SELF-CONSISTENT CHARGE AND CONFIGURATION ( SCCC ) CALCULATIONS ON 1 , 6-DICARBA-CLOSO-HEXABORANE

The bonding in 1, 6-dicarba-closo-hexaborane [61 [I , [C B H {P~(co) 11 [I11 .2,4-dicaiba-closo-heptaborane[7] [IIII . [C2B4H6{Pe(Cb):~ IN], ana [C B H { Fe(C0) ) ] [V] was investigated by c a y i n s out self consistent andZc~fiflguration [ ~ C C ] calculations. These investigations show that an apical boroh atom pses 2px, 2p atomic orbitals and a [2s, 2pZl hybrid orbital for bonding with rest of thy cluster. In cluster compounds containing Fe(C0) units, the iron atom uses predominantly [3dz. 4p I and [3d 4p I 3 combinations for bonding with the rest of the cluster and t h s e is no eevigce &r the involvement of a [4s, 4pZ, 3dZ21 hybrid orbital similar t o the [2s, 2pZl hybrid observed in the boron analogue. Analysis of the total overlap population associated with metallo.group and the rest of the cluster shows that the Fe(C0)3 group is weakly bonded ifito the cluster when compared with BH group of compounds in which Fe(C0) is replaced by BH. This analysis also indicates that Fe(C0) .group uses less than 2wo electrons for cluster bonding. 3

Understanding of the electronic structure and bonding of metal carbonyl clusters is of present interest.The number of orbitals invoIved in bonding [ > 100 atomic orbitals] makes it difficult to perform detailed molecular orbital calculations on metal carbonyl clusters.But it is believed that certain metallo groups such as Fe(C0)3 and CO(CO)~ are isolobal and isoelectronic h t h the BH and CH groups respectively.In terms of Wade's approacd9 a 3H or a Fe(C0) group formally supplies two electrons for cluster bonding whereas CH and Co(C0) groups supply three each.In addition, many boranes, carboranes, metadoboranes, rnetallocarboranes, and metal carbonyl clusters have similar geometries?3919 Thus the study of the electronic structure and bgnding of boranes, carboranes, metallo-boranes and metallocarboranes cauld be used to compare the bonding capabilities of transition metal carbonyl fragments, M(C0)3 with those of the BH or CH Units in cluster compounds.In our study, self-consistent charge and configuration (SCCC) calculations were used to investigate the bonding in 1,6-dicarba- The geometries of carboranes used were taken from reported,17f18 electron diffraction data.The same geometries were used for metallocarboranes.The geometry of the FelCO) unit was taken from that of [Fe(CO) $.    .

Results and Discussion
The details of the cluster bonding in carbsranes and metallocarboranes can be considered from three pieces of information provided by the SCCC calculation.They are [i] the gross atomic charges [ii] the overlap popula-.tions and [iii] the molecular orbital energy levels and their LCAO expansions.

1,6-C2B,H6 [I] and 2,4-C2B, H, [111]
The gross atomic charges (Table 1) and the overlap populations (Tiable 3) indicate that the four BI-I units in 1,6-C,B4H6 are equivalent and so are the two CH units.This is in agreement with the predicted1 D4,, symmetfy of the molecule.The presence of three distinct type of BH units in 2 , 4

Self-consistent Charge and Configu~ation
C2 B5 33, is shown by the localised charges [Tables 1 and 21 11 the net negative charge on carbons by 0.041 and decreases the positive charge on boron by values in the range 0.020-0.037.Table 3 shows that the overlap population bonding the metallo-unit to the C2B H base is about 5 7% of that bonding the BH in 1,6-C B4H6.In other words t i e replacement of a BH unit by a Fe(CO)3 group maftes the resulting compound even more electron-deficient than the parent carborane.A similar result has been observed in borane c1uste1-s.~Table [I] shows that the iron atom of ferracarborane [II] cairies a positive charge 10.7331 and this may be the reason for the reduction in overlap population betwen the metallounit and carborane base.The positive charge on iron atom may be due to the valence electrons in iron atom being largely delocalised over the carbonyl ligands.Replacement of a BH unit in 1,6-C2B4H6.by a Fe(C0)' unit did not change the energy of the cluster orbitals appreciably.The comparison of the cluster bonding molecular orbitals shows that the roles of the boron 2p and 2py.atomic orbitals in carboranes are taken up by the iron 3dxz an3 -3dyz mth some admixture of 4px and 4p .According to the isolobd principle the 3dz2, 4s and 4pz metal atomic orsitals should combine to form a hybrid orbital which takes on the role of the boron 2s and Zp, orbitals.

