), the ar;on B,H,2-29(9 pairs), the carborane CzB6H,30(9 pairs) and many other 9-pair systems, and the nickelaborane (CSHJ4Ni,B4H,r2 (ten pairs). The localized bond networks that can be drawn for these three different numbers of skeletal electron pairs are illustrated in Fig. 7. The average edge bond orders that they imply are given in Table 3, which also gives the interatomic distances in B,Cls9 and B,Hg2- .29Qualitatively, the localized bond schemes provide a satisfactory explanation of the differences in edge lengths between these two octaborane clusters-bond orders increase where B-B distances decrease. Moreover, the two types of edge that link 4-coordinate to 5-coordinate atoms (types x and y in Fig. 7) suffer a reversal of their relative bond orders on going from B&l, to B,Hr2-, a reversal matched by their relative lengths. These features correlate precisely with the character of the HOMO of BsHs2-,28 which is

lb)

ICI

for D,, I-atom clusters with (a) eight skeletal electron pairs (e.g. B&l,; eight 3-centre bonds), (b) nine skeletal electron pairs (e.g. B,Hs2-; three 2-centre and six 3-centre bonds), or (c) ten skeletal electron pairs (e.g. (CSHJ4C04B4H4; six 2centre and four 3-centre bonds).

Fig. 7. Localized bond networks appropriate

bonding for edges of types w, y and z, but antibonding for edges of type x. No homonuclear 8-atom IO-electron pair D2,, dodecahedral cluster is known at present with which to test the capacity of localized bond schemes to explain or predict the interatomic distances in such a system. From the character of the LUMO of B,Hg2- (the orbital that must accommo-

Table 3. Average edge bond orders, e, predicted for D, B&I,, B,Hg2- and B,HS4- from the localized bond networks shown in Fig. 7, compared with interatomic distances d (pm) Edge type (Fig. 7) Ill

Ref.

x

Y

2

I

0.66'

0.50

0.33'

0.33'

d

168

175

178

200

I

0.83'

0.33'

0.83'

0.33'

d

158

178

174

193

B8"84-

Q

1.0

0.83'

0.33'

0.33'

288"s

HOKlf

b

ab

b

b

16.2;

2B8"8

LUMD*

ab

ab

ab

b

16.2

B&'8

2B8"8

Entries

In these mus

9

29

indicate the bonding (b) or antlbonding tab) character

of the HOMO and LUMO of BBH~~'.

206

M. E. O’NEILL and K. WADE

date the tenth pair of electrons), which is antibonding for polyhedron edges of types w, x and y, and bonding for edges of type Z, one would expect the former to be longer and latter shorter in a D, species B,HS4- than in B,Hg2-. The related nick-

elaborane (C,H,),Ni4B4H4’* contains four %B polyhedral edge bonds, all of type z (Fig. 7), for which all three localized bond schemes, whether using eight, nine or ten skeletal electron pairs, predict a bond order of 0.33’. Type z bond lengths are 200pm in B,Cl,,9 193 pm in BsHs2-,29 and 192 pm in (C,H5)4Ni,B,H4.12 The consistency of these last two figures with the expectations of a localized bond treatment must be regarded as fortuitous, since the effect of replacing boron atoms by nickel atoms on going from BsHS4- to the nickelaborane is ignored. Anyway, the localized bond treatment using ten skeletal bond pairs can be faulted because it assigns a bonding role to the tenth pair of electrons which MO treatments,28 as mentioned above, show to be essentially antibonding (antibonding for w, x and y, bonding for z). However, Table 3 shows that the localized bond treatment requires the tenth pair of electrons to make edges of types w and x more strongly bonded, edges of type y to be less strongly bonded, and edges of type z to remain the same compared with the 9-skeletal pair system B,H,‘-. Localized bond and MO treatments are thus in agreement in indicating that the 8-atom D,, dodecahedra1 skeleton is compatible with the presence of eight, nine or ten skeletal electron pairs, and in their assessment of how the eight or nine pairs are distributed about the skeleton. However, the localized bond treatment overestimates the bonding role of the tenth pair of electrons, which it distributes misleadingly. D,, tricapped trigonal prismatic B,H, systems Like the D2d dodecahedral B,H,‘-, the D,, tri-

capped trigonal prismatic B,H,2- has nondegenerate frontier oribitals.13 The HOMO has symmetry a;, and is antibonding for edges of type f(Fig. 8), bonding for edges of types g and h. The LUMO has symmetry a;, with precisely the reverse edge-bonding or -antibonding characteristics: it is bonding for edges of typef, antibonding for edges of types g and h. Closed shell electronic configurations are therefore possible for D3* tricapped trigonal prismatic nine-atom clusters with nine, ten or eleven skeletal electron pairs, exemplified by the homonuclear clusters B,Cl,‘“, B H 2- 31 and Bi 5+13respectively. Bonding is explctid ;o be strogngest when there are ten skeletal bond pairs available. Adding or removing one or

lb)

