DALTON FULL PAPER J. Chem. Soc., Dalton Trans., 1998, Pages 2155–2162 2155 Molecular structures of tetraborane(10) derivatives: ab initio calculations for (CH3)2MB3H8 (M 5 B, Al, Ga or In) and gas-phase electron diVraction studies of (CH3)2AlB3H8 and (CH3)2GaB3H8 † Carole A. Morrison,a Bruce A. Smart,a Paul T. Brain,a David W. H. Rankin *,a and Anthony J. Downsb a Department of Chemistry, University of Edinburgh, West Mains Road, Edinburgh, UK EH9 3JJ b Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, UK OX1 3QR Structural trends in the family of compounds (CH3)2MB3H8 (M = B, Al, Ga or In) have been investigated by ab initio molecular orbital calculations.In addition, the gas-phase molecular structures of (CH3)2AlB3H8 and (CH3)2GaB3H8 have been re-determined by gas-phase electron diVraction using the SARACEN method of structural analysis. Salient structural parameters (ra 0) for the aluminium and gallium compounds were found respectively to be: r[B(1) ? ? ? M(2)] 231.6(7), 234.2(8); r[B(1)]B(3)] 178.2(12), 178.9(23); r[B(1)]B(4)] 184.4(10), 184.3(23); r[B(1)]H(1,2)] 124.6(11), 121.6(18); r[M(2)]H(1,2)] 182.5(13), 186(6); r[B(1)]H(1,4)] 126.2(11), 122.9(18); r[B(4)]H(1,4)] 142.6(11), 140(3) pm; butterfly angle 123.8(20), 119.8(13)8.The introduction of the SARACEN method1,2 for the analysis of gas-phase electron diVraction (GED) data has led to a considerable improvement in the reliability and quality of structural refinements. In this method parameters which cannot be refined (both geometric and vibrational) are assigned restraints derived from an array of ab initio calculations. All geometric parameters and significant amplitudes of vibration are then refined as a matter of principle.The series of compounds under investigation in this paper is based on the compound tetraborane(10) with one terminal BH2 unit replaced by a M(CH3)2 unit (where M = B, Al, Ga or In).All four compounds have been investigated by ab initio calculations, and for (CH3)2AlB3H8 and (CH3)2GaB3H8 by electron diVraction. For these types of compound the structural information which can be obtained by electron diVraction alone is somewhat limited. The distances B]B, M]C and M]Hb are of similar length and therefore strongly correlated and, with the heavy atoms dominating the molecular scattering, locating the precise positions of the hydrogen atoms is a particularly diYcult exercise.Consequently, in the original refinements reported for these compounds,3 several parameters had to be fixed at assumed values and other assumptions had to be made to simplify the structural analysis. In addition, no reliable force fields were available to assess the eVects of vibration. Thus, the preliminary structures reported for these molecules are of a very basic nature. With the availability of ab initio harmonic force fields and the development of the SARACEN method much improved structures can now be secured.In addition to the new SARACEN refinements, the structural trends and similarities identified within the series (CH3)2- MB3H8 by ab initio calculations are also discussed. Finally, the calculated structure of (CH3)2InB3H8 is compared with the experimental structure found in the solid phase.4 This paper represents the final section of a structural exploration of † Supplementary data available: tables of ab initio geometries and energies and Cartesian coordinates from the 6-311G**/MP2 ab initio calculation for (CH3)2MB3H8 (M = B, Al, Ga or In), and final coordinates and least-squares correlation matrix for the SARACEN study of (CH3)2MB3H8 (M = Al or Ga).For direct electronic access see http:// www.rsc.org/suppdata/dt/1998/2155/, otherwise available from BLDSC (No. SUP 57391, 14 pp.) or the RSC Library. See Instructions for Authors, 1998, Issue 1 (http://www.rsc.org/dalton). tetraborane(10) derivatives, new molecular structures for the parent compound tetraborane(10) 2 and the derivative series H2MB3H8 (where M = Al, Ga and In) 5 having been published previously.Experimental (a) Ab initio calculations Theoretical methods. All calculations were carried out on a DEC Alpha APX 1000 workstation with the exception of the 6-31G*/MP2 and 6-311G**/MP2 (CH3)2InB3H8 calculations, which were carried out on the Rutherford Laboratory DEC Alpha 8400 5/300 workstation. The GAUSSIAN suite of programs was used throughout.6 Geometry optimisations.Details of the graded series of calculations performed for the dimethyl series of compounds are the same as for the hydride series reported in the preceding paper.5 It is noted that, as no standard basis set for indium is available beyond the 3-21G* level, the basis set of Huzinaga7 with an additional diVuse d-function (exponent 0.10), contracted to (21s, 17p, 1111d)/[15s, 12p, 711d], was used for all higher level calculations.It is also worth repeating the special treatment used to describe the 3d and 4d electrons of gallium and indium, respectively. The default setting in the GAUSSIAN program placed these orbitals in the core region. A close examination of the calculated orbital energies, however, clearly