P
In Fe(CO),, the 3dZ2 atomic orbital is involved in bonding but plays no significant part in cluster bonding, whereas, the al cluster molecular orbital of BH unit (which is equivalent to 2s, 2pl hybnd of boron atom] plays a significant part in cluster bonding.A simllar result has been reported8 in metdoboranes.LCAO expansion of HOMO of [11] shows that it has a small contribution from the 3d 2 2 of Fe and carbonyl carbon and oxygen x -Y atomic orbitals.

[C2B4H, (F~(co)$] [IV]
The replacement of an apical BH unit in  51 indicate that the l-isomer [IVa] is more stable than the 5-isomer [IVb] .As mentioned earlier, the 2,4-C B5H7 has three cluster bonding molecular orbitals.two of C2B5 cornginations and the third VOMO] of basal carbon and boron atoms combination.The replacement of either the apicaI BIH or basal B5H by a Fe(C0)3 unit did not change the energy of any of these orbitals appreciably.The comparison of the LCAO expansion of these orbitals shows that there is no significant contribution from the metal 3dZ2, 4s and 4pZ atomic orbitals t o these cluster bonding, molecular orbitals and the roles of 2px and 2py atomic orbitals of boron are taken up by iron 3dxz and 3dyz atomic orb~tals with small contributions from 4px and 4p .LCAO expansion of HOMOS of both the ferracarboranes PVa] and [ ~V b r skiow that they have a small contribution from the 3dx:-y~ atomic orbital of iron and carbonyl carbon and oxygen atomic orbitals.
. .  3 and 41 also show that the CH unit uses only one electron from carbon for the C-H bond.Hence the fourth electron froni carbon must have become delocalised into the cluster bonding.The total overlap populations associated with the bonding of Fe(C0)3 groups into the cluster in all ferracarboranes studied are mudh smaller than those of the BH replaced.Table 1 shows that in ferracarboranes [except the Fel of (Vb)] the iron atoms cany net gross positive atomic charges and these positive charges on iron atoms may be the reason for the reduction in total overlap population between the Fe(CO)3 unit and the rest of the cluster unit.The analysis of localised charges on the Fe(C0)3 units [Table 21 and the gross atomic charges on the carbonyl carbon and the oxygen atoms [Table I ] suggest that the high positive charges on iron atoms may be due t o the valence electrons in iron atom being largely delocalised over the carbonyl ligands and this may be the reason for weak bonding between the Fe(C0)3 unit and the rest of the cluster unit.
As discussed earlier, the analysis of LCAO of the cluster bonding molecular orbitals shows that only 3dx,, 3dyZ, 4px and 4p atomic orbitals [IVb] , [V] and [Vb] show that even though in terms of Wade's approach, the BH and the Fe(C0) units are considered to be isolobal and isoelectronic, the Fe(C0)3 unit is weakIy bonded into the cluster when compared with the BPI unit replaced and this may be due to the valence electrons in iron atom being largely delocalised over the carbonyl ligands in ferracarboranes.Our calculations also show that even though the CH unit appears to use only two electrons for cluster bonding the third electron may be delocalised into the cluster.The comparison of the LCAO of the cluster bonding molecular orbitals shows that even though the roles of 2px and 2p atomic orbitals of Y boron are taken up by the iron 3dxZ and 3dyZ orbitals w t h some admixture of 4px and 4p atomic orbitds there is no evidence for the involvement of [4s, 4pz, 3dz2f hybrid orbital which is analogous t o boron [2s, 2pz] hybrid.
~a j e s w a s j Mageswaran and N. J. Fitzpatrick closo-hexaborane [6] [I] , [C2 BI HI {F~(co) ] [11] , 2,4-dicarba-close heptaborane [7] [111] , [CIB4HI { F ~( c o ) ~~ ] [IV] and [C,B3H, {F~(CO) 3) 1 [Vl 2. Computational Method The method used was the FORT ICON^ of Hoffman and co-worker^?^This calculation is an all valence electron, extended Huckel calculation [3d, 4s and 4p atomic orbitals ontransition metal atoms, 2s and 2p on second row atoms and on hydrogen atom are used] and was used in its charge iteration mode according to Hii = VSIE [QJ where Hii is the diagonal Hamiltonian matrix element and VSIE[OJ is the valence state ionisation energy of drbital -i when the atom has total charge Q.The off diagonal Hamiltonian matrix elements are calculated in the normal manner9 using the expression, where ki is a constant.The VSIE [Q] functions are assumed t o be of the form, VSIE [Q] = A Q ~ + BQ + C where A,B and C are parameters~6~z0 which depend on the atom and the orbital.Iterations are continued hntd successive ones producedd 1 0 -~e change in the charge on any atom [e = electro'hic charge].The well known problem of obtaining convergence with such self-cornistent charge calculations was eased by an improved damping scheme and by the use of a Made: lung correction.The orbital occupations are summed separately over the p and d orbitals on each atom.The resulting p and d occupations, along with s occupations, are damped according to the equation the summed orbital occupation of a given type, s,p^ar d, indexed by r on the kth cycle andxis a damping parameter.
-C4H I ' O -Fe -C and C-d bond lengths of.0.182 nm and 0.1 15 nm respectlvefy were used.Changing the position of the metallo-units by 2 10% with respect to the carborane base produced no significant change in the results.
, the boron atom in apical position being more positively charged.The overlap populations [Table 41 bonding these BH units into the cluster [in 2,4C2B, H,] are slightly different and reflect the positive charges on boron atoms!Thus &e two apical BH units ate less strongly bonded into the cluster when compared with the three basal BI-I units.The gross atomic charges on carbons and borons agree with the more electronegative character of carbon compared with boron.Our values for located charges on C--H and B-H moieties [-0.045 and 0.022 respectively] of 1,6-C2B4H, arek comparable with the ' values [-0.05 and 0.03 respectively] reported1 eadier by a different SCF