(c)

Fig. 8. Localized bond networks appropriate for D,,, 9-atom tricapped trigonal prismatic clusters with (a) nine skeletal electron pairs (e.g. B&l,; nine 3-centre bonds), (b) ten skeletal electron pairs (e.g. B,Ht-; three 2-centre and seven 3-centre bonds) or (c) eleven skeletal electron pairs (e.g. Bi,‘+; SIX 2-centre and five 3-centre bonds).

two electrons to or from the lo-pair system is expected to give rise to precisely the same type of distortion. As one moves away from the ideal number of ten skeletal bond pairs, the trigonal prism is expected to get longer and narrower as g increases and f decreases in length, while the bonds (type h) to the capping atoms are also expected to lengthen. Localized bond networks for such systems are illustrated in Fig. 8. The mean bond orders that they imply for the three types of edge are given in Table 4, which also lists the edge lengths in B,Cl,1o, B,H,‘- and Bi,5+ .13Interestingly, a bond order of 0.33’ is indicated for both types of prism edge cf and g), irrespective of the number of electrons available, though the edges of type h connecting the capping atoms to the rectangular prism faces are expected to increase in bond order from 0.50 through 0.58-0.66’ as the number of skeletal electron pairs increases from nine to eleven. The lengths of these edges should therefore decrease relative to the lengths of the other edges going from B&l, through B,H,2 to Bi,’ + . The inter-

207

Closo clusters with unusual electron numbers Table 4. Average edge bond orders, e, predicted for D3h9-atom clusters with 9, 10 or 11 skeletal electron pairs from the localized bond networks shown in Fig. 8, with interatomic distances d (pm) in some representative systems

Ref.

Edge type (Fig. 8) f

g

h

Q

0.33'

0.33'

0.50

d

180

208

175

I

0.33'

0.33'

0.583'

d

188

181

171

I

0.33'

0.33'

0.66'

d

324

374

309

13

8g"g2-

HOPIO'

ab

b

b

31

8g"g2-

LIJKP

b

ab

ab

31

841,

26g"g

81g5+

10

31

* Entries In these rows Indicate the bondfng (b) or antibonding (ab) character of the HOMO and LUMD of 8gHg2- .

atomic distances listed in Table 4, however, show roar carrel&an wi& these pre&G~~ GX &C$, for example, the edges of types f and g, both formally of bond order 0.33’, and both linking atoms of connectivity k = 5, actually differ in length by as much as 28 pm. The edges of type h are admittedly the shortest in this compound, as required of those of highest bond order, but this feature might otherwise be attributed to the lower connectivity (k = 4) of the capping atoms. The anion B,H,2-, with ten skeletal bond pairs assigned to three 2-centre and seven 3-centre skeletal bonds, presents a slightly less unsatisfactory Tic cure, with
Dti bicapped square antiprismatic B,,,H,, systems MQ
t%isitmntts

of tf\e bicap@

square antiprismatic anion B,,H,,*- have shown both HOMO and LUMO to be doubly degenerate.16 Adding or removing two electrons to or from the twenty-two involved jn skeletal bonding woulc) generate paramagnetic reactive species if there were no change in symmetry. The &so shape is therefore compatible with eleven skeletal bond pairs, but not with ten or twelve skeletal pairs. The eleven skeletal pair system B,oHro2- can be treated in terms of three 2-centre and eight 3-centre localized bonds in a variety of waysI (Fig. 9). The a%Y&ge 6Q& 0%&S of th% trG% typ% of edge, giving equal weight to each of the six possible types of bond arrangement, are 0.583’ for edges of type a, 0.375 for edges of type b, and 0.416’ for type c. The actual edge lengths are a = 173 pm, 181 pm.3 The sequence a < c < b b=186pm,c= \S ths