showed these orbitals to lie closer in energy to the outer valence orbitals, rather than the inner core orbitals. Calculations were therefore performed with these orbitals defined as valence.Calculations beyond the MP2 level of theory were not attempted as higher level calculations were expected to give rise to only small changes in geometry, based on the evidence obtained from the larger series of calculations performed on the hydride analogues.5 Frequency calculations. Frequency calculations were performed at the 6-31G*/SCF level for (CH3)2B4H8, (CH3)2AlB3H8 and (CH3)2GaB3H8, confirming Cs symmetry as a local minimum in each case. Performing the 6-31G*/SCF frequency calculation in Cs symmetry for (CH3)2InB3H8 gave rise to one imaginary frequency (at 25 cm21), indicating that the Cs2156 J. Chem.Soc., Dalton Trans., 1998, Pages 2155–2162 Table 1 GED data analysis parameters for (CH3)2AlB3H8 and (CH3)2GaB3H8 Camera distance/ Weighting functions/nm21 Correlation Scale Electron wavelength b/ Compound (CH3)2AlB3H8 (CH3)2GaB3H8 mm 128.16 285.06 128.45 285.06 Ds 4242 smin 72 24 68 24 sw1 92 42 100 44 sw2 280 130 230 130 smax 328 160 288 166 parameter 0.1908 0.2430 0.0999 0.2442 factor, ka 0.676(23) 0.882(17) 0.871(47) 0.850(38) pm 5.8720 5.1189 5.1336 5.0969 a Figures in parentheses are the estimated standard deviations.b Determined by reference to the scattering patterns of benzene vapour. geometry is not a local minimum on the potential energy surface at this level. However, lowering the symmetry to C1 resulted in the location of a local minimum less than 0.01 kJ mol21 below the Cs geometry at the 6-31G*/SCF level, with the two methyl groups rotated by only 78.It is not clear whether improvements in the theoretical treatment would lead to a Cs or a C1 minimum for this compound; however, it is clear that the potential-energy surface is very flat and that any distortion from Cs symmetry is small. For (CH3)2AlB3H8 and (CH3)2Ga- B3H8 the force fields described by Cartesian force constants at the 6-31G*/SCF level were transformed into ones described by a set of symmetry coordinates using the program ASYM40.8 Since no fully assigned vibrational spectra were available for these compounds, the force fields were adjusted using scaling factors of 0.94, 0.96 and 0.92 for bond stretches, angle bends and torsions, respectively.‡ (b) Gas-phase electron diVraction (GED) GED data.The new refinements for (CH3)2AlB3H8 and (CH3)2GaB3H8 reported here are based on the original data sets 3 recorded on the Edinburgh apparatus. As with H2GaB3H8 reported in the previous paper,5 these compounds were found to react with the photographic emulsion of the GED plates, giving rise to data with higher than usual noise levels.Standard programs9 were used for the data reduction with the scattering factors of Ross et al.10 The weighting points used in setting up the oV-diagonal weight matrices, the s ranges, scale factors, correlation parameters and electron wavelengths are given in Table 1. GED model. As both (CH3)2AlB3H8 and (CH3)2GaB3H8 possess Cs symmetry, the same set of geometric parameters was used to describe the two structures.The model used was essentially based on that for H2GaB3H8 5 with an additional two parameters [r(C]H) and angle H]C]M] to locate the positions of the hydrogen atoms in the two methyl groups attached to the M atom, which were assumed to possess local C3v symmetry (see Fig. 1). Thus, twenty-two geometric parameters are required to define the structures fully in Cs symmetry, as given in Table 2.It should be noted that the new model system incorporates an additional five geometric parameters, compared with the model used in the original refinement.3 These parameters allow a further five structural features to be investigated, namely the deviations of the bridging hydrogen atoms from the heavy-atom planes M(2)]B(1)]B(3) and B(1)]B(3)] B(4), the diVerences between the terminal B]Hendo/exo and M]Cendo/exo distances, and finally the tilting of the terminal BH2 unit towards or away from the heavy-atom cage.Analogous parameters have been introduced in the recent re-refinements of B4H10 2 and H2GaB3H8.5 The heavy cage atoms required four parameters to locate their positions: the weighted average and diVerence of the two B]B distances (p1,2), r[B(1) ? ? ? M(2)] (where M = Al or Ga) (p3) and the butterfly angle (p20) describing the angle between the ‡ Scaling constants as used in the force fields for B4H10 2 and for H2GaB3H8.5 planes B(1)]B(4)]B(3) and B(1)]M(2)]B(3).The remaining parameters locate the eight hydrogen atoms in the boron cage and the two methyl groups. Parameter p4 is defined as r[M(2)]H(1,2)], p5 as the weighted mean of all B]H distances in the molecule, and p6 as the average B]H bridging distance minus the average B]H terminal distance. Parameter p7 is the diVerence between the outer bridging distance B(4)]H(1,4) and the average of the two inner bridging distances B(1)]H(1,2) and B(1)]H(1,4); p8 is r[B(1)]H(1,4)] minus r[B(1)]H(1,2)]; p9 is the diVerence between rB(1)]H(1) and the average B]Hendo/exo