Figure 1 .
Figure 1.The orbitals available for cluster bonding on BH and Fe(C0)3 units.

Y
of iron atom are used in cluster bonding but aU Zs, 2p,, 2p and 2pZ orbitals Y of both boron and carbon atoms are used.4. Conclusion SCCC calculations on carbones [I] and [111] and ferracarboranes [11] [IVa] ,

Table 11 .
The total overlap popdation associated with the metallogroup in[IVb]is markedly less than that in [IVa] and is much smaller than that of the BII replaced [Ca 54%].There is a corresponding increase in overlap population between adjacent boron and carbon atoms in [IVa] and [IVb] [Table41compared with those in 2,4 C2B5H7.The total overlap population associated with the metallo-group and the total energy of valence electrons [Table 2,4-C2B5H7 as in[IVa], [il increases the net negative charge on carbon atoms by 0.040 [ii] decreases the positive charges on boron atoms [Table11 and [iiil decreases the overlap population bonding the replaced site Fe(CO), , c.f.BH, to the C2B H5 base by about 27%.The replacement of a basal BH unit by a ~e ( d o ) , unit in 2,4-C2 B5 11, as in[IVb], also increases the net negative charges on carbon atoms but the increase is low [0.015 on c2 and 0.022 on C4] and decrease the positive charges on boron atoms [again the decrease is low, The replacement of the second apical BH unit by a Fe(C0) unit as in[Val,increases the negative charge on carbon atoms further but the increase is low [0.012 compared with 0.040 in IVa] and decreases the positive charge on basal boron atoms by similar ratios [TableI].The total overlap population associated with bonding of Fe(C0)3 unit with C2B3H, base had also been decreased further by about the same ratio [Ca 27%].The replacement of the basal B" H unit by the Fe(C0)3 unit, as in[Vb], changes the charge on c2 from -0.062 to +0.010 [but the charge on c4 has changed only slightly from -01062 t o 0.0651 and increases the positive charges on boron atoms [Table11.Also, it should be noted in[Vb], Fel atom has a negative net charge whereas I?e5 atom has a high positive net charge [Table11.The total overlap populations associated with the bonding of metallo-groups with the rest of the cluster units in[Vb]are markedly less than those.in[Valandshowsthat the basal Fe5 (CO) unit is weakly bonded into the cluster unit when compared with t i e apical Fe(C0) unit.The total overlap population associated with the bonding of metallo-groups with the rest of the cluster unit and the total energy of valence electrons [Table51suggest that the compound [Val is more stable than compound[Vb].It is interesting to note that the compound 1 , 7 , 2 , 4 -[ ( ~5 -C , H ~) ~ Coinparison of bonding by BH and Fe(C0)3 units As mentioned earlier in terms of Wade's approach the BH and the Fe(C0)3 units use two electrons each and the CH unit uses 3 electrons for cluster bonding.The overlap population and the atomic orbital contributions in cluster molecular orbitals in carboranes and metallocarboranes studied show that the BH and the CH units use approximately two electrons each and that the Fe(C0)3 unit uses less than two electrons [varies with the position and the number of BH units replaced by Fe(C0)3 units] for cluster bonding.Our results [Tables SCHEME [ Z ]