e.tiw.c-J -c,wx&tc.t

WWA tk

SRpuencR of

decreasing bond order. Moreover, the total bond order, ke, for the two types of skeletal atom is 2.33 for the capping (polar) atoms of connectivity k = 4, and 2.16’ for the other (tropical) atoms of connectivity k = 5, indicating that the atoms of lower connectivity, by forming a set of bonds of higher total bond order than their more highly cQW&~&~ ntigVWSY%, aI% eY<&.ent(ytke rnW% negatively charged atoms. These localized bond networks thus provide a satisfactory rationale for the interatomic distances and charge distribution

208

M. E. O’NEILL and K. WADE C,, octadecahedral B,,H,, systems

Fig. 9. Localized bond networks (only one of the six possible networks shown; the other networks have the 2-centre bonds linking the following pairs of atoms; (i) 1-3, 1-4, 5-9, (ii) 1-3, 1-4, 6-9, (iii) 1-3, 1-4, 9-10, (iv) 1-3, 4-8, 2-9, (v) 1-3, 4-8, 9-10.) of the three 2-centre and eight 3-centre bonds compatible with the D, bicapped square antiprismatic structure of B,,H:; .

in the anion B,,H,,2-, and the large number of alternative networks consistent with the connectivity requirements of this anion suggests that it is likely to benefit from considerable resonance stabilisation, as indeed is indicated by its chemistry. If one attempts to describe the skeletal bonding in hypothetical species B,,H,, and B,,Hro4-, assuming D4d structures like that of B,oH,02-, and using localized 2- and 3-centre bonds, a different picture emerges. A species B,,H,,, having ten skeletal electron pairs, would require these to be allocated to ten 3-centre bonds if each boron atom is to participate in three skeletal bonds. Considering firstly the requirements of the capping atoms of connectivity, k = 4, one would need to allocate six of the ten 3-centre bonds to these atoms, three to each of the square pyramids, leaving four 3-centre bonds to be allocated to faces linking the tropical atoms of one hemisphere to those of the other, an allocation that is not compatible with the bonding requirements of these tropical atoms once the polar bonds have been assigned as described. A ten-atom ten-electron pair cluster with a D,, bicapped square antiprismatic structure is therefore not expected either on MO or on localized bond considerations. The hypothetical IO-atom 1Zelectron pair species B,oH,04- poses similar problems if one attempts to allocate the required six 2-centre and six 3-centre bonds to a D, bicapped square antiprismatic structure, such bonds being incompatible with the connectivities of this polyhedron. Thus both MO and localized bond treatments are in agreement that eleven skeletal bond pairs, but not ten or twelve pairs, are appropriate for the DM bicapped square antiprism.

Although the structure of the anion B,rH,,*- has not been confirmed by an X-ray crystallographic study, its spectra32 are consistent with a C,, structure related to that of decaborane, B,0H,4, with the extra atom completing the 1l-vertex polyhedron by occupying’the highly coordinated (k = 6) site on the 2-fold axis. This structure is analogous to that established for the isoelectronic carborane and is supported by MO calculations.34 C,B,H,,,33 Although these latter gave no details of the frontier orbitals, the C,, symmetry requires both HOMO and LUMO to be nondegenerate. Removal or addition of an electron pair need not therefore distort the cage substantially, and so species B,,H,, or B,,Hl14-, like B,,H,,2-, might in principle have close C,, structures. No such species are as yet known, though a nido type geometry based on an icosahedron is indicated for derivatives of B,,H,r4and the isoelectronic carborane anions CB,,H,i3and C2B,H,,2-.20 Localized bond networks compatible with a C,, octadecahedral close shape can be devised for all three species B,,H,,, B,,H,,‘- and B,,Hn4- (Fig. 10). The distribution of the bonds is effectively governed by the presence of the unique atom with k = 6, which must participate in three 3-centre bonds (Fig. 3). Each edge radiating from that atom therefore acquires a formal bond order of 0.33’. The problem of allocating the remaining bonds to the decaborane-like residue thus reduces to allocating eight 3-centre bonds (B,,H,,), three 2-centre and six 3-centre bonds (B,,H,,‘-), or six 2-centre and four 3-centre bonds (B,,Hn4-) to meet the connectivity requirements of the two atoms with k = 4 and eight with k = 5. The ways in which this can be achieved are illustrated in Fig. 10. The “normal” species B,,H,,‘- offers the greatest scope for alternative bonding networks, and so may be regarded as that most likely to benefit from resonance stabilization, though plausible bond networks for B,,H,, and B,,H,,4- can be devised. The bond orders they imply for the nine distinct types of bond in the C,, octadecahedron are listed in Table 5, which also shows how the total order of the bonds to particular atoms varies with their connectivity and with the number of skeletal electron pairs. The C,, octadecahedron of B,,H,,‘- or C,B,H,, thus resembles the Dzd dodecahedron of B,HS2and the D,, tricapped trigonal prism of B,Hg2- in being an n-vertex deltahedron which, on both MO and localized bond grounds, is compatible with the presence of (n + 1) skeletal electron pairs. Both MO and localized bond arguments are in agree-