distance, and p10 rB]Hendo minus rB]Hexo.Parameters p11 and p12 are defined as the average of, and diVerence between, the two M]C distances, respectively, and p13 is the distance C]H. The six bond-angle parameters required are B(3)]B(1)]H(1) (p14), C(2)endo]M(2)]C(2)exo (p15), H(4)endo]B(4)]H(4)exo (p16), the MC2 and BH2 tilt parameters (p17 and p18), defined as the angles between the bisectors of the C(2)endo]M(2)]C(2)exo and H(4)endo]B(4)]H(4)exo wing angles and the planes B(1)]M(2)] B(3) and B(1)]B(4)]B(3), respectively, with positive values indicating tilting into the heavy atom cage, and finally the angle H]C]M (p19).The last two parameters are the torsion angles, ‘H(1,2) dip’ and ‘H(1,4) dip’ (p21 and p22), which define the elevation of the H(1,2) and H(1,4) bridging atoms above the B(1)]M(2)]B(3) and B(1)]B(4)]B(3) planes, respectively [i.e.the angles between the two sets of planes B(1)]M(2)]B(3) and B(1)]M(2)]H(1,2), and B(1)]B(4)]B(3) and B(4)]B(1)] H(1,4)]. Results and Discussion (a) Ab initio calculations In light of the many calculations performed on this series of compounds the full set of results obtained is confined to SUP 57391 Tables 1–4. Results obtained from the highest level calculations, 6-311G**/MP2, are reported for all four compounds in Table 3 of this paper. A number of trends in geometry were observed to accompany improvements in basis set and level of theory, with the Fig. 1 Molecular framework of (CH3)2MB3H8 (M = B, Al, Ga or In)J. Chem. Soc., Dalton Trans., 1998, Pages 2155–2162 2157 most significant changes generally arising as a result of the introduction of electron correlation to the MP2 level. The main changes observed are summarised below. Cage structure. The sensitivity of the cage distances to improvements in basis set and level of theory showed many parallels to the cage distance in the H2MB3H8 series of derivatives reported in the previous paper.5 In particular, r[B(1)]B(3)] in both sets of derivatives lengthened on average less than 1 pm on improving the basis set from 6-31G* to 6-311G** at both the SCF and MP2 level.The r[B(1)]B(4)] distance was found to be more sensitive to change; it increased by about 1–1.5 pm at both SCF and MP2 levels for the boron, aluminium and indium analogues, and shortened by just over 3 pm at SCF (remaining largely unaVected at the MP2 level) for the two gallium compounds.This diVerence in behaviour for the gallium compounds can largely be attributed to the poor quality of the 6-31G* basis set, which is deficient in the number of basis functions describing the core region of such a large atom. The introduction of electron correlation had similar eVects for all four compounds in both series, with r[B(1)]B(3)] shortening by about 2 pm with both the 6-31G* and 6-311G** basis sets.In contrast, r[B(1)]B(4)] was found to be less aVected by electron correlation in the (CH3)2MB3H8 series than in the H2MB3H8 series. It shortened by 1–2 pm in (CH3)2B4H8 for Table 2 Geometric parameters (ra 0/pm, angles in 8) for the SARACEN refinements of (CH3)2AlB3H8 and (CH3)2GaB3H8 Results c Parameters a,b Me2AlB3H8 Me2GaB3H8 Independent p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p20 p21 p22 av. r(B]B) diV.r(B]B) r[B(1) ? ? ? M(2)] r[M(2)]H(1,2)] av. r(B]H) av. r(B]Hb) 2 r(B]Ht) diV. [r(B]Hb)] (outer 2 inner) diV. [r(B]Hb)] (inner) r[B(1)]H(1)] 2 av. r[B(4)]Ht] diV. r(B]Ht) (endo 2 exo) av. r[M]C] diV. r(M]C) (endo 2 exo) r(C]H) B(3)]B(1)]H(1) C(2)endo]M(2)]C(2)exo H(4)endo]B(4)]H(4)exo MC2 tilt BH2 tilt H]C]M Butterfly angle H(1,2) dip H(1,4) dip 182.3(9) 6.1(13) 231.6(7) 182.5(13) 126.5(7) 11.6(12) 17.2(6) 1.6(13) 20.5(4) 0.2(1) 193.9(5) 0.2(1) 107.2(4) 112.3(12) 132.0(23) 118.5(13) 27.1(4) 0.7(13) 111.0(15) 123.8(20) 13.4(13) 1.5(16) 182.5(22) 5.3(13) 234.2(8) 186(6) 123.4(14) 11.6(18) 17(3) 1.3(13) 20.6(1) 0.3(3) 193.2(4) 0.3(3) 111.0(10) 111.6(13) 132.5(15) 118.5(13) 24.7(23) 0.5(21) 108.6(10) 119.8(13) 14.3(16) 20.2(21) Dependent B(1)]B(4)]B(3) B(1)]M(2)]B(3) r[B(1)]B(3)] r[B(1) ? ? ? B(4)] r[B(1)]H(1,4)] r[B(4)]H(1,4)] r[B(1)]H(1,2)] r[B(1)]H(1)] r[B(4)]H(4)endo] r[B(4)]H(4)exo] r[M(2)]C(2)endo] r[M(2)]C(2)exo] 57.8(4) 45.3(3) 178.2(12) 184.4(10) 126.2(11) 142.6(11) 124.6(11) 119.4(10) 119.8(10) 119.6(10) 194.0(5) 193.8(5) 58.1(5) 44.9(7) 178.9(23) 184.3(23) 122.9(18) 140(3) 121.6(18) 116.3(17) 116.8(17) 116.5(17) 193.4(4) 193.1(4) a For definition of parameters see the text; b = bridging, t = terminal.b For atom numbering see Fig. 1. c For details of the refinements see the text. Estimated standard deviations (e.s.d.s) obtained in the leastsquares refinement are given in parentheses. both basis sets (compared to 4–5 pm in B4H10), 4–5 pm in (CH3)2AlB3H8 (cf. 5–6 pm in H2AlB3H8), ca. 3 pm in (CH3)2- GaB3H8 (cf. 4–7 pm in H2GaB3H8), and 2–3 pm in (CH3)2- InB3H8 (3 pm in H2InB3H8) for both basis sets. The distance r(B ? ? ? M) was found to vary in a similar fashion for the two series of derivatives on improving the basis set from 6-31G* to 6-311G**, resulting in a lengthening at the SCF and MP2 levels. The two exceptions were r(B ? ? ? Al) and r(B ? ? ? In) which shorten by 0.7 pm and 2.4 pm, respectively, at the SCF level.Electron correlation at the MP2 level resulted in a shortening of the r(B ? ? ? M) distance in both series of derivatives. The eVect was more pronounced in the (CH3)2- MB3H8 series, with r(B ? ? ? M) shortening by ca. 11 pm in (CH3)2B4H8 for both basis sets (cf. 4–5 pm in B4H10); 3–5 pm in (CH3)2AlB3H8 (cf. 2–4 pm in H2AlB3H8); 7.5–10.5 pm in (CH3)2GaB3H8 (cf. 3–6.5 pm in H2GaB3H8), and 9–11 pm in (CH3)2InB3H8 (7–9 pm in H2InB3H8). Bridge region.Of the three B]H bridging distances, r[B(4)]H(1,4)] was observed to be the most sensitive to changes in theoretical method, with many changes paralleling those found for the H2MB3H8 series. In particular, improving the basis set from 6-31G* to 6-311G** resulted in a lengthening of all three B]H distances in the boron, aluminium and indium compounds in the two series by about 0.5 pm at both the SCF and MP2 levels. The analogous distances in the two gallium compounds behaved diVerently to the other members on the series, with r[B(1)]H(1,2)] increasing by about 1 pm, r[B(1)] H(1,4)] shortening by about 0.3 pm, and r[B(4)]H(1,4)] lengthening by about 3 pm at both the SCF and MP2 levels.Again, this diVerence in behaviour for the gallium compounds is principally a reflection of the poor quality of the 6-31G* basis set. The introduction of electron correlation at the MP2 level showed several similarities in the two sets of derivatives with, for example, the inner bridging distances r[B(1)]H(1,4)] lengthening and r[B(1)]H(1,2)] shortening on average by 1 pm for all compounds.The most significant diVerence between the two sets of derivatives relate to the two boron compounds using both basis sets; the outer bridging distance r[B(4)]H(1,4)] shortens by almost 5 pm in (CH3)2B4H8 compared to just 1 pm Table 3 Structural trends observed in the (CH3)2MB3H8 series (M = B, Al, Ga or In) by ab initio (6-311G**/MP2) calculations (re/pm, angles in 8) M Fragment Cage Bridge Terminal Parameter a Covalent radius c Ionic radius c Mulliken charge c r[B(1)]B(3)] r[B(1)]B(4)] r[B(1) ? ? ? M(2)] Butterfly angle r[B(1)]H(1,2)] r[M(2)]H(1,2)] r[B(1)]H(1,4)] r[B(4)]H(1,4)] B(1)]H(1,2)]M(2) H(1,4) dip H(1,2) dip r[M(2)]C(2)endo] r[M(2)]C(2)exo] r[B(4)]H(4)endo] r[B(4)]H(4)exo] r[B(1)]H(1)] C(2)endo]M(2)]C(2)exo H(4)endo]B(4)]H(4)exo B(3)]B(1)]H(1) B 88 — 10.2 173.5 185.3 189.9 120.8 124.1 145.4 125.8 141.8 89.2 10.6 11.0 160.3 159.3 119.4 119.0 118.4 119.0 118.7 114.3 Al 125 68 11.0 178.2 184.5 230.4 119.2 124.0 182.5 125.6 141.9 95.6 1.5 13.4 195.3 195.1 119.4 119.2 118.8 128.6 118.6 112.1 Ga 125 76 10.7 178.6 184.1 232.6 119.6 124.4 185.0 125.6 142.2 95.5 0.2 13.2 195.6 195.3 119.5 119.3 118.8 132.4 118.4 111.6 In b 140 94 11.3 179.7 183.5 256.3 120.2 124.4 205.2 125.7 142.4 99.1 3.3 15.4 217.2 216.9 119.6 119.4 119.0 137.2 118.3 111.1 a For definition of parameters see the text.b For In basis set used see the text.c Ref. 11.2158 J. Chem. Soc., Dalton Trans., 1998, Pages 2155–2162 in B4H10. In contrast, the r[B(4)]H(1,4)] distance shortens by 1–2 pm in the aluminium and gallium compounds in both series of derivatives and by ca. 3 pm in the two indium compounds on improving the level of theory from SCF to MP2 using 6-31G* or 6-311G** basis sets. The M]H bridging distance in the two derivative sets was also found to behave in a similar fashion, with r[Al(2)]H(1,2)] shortening by about 0.5 pm, r[Ga(2)]H(1,2)] shortening by an average of 5 pm, and r[In(2)]H(1,2)] shortening by about 1 pm on improvement of the basis set at both levels of theory.Electron correlation results in a change of less than 1 pm in r[M(2)] H(1,2)] (M = Al, Ga or In) irrespective of the basis set. Terminal region. The B]H terminal distances in all eight compounds were found to be largely insensitive to change, with all distances varying on average by less than 0.5 pm with improvements in basis set and less than 1 pm for improvements in the level of theory.Similarly the M]C distances were found to vary by no more than 0.6 pm for basis set improvement and less than 1 pm (M = B or Al) or 2 pm (M = Ga or In) with electron correlation. (b) Gas-phase electron diVraction (GED) In the original refinements of (CH3)2AlB3H8 and (CH3)2- GaB3H8 several structural assumptions had to be made since the amount of information that can be derived solely from the GED data is somewhat limited.3 In particular, the B]B, M]C and M]Hb distances, being of similar length, are all subject to strong correlation, and locating the hydrogen atoms is a particularly diYcult task as the heavy atoms dominate the molecular scattering.The following assumptions had to be made: (a) several parameters were fixed at values derived from the original B4H10 study,12 i.e. the two B]B distances, the angles B(3)]B(1)]H(1) and H(4)endo]B(4)]H(4)exo, the diVerence between the outer B(4)]H(1,4) and inner B(4)]H(1,4) bridging distances, and finally the diVerence between r[B(1)]H(1)] and the average B(4)]H(4)endo/exo distance; (b) the diVerence between the two inner B]Hb