209

Closo clusters with unusual electron numbers

la)

Ibl

ICI

Fig. 10. Localized bond networks appropriate for C,, 1l-atom octadecahedral clusters with (a) eleven skeletal pairs (e.g. a hypothetical B,,H,,; eleven 3-centre bonds), (b) twelve skeletal electron pairs (only one of the four possible bond networks shown; the other networks have the 2-centre bonds linking the following pairs of atoms (i) 2-3, 4-5, 8-l 1, (ii) 2-3, 4-9, 2-8, (iii) 2-3, 4-9, 8-l 1.) (e.g. B,,H:;: three 2centre and nine 3-centre bonds) or (c) thirteen skeletal electron pairs (e.g. a hypothetical B,,H:;; six 2-centre and seven 3-centre bonds).

by Longuet-Higgins and Roberts 3s from MO considerations, that this would require thirteen skeletal electron pairs for a closed shell electronic configuration, with quadruply degenerate HOMO and,LUMO (of symmetries U, and U, respectively). This prediction was later confirmed by the isolation and structural characterization of the anion B,2H,22- .‘6,19*20 Adding two electrons to or removing two electrons from this in that it was predicted

ment in predicting weaker bonding when there are only n skeletal electron pairs, but the localized bond treatment in all cases is misleading in implying stronger bonding when there are (n + 2) skeletal bond pairs.

I,, icosahedral B,$-I,, systems The icosahedral arrangement is of interest in the development

of twelve BH units of cluster bonding

Table S(a). Average edge bond orders, e, predicted for C, octadecahedral B,,H,,, B,,H:; B,,H:; species from the localized bond networks shown in Fig. 10

b

C

Edge type (Ffg.

10)

d

f

t

g

h

i

Table 5(b). Total bond order, ke, of the bonds radiating from atoms in C,, octadecahedral B,,H,,, B,,H:; and B,,Hj; as a function of their connectivities k Atom Number (Fig.

10)

Total Bll”ll

bond order. %I”11 2-

and

& Bll”l1 4-

1

2.0

2.0

2.0

2.5

2.0

2.33’

2.66’

3.4.6.7

2.0

2.33’

2.33’

8.10

2.0

2.25.

2.33’

9.11

2.0

2.06

2.33’

species

210

M. E. O’NEILL and K. WADE

la)

Ib)

Fig. 11. Apparently satisfactory bond networks for icosahedral species (a) B,,H,, (twelve 3-centre bonds) (b) B,,Hi; (three 2-centre and ten 3-centre bonds) (c) B,,H:; (six 2-centre and eight 3-centre bonds).

products B,,H,,4- or B,,H,, with incomplete electron configurations, prone to Jahn-Teller type distortions. Localized bond treatments of icosahedral species B,,H,, with twelve, thirteen or fourteen skeletal electron pairs give no indication that the systems with twelve or fourteen pairs are in any way unsatisfactory. Indeed, as illustrated in Fig. 11, the allocation of six 2-centre bonds to an octahedrallyrelated set of edges, with eight 3-centre bonds symmetrically disposed in relation to these, appears to provide a particularly apt bonding network for a hypothetical icosahedral species B,,H,,4-. Likewise, twelve 3-centre bonds can be allocated in a symmetrical manner (Fig. 11) to all but eight of the icosahedral faces to provide an apparently satisfactory bonding description for a hypothetical species B,,H,,. Allowing for resonance, these localized bond networks correspond to average edge bond orders e of 12130, 13130 and 14/30 for B,ZH,2, B,,H,,‘and B,,H,,4- respectively. The icosahedron of B,SH,22-, like the octahedron of B,Hz-, is thus another shape for which MO treatments suggest a compatibility with only (n + 1) skeletal bond pairs, whereas localized bond treatments suggest that n, (n + 1) or (n + 2) skeletal pairs are all possible. species would generate