distances was set at zero; (c) the bridging hydrogen atoms were taken to lie in the heavy-atom planes B(1)]M(2)]B(3) and B(1)]B(4)]B(3); and finally (d) as no force field was available, vibrational amplitudes were fixed at values in line with those determined for the related molecules B4H10 11 and (CH3)2MBH4 (M = Al or Ga).13 In the earlier study 3 nine or ten of the seventeen geometric parameters used to describe the structures were successfully refined, along with three or four vibrational amplitudes.Final RG values recorded were 0.159 for (CH3)2AlB3H8 and 0.139 for (CH3)2GaB3H8. The structures deduced were largely in accord with those of similar compounds. However, with almost half of the geometric parameters fixed at assumed values, several severe structural assumptions made and the adoption of a very crude approximation concerning vibrational eVects, the quality of the original refinements was necessarily limited. As the SARACEN method allows the refinement of all geometric parameters and removes the need to make any structural assumptions in the GED model, a more flexible model can now be used, leading to much more reliable and realistic structures.In addition, the determination of reliable harmonic force fields by ab initio calculations removes the earlier assumptions concerning the eVects of vibration on the molecular structures.(CH3)2AlB3H8. The results obtained in the new refinement of the structure of (CH3)2AlB3H8 are given in Table 2. The radialdistribution curve [shown in Fig. 2(a)] is composed mainly of four peaks, with distances r[B(1) ? ? ? Al(2)], r[Al(2)]C(2)endo/exo], r[B(1)]B(2)] and r[B(1)]B(3)] forming the dominant features. The parameters p1 (the average B]B distance), p3 [rB(1) ? ? ? Al(2)], p5 (the average B]H distance), p11 (the average Al] Cendo/exo distance) could all be refined freely, together with p13 [r(C]H)] and p19 (Al]C]H) which, with multiplicities of six, would be expected to be well defined by the GED data.In addition, the angles C(2)endo]M(2)]C(2)exo (p15), MC2 tilt (p17) and the butterfly angle (p20) could also be refined to realistic values with reliable e.s.d.s. The remaining thirteen geometric parameters could be refined successfully only with the aid of flexible restraints (documented in Table 4) in accordance with the SARACEN method.§,¶ Four amplitudes of vibration, corresponding to distances u13[B(1) ? ? ? Al(2)], u17[B(1) ? ? ? C(2)endo], u18[B(1) ? ? ? C(2)exo] and u21[B(4) ? ? ? Al(2)] could be refined.With the inclusion of twelve vibrational amplitude restraints (given in Table 5), a further seventeen vibrational amplitudes yielded to refinement (see Table 6).Thus, all the amplitudes associated with distances contributing greater than 10% weighting of the most intense Fig. 2 Observed and final diVerence radial-distribution curves for (a) (CH3)2AlB3H8 and (b) (CH3)2GaB3H8. Before Fourier inversion the data were multiplied by s?exp[(20.000 02s2)/(ZM 2 fM)(ZB 2 fB)] (M = Al or Ga) § Each geometric restraint has a value and an uncertainty derived from the graded series of ab initio calculations. Absolute values are taken from the highest level calculation and uncertainties are estimated from values given by lower level calculations, or based on a working knowledge of the reliability of the calculations for electronically similar molecules. ¶ As a result of the large number of basis functions required to describe (CH3)2AlB3H8 and (CH3)2GaB3H8, it was not possible to perform calculations to a high enough level to display satisfactory convergence (see SUP 57391 Tables 2 and 3).However, the large array of calculations performed on the parent compound B4H10 (see previous paper),5 shows that the heavy cage atoms are much better described at the MP2 level of electron correlation than at the SCF level. Accordingly the uncertainty of 1 pm chosen for the cage parameter diV.r(B]B) (p2) for both refinements is based on the variation revealed in the B]B cage distances of B4H10 by calculations performed at the MP2 level and above. The derivation of the remaining geometric restraints is based on results obtained from the (CH3)2AlB3H8 and (CH3)2GaB3H8 series of calculations, and is documented in Table 4.J.Chem. Soc., Dalton Trans., 1998, Pages 2155–2162 2159 Table 4 Derivation of the geometric restraints used in the SARACEN refinements of (CH3)2AlB3H8 and (CH3)2GaB3H8 (r/pm, angles in 8) Basis set/level of theory Compound (CH3)2AlB3H8 (CH3)2GaB3H8 p2 p4 p6 p7 p8 p9 p10 p12 p14 p16 p18 p21 p22 p2 p4 p6 p7 p8 p9 p10 p12 p13 p14 p15 p16 p18 p21 p22 Parameter a diV.r(B]B) r[Al(2)]H(1,2)] av. B]Hb 2 av. B]Ht diV. [r(B]Hb)] (outer 2 inner) diV. [r(B]Hb)] (inner) r[B(1)]H(1)] 2 av. r[B(4)]Ht] diV. r(B]Ht) (endo 2 exo) diV. r(Al]C) (endo 2 exo) B(3)]B(1)]H(1) H(4)endo]B(4)]H(4)exo BH2 tilt H(1,2) dip H(1,4) dip diV. r(B]B) r[Ga(2)]H(1,2)] av. r(B]Hb) 2 av. r(B]Ht) diV. [r(B]Hb)] (outer 2 inner) diV. [r(B]Hb)] (inner) r[B(1)]H(1)] 2 av. r[B(4)]Ht] diV. r(B]Ht) (endo 2 exo) diV. r(Ga]C) (endo 2 exo) r(C]H) B(3)]B(1)]H(1) C(2)endo]Ga(2)]C(2)exo H(4)endo]B(4)]H(4)exo BH2 tilt H(1,2) dip H(1,4) dip 6-31G*/ SCF 8.7 182.1 11.9 17.8 1.4 20.1 0.2 0.2 113.2 119.3 0.4 13.2 0.5 10.6 190.2 10.8 14.8 1.6 20.1 0.0 0.0 108.6 112.2 129.9 119.1 2.2 12.8 2.0 6-311G**/ SCF 9.0 181.9 12.4 18.0 0.5 20.2 0.2 0.3 113.1 119.5 20.3 12.3 0.1 7.0 186.2 12.8 19.2 20.2 20.2 0.2 0.2 108.6 112.2 131.2 119.2 20.6 12.0 0.7 6-31G*/ MP2 6.0 183.2 10.7 16.6 1.6 20.6 0.2 0.3 112.3 117.7 0.0 14.0 0.2 6.1 190.7 10.2 14.7 2.0 20.5 0.1 0.1 109.4 110.9 131.2 117.3 2.2 14.0 2.8 6-311G**/ MP2 6.3 182.5 11.4 17.1 1.6 20.5 0.2 0.2 112.1 118.6 0.8 13.4 1.5 5.5 185.0 11.6 17.2 1.2 20.6 0.3 0.3 109.4 111.6 132.4 118.4 0.6 13.2 0.2 Value used 6.3(10) 182.5(10) 11.4(10) 17.1(5) 1.6(1) 20.5(1) 0.2(1) 0.2(1) 112.1(10) 118.6(10) 0.8(10) 13.4(10) 1.5(13) 5.5(10) 185.0(50) 11.6(14) 17.2(20) 1.2(10) 20.6(1) 0.3(2) 0.3(2) 109.4(15) 111.6(10) 132.4(12) 118.4(10) 0.6(16) 13.2(12) 0.2(16) a For definition of the parameters see the text.b For method of electron correlation used for Ga see the text.Table 5 Derivation of vibration amplitude restraints for the SARACEN studies of (CH3)2AlB3H8 and (CH3)2GaB3H8 Compound (CH3)2AlB3H8 (CH3)2GaB3H8 Parameter u1[B(1)]B(3)]/u12[B(1)]B(4)] u2[B(1)]H(1)] u3[B(1)]H(1,4)] u4[B(1)]H(1,2)] u5[B(4)]H(1,4)] u8[Al]C(2)endo]/u9[Al]C(2)exo] u10[Al]H(1,2)] u14[Al ? ? ? H(methyl)endo]/u15[Al ? ? ? H(methyl)exo] u16[C(2)endo]C(2)exo] u19[Al]H(1,4)]/u20[Al]H(1)] u22[B(4) ? ? ? C(2)endo] u23[B(4) ? ? ? C(2)exo] u1[B(1)]B(3)] u8[Ga(2)]C(2)endo]/u9[Ga(2)]C(2)exo] u12[B(1)]B(4)] u10[Ga(2)]H(1,2)] u14[Ga]H(methyl)endo]/u15[Ga]H(methyl)exo] u16[B(1)]C(2)endo]/u17[B(1)]C(2)exo] u18[Ga(2) ? ? ? H(1,4)] u19[Ga(2) ? ? ? H(1)] Value a 0.83 8.2 9.1 9.1 12.9 1.0 12.6 1.0 11.0 0.96 12.9 21.8 6.8 1.00 8.6 14.8 1.0 1.00 14.0 15.0 Uncertainty b 0.04 0.82 0.91 0.91 1.29 0.05 1.26 0.05 1.1 0.05 1.29 2.2 0.68 0.05 0.86 1.48 0.05 0.05 1.4 1.5 a Values for amplitude restraints calculated from 6-31G*/SCF force field.b Uncertainties are 5% of amplitude ratio, 10% of absolute values. feature in the radial-distribution curve were determined. Values for the amplitude restraints were calculated directly from the scaled 6-31G*/SCF force field, with uncertainty ranges of 5% adopted for amplitude ratios or 10% for absolute values. Direct amplitude restraints were found to be necessary in the case of u2[B(1)]H(1)], u3[B(1)]H(1,4)] and u4[B(1)]H(1,2)] as the normal practice of restraining ratios resulted in the return of unrealistic vibrational amplitude values in the least-squares refinement as a result of the high correlation eVects.Cage structure. The three cage distances r[B(1)]B(3)], r[B(1)]B(4)] and r[B(1) ? ? ? Al(2)] refined to final values of 178.2(12), 184.4(10) and 231.6(7) pm, respectively, compared with their 6-311G**/MP2 ab initio values of 178.2, 184.5 and 230.4 pm. The butterfly angle (p20) refined to 123.8(20)8, compared with its ab initio value of 119.28.Bridge region. The four bridging distances r[B(1)]H(1,4)], r[B(4)]H(1,4)], r[B(1)]H(1,2)] and r[Al(2)]H(1,2)] refined to 126.2(11), 142.6(11), 124.6(11) and 182.5(13) pm, respectively, in agreement with their 6-311G**/MP2 ab initio values to within one standard deviation. Terminal region. The three terminal B]H distances, r[B(1)] H(1)], r[B(4)]H(4)endo] and r[B(4)]H(4)exo], refined to 119.4(10), 119.8(10) and 119.6(10) pm, respectively, in agreement with their respective 6-311G**/MP2 ab initio values to within one2160 J.Chem. Soc., Dalton Trans., 1998, Pages 2155–2162 standard deviation. The final two terminal distances, r[Al]Cendo] and r[Al]Cexo], at 194.0(5) and 193.8(5) pm, are slightly shorter than their predicted ab initio values of 195.3 and 195.1 pm. Of the six angles required to define the locations of the terminal atoms four parameters (p14, p16, p18 and p19) all refined to values within one standard deviation of their ab initio values. Angle C(2)endo]Al(2)]C(2)exo (p15) refined to 132.0(23)8, within two e.s.d.s of its ab initio value of 128.68, and the AlC2 tilt angle (p17) refined to 27.1(4)8, compared with its ab initio value of 24.68, the negative value indicating a tilt out of the heavy atom cage.(CH3)2GaB3H8. The results obtained for the new refinement of the structure of (CH3)2GaB3H8 are also given in Table 2. The radial-distribution curve [given in Fig. 2(b)] shows many similarities to that characterising (CH3)2AlB3H8 [see Fig. 2(a)] resulting from the similarities in molecular structure. The main diVerence between the two curves relates to the relative contributions from distances associated with gallium compared with aluminium. With an atomic number more than twice that of aluminium, gallium contributes much more to the molecular scattering through the atom pairs it forms, and contributions from other atom pairs necessarily give rise to less structural information.Consequently, only seven of the twenty-two geometric parameters in (CH3)2GaB3H8 could be refined freely {viz. p1 av. r(B]B), p3 r[B(1) ? ? ? Ga(2)], p5 av. r(B]H), p11 av. r(Ga]Cendo/exo), p17 GaC2 tilt and p19 H]C]Ga}, compared with nine for (CH3)2AlB3H8. The derivation of the