CONCLUSIONS In this paper, we have attempted to describe the bonding in a series of real and hy;othetical deltahedral cluso boranes B,Hz -, where c = 0, 2 or 4, by using 2- and 3-centre bond networks that ensure that each boron atom participates in three bonds and that each polyhedron edge is always accounted for, either by a 2-centre bond along that edge, by one or two 3-centre bonds adjacent to that edge, or by a combination of these in resonance. For all species shown by MO calculations to have closed shell electronic configurations, i.e. for B,H, (n = 4, 8,9 or 1 1), for B,Hz- (n = 5+ 12), and for B,HJ(n = 4, 8, 9 or 1l), it was found possible to devise localized bond networks compatible with the atom connectivities involved. This is not unexpected, since the localized bonds used represent acceptable though rather crude alternative ways of describing how the electron density is distributed about the surfaces of these clusters. What is perhaps less expected is the way that topological factors-local connectivity requirements-prevent satisfactory bond networks from being devised for systems that, on MO grounds, would contain unpaired electrons. The systems B,H,*-, and B,Hn4- (n = 5, 7 or 10) fall into this category (Table 6). Such species are thus predicted to be unstable on both MO and localized bond arguments. It is only for the octahedron and icosahedron that discrepancies arise between the two approaches as to what electron numbers are expected. Apparently satisfactory localized bond networks can be devised for such species using n, (n + 1) or (n + 2) bond pairs, whereas MO treatments indicate that only the dianions B,H:- and B,,H,:-, i.e. the systems with (n + 1) skeletal bond pairs, are expected to be stable for these particular polyhedra. The disagreement between localized bond and MO arguments in these cases may be associated with their high symmetry. A more serious discrepancy between the localized bond approach and MO theory is in the assignment of a bonding role to the (n + 2)‘th electron pair in the former, whereas these electrons are antibonding according to the latter. The electrons are, moreover, distributed misleadingly about the polyhedra. For the systems with IZ or (n + 1) bonding electron pairs, however, the localized bond treatment provides at worst a rough but realistic indication of how they are distributed, and at best, provided the various canonical forms are considered, a very helpful indication of the electron distribution, allowing edge bond orders to be estimated.

211

Closo clusters with unusual electron numbers Table 6. The numbers of skeletal electron pairs predicted by molecular orbital and localized bond treatments to be compatible with n-vertex close deltahedral shapes for clusters B,H,‘- (c = 0,2 or 4) and related clusters Number of polyhedrorlvertices. n

Number of 4

5

6

7

8

9

10

11

12

n

+

-

0

-

+

+

-

+

0

n+l

-

+

+

+

+

+

+

+

+

n+2

+

-

0

-

+

+

-

+

0

reletal pairs

+

Systems shown by MO treatments to have closed shell electronic configuratlons for which localized bond networks can be devised.

-

Systems shown by MO treatments to have incompletely filled MO's, for which localized bond networks cannot be devised.

0

Systems shown by MO treatments to have incompletely filled MO's, for which locallred bond networks can be devised.

Acknowledgements-We thank SERC for support, and the University of Notre Dame (where this paper was written) for the generous hospitality shown to KW as a visiting professor. REFERENCES

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212

M. E. O’NEILL and K. WADE

3 1. L. J. Guggenberger, Inorg. Chem. 1968, 7, 2260. 32. F. Klanberg and E. L. Muetterties, Inorg. Chem. 1966, 5, 1955. 33. C. Tsai and W. E. Streib, J. Am. Chem. Sot. 1966, 88, 4513. 34. M. J. S. Dewar and M. L. McKee, Inorg. Chem.

1978, 17, 1569. See also E. H. Wong, L. Prasad, E. J. Gabe and M. G. Gatter, Inorg. Chem. 1983, 22, 1143 for the structure of Et4N+B,,H,,SMe2-. 35. H. C. Longuet-Higgins and M. de V. Roberts, Proc. Roy. Sot. (London) 1955, A230, 110.