fifteen geometric restraints required to allow all the geometric parameters to refine is given in Table 4. Values adopted for the restraints were derived in the same way as for the aluminium analogue, with p2 [diV.r(B]B)] based on the large array of calculations performed on the parent compound B4H10.5 In addition, three amplitudes of vibration, u13[B(1) ? ? ? Ga(2)], u15[B(1) ? ? ? C(2)endo] and u16[B(1) ? ? ? C(2)exo], could be refined freely. A further nine were successfully refined with the inclusion of eight amplitude restraints (given in Table 5), resulting in the refinement of all amplitudes associated with distances contributing greater than 10% weighting of the most intense feature in the radial-distribution curve (see Table 7).Table 6 Selected bond distances (ra/pm) and amplitudes of vibration (u/pm) obtained from the SARACEN refinement of (CH3)2AlB3H8 i 123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Atom pair B(1)]B(3) B(1)]H(1) B(1)]H(1,4) B(1)]H(1,2) B(4)]H(1,4) B(4)]H(4)endo B(4)]H(4)exo Al(2)]C(2)endo Al(2)]C(2)exo Al(2)]H(1,2) C]H(methyl) B(1)]B(4) B(1) ? ? ? Al(2) Al ? ? ? H(methyl)endo Al ? ? ? H(methyl)exo C(2)endo ? ? ? C(2)exo B(1) ? ? ? C(2)endo B(1) ? ? ? C(2)exo Al(2) ? ? ? H(1,4) Al(2) ? ? ? H(1) B(4) ? ? ? Al(2) B(4) ? ? ? C(2)endo B(4) ? ? ? C(2)exo Distance 178.7(12) 121.8(10) 128.2(11) 126.1(12) 143.9(11) 122.1(10) 122.3(10) 194.8(5) 194.5(5) 183.0(13) 108.7(4) 185.2(10) 231.6(7) 253(7) 253(7) 355(3) 366.5(22) 340(3) 325(3) 314.6(13) 331(3) 405(3) 480.6(17) Amplitudea,b 7.2(13) 7.8(10) 9.2(11) 9.0(11) 13.0(16) 8.3 fixed 8.3 fixed 6.4(5) 6.4(5) 12.7(16) 8.0(8) 8.7(16) 9.9(5) 22(4) 22(4) 10.9(14) 9.3(21) 9(4) 6(6) 7(6) 19(9) 13.8(14) 20.5(24) a Estimated standard deviations, obtained in the least-squares refinement, are given in parentheses. b Amplitudes which could not be refined are fixed at values derived from the 6-31G*/SCF scaled force field.Cage structure. The three cage distances r[B(1)]B(3)], r[B(1)]B(4)] and r[B(1) ? ? ? Ga(2)] refined to 178.9(23), 184.3(23) and 234.2(8) pm, respectively, compared with their 6- 311G**/MP2 ab initio values of 178.6, 184.1 and 232.6 pm.The small standard deviation for r[B(1) ? ? ? Ga(2)] reflects the dominant electron scattering properties of the gallium and boron atoms. The butterfly angle (p20) refined to 119.8(13)8, compared with its ab initio value of 119.68. Bridge region. The four bridging distances, r[B(1)]H(1,4)], r[B(4)]H(1,4)], r[B(1)]H(1,2)] and r[Ga(2)]H(1,2)], refined to 122.9(18), 140(3), 121.6(18) and 186(6) pm, respectively, in agreement with their 6-311G**/MP2 ab initio values to within one or two standard deviations.The distance Ga(2)]H(1,2), with a standard deviation of 6 pm, was found to be poorly defined by the GED data as a result of its closeness to the B]B distances. In the derivation of the restraint for this parameter [185(5) pm] it was necessary to stipulate a large uncertainty to allow for the significant variation that occurs in this bond length with improvements in basis set and level of theory (see Table 4).Although the restraint is very flexible, it enabled the Ga(2)]H(1,2) distance to be determined with much greater confidence than was possible using the GED data alone. Terminal region. The terminal B]H distances, r[B(1)]H(1)], r[B(4)]H(4)endo] and r[B(4)]H(4)exo], refined to 116.3(17), 116.8(17) and 116.5(17) pm, in agreement with their respective 6-311G**/MP2 ab initio values to within two standard deviations. The distances Ga]Cendo and Ga]Cexo [like r(Al]Cendo) and r(Al]Cexo) in (CH3)2AlB3H8] refined to values slightly shorter than their predicted ab initio values [193.4(4) and 193.1(4) pm by GED, 195.6 and 195.3 pm ab initio].Four of the six angles required to define the locations of the terminal atoms, p14–16 and p18, refined to values within one standard deviation of their 6-311G**/MP2 ab initio values. Parameters p17, MC2 tilt, and p19, H]C]Ga, refined freely to values of 24.7(23)8 and 108.6(10)8, compared with their ab initio values of 24.88 and 110.68.The RG factors recorded for these refinements were 0.081 [(CH3)2AlB3H8] and 0.111 [(CH3)2GaB3H8], the slightly high values being attributable to the rather high noise levels in the GED data resulting from fogging of the photographic plates by the (CH3)2MB3H8 vapours. With all twenty-two geometric parameters and all significant vibrational amplitudes refining, the structures are the best that can be obtained using all avail- Table 7 Selected bond distances (ra/pm) and amplitudes of vibration (u/pm) obtained from the SARACEN refinement of (CH3)2GaB3H8 i 123456789 10 11 12 13 14 15 16 17 18 19 20 Atom pair B(1)]B(3) B(1)]H(1) B(1)]H(1,4) B(1)]H(1,2) B(4)]H(1,4) B(4)]H(4)endo B(4)]H(4)exo Ga]C(2)endo Ga]C(2)exo Ga]H(1,2) C]H(methyl) B(1)]B(4) B(1) ? ? ? Ga Ga ? ? ? H(methyl)endo Ga ? ? ? H(methyl)exo B(1) ? ? ? C(2)endo B(1) ? ? ? C(2)exo Ga ? ? ? H(1,4) Ga ? ? ? H(1) B(4) ? ? ? Ga Distance 179.4(23) 118.5(17) 124.5(18) 123.7(19) 140(3) 119.4(17) 118.7(17) 194.1(4) 193.9(4) 186(6) 112.4(9) 185(23) 234.4(8) 253(7) 253(7) 364(5) 346(5) 321(3) 316.1(18) 328.0(15) Amplitudea,b 6.7(9) 8.3 fixed 9.0 fixed 9.2 fixed 13.9 fixed 8.3 fixed 8.3 fixed 5.9(7) 5.8(7) 15.3(19) 7.6 fixed 8.5(11) 7.5(9) 11(3) 11(3) 11(5) 12(6) 13.6(19) 14.6(20) 9.3(20) a Estimated standard deviations, obtained in the least-squares refinement, are given in parentheses. b Amplitudes which could not be refined are fixed at values derived from the 6-31G*/SCF scaled force field.J.Chem. Soc., Dalton Trans., 1998, Pages 2155–2162 2161 able data, both experimental and theoretical, and all standard deviations should be reliable estimates, free from systematic errors resulting from limitations of the model. A selection of bond distances (ra) and vibrational amplitudes (u) for (CH3)2- AlB3H8 and (CH3)2GaB3H8 are given in Tables 6 and 7, respectively. Cartesian coordinates and final least-squares covariance matrices can be found in SUP 57391.The final radialdistribution curves and combined molecular scattering curves are shown in Figs. 2 and 3, respectively. (c) Structural trends within the series (CH3)2MB3H8 predicted ab initio: the eVects of changing M The main structural changes predicted by the 6-311G**/MP2 ab initio calculations for the series of dimethyltetraborane(10) derivatives (CH3)2MB3H8 (M = B, Al, Ga or In) are given in Table 3. Many of the trends observed with this series parallel those found in the hydride series reported earlier, and can be summarised as follows.Changes in M]B/H distances. As with the hydride derivatives, 5 the increasing values of r[B(1) ? ? ? M(2)], r[M(2)] H(1,2)], on moving from B to In can be attributed largely to the increase in atomic (or ionic) radius of the atom M (see Table 3). Thus, significant changes in these bond distances occur on replacing boron with aluminium and gallium with indium, but small changes are also observed on replacing aluminium with gallium.As noted with the hydride series, a secondary factor may be the decrease in Mulliken charge calculated ab initio for atom M (also given in Table 3). As the oxidation state approaches 11 the system can be thought of as approaching the formulation [(CH3)2M]1[B3H8]2. This dissociation will result in r[B(1) ? ? ? M(2)] and r[M(2)]H(1,2)] increasing by an amount greater than the radius of atom M.Note: with the formal charge assignment on atom M in the dimethyl series being Fig. 3 Observed and final diVerence combined molecular scattering curves for (a) (CH3)2AlB3H8 and (b) (CH3)2GaB3H8. Theoretical data were used in the s ranges for which no experimental data are available closer to 11, the two distances are 1–4 pm longer compared to the hydride series. Angles correlated with atom M. The angle C(2)endo]M(2)] C(2)exo was found to widen in a manner largely correlating with the increasing size and decrease in charge calculated for atom M.With the formal Mulliken charge assignment on atom M approaching 11 (see Table 3), the C2M unit will tend towards a linear structure. It is interesting to note that as the charge assignment is much closer to 11 in the dimethyl series than in the hydride, the angle C(2)endo]M(2)]C(2)exo is wider than H(2)endo]M(2)]H(2)exo by 1–38. The bridging angle B(1)]H(1,2)] M(2) varied in accordance with the increasing distance B(1) ? ? ? M(2).This angle was found to be ca. 18 wider in the dimethyl than in the hydride series, which can be attributed to the longer B(1) ? ? ? M(2) distance observed in the dimethyl series, as described above. Changes in the B3H8 fragment. As with the hydride series, the distance B(1)]B(3) was found to be aVected by the size of the atom M, with a significant lengthening observed when B is replaced with Al, and a further slight lengthening when In replaces Ga.The distance was found to be less than 1 pm longer in the dimethyl series. The angle B(3)]B(1)]H(1) narrowed slightly on moving from B to In, possibly due to a correlation with r[B(1)]B(3)]. As observed with the hydrides, r[B(1)]B(4)] shortened slightly across the dimethyl series, which can be attributed to a greater Mulliken charge disparity between atoms B(1) and B(4) as M = B æÆ In, resulting in the distance shortening slightly due to a simple electrostatic force. The same general trend was observed in both sets of derivatives for the positions of the bridging hydrogen atoms above the BBB/M plane [the H(1,2) and H(1,4) dip angles], with a greater elevation of the bridging atoms above the B(1)]M(2)] B(3) plane [H(1,2) dip] than above the B(1)]B(4)]B(3) plane [H(1,4) dip].This observation was accounted for in the hydride series by the tilting of the wing units. In the dimethyl series the MC2 unit tilts || out of the cage by 58 (cf. hydride MH2 38) and the BH2 unit tilts into the cage by 18 (M = Al æÆ In), in accordance with the hydride series.Thus H(1,2) dip would be expected to be more pronounced in the dimethyl derivatives, and H(1,4) would be expected to be about the same for both sets of compounds. This was indeed found to be the case, with H(1,2) raised ca. 138 above the B(1)]M(2)]B(3) plane in the aluminium and gallium compounds (cf. ca. 10.58 in H2AlB3H8 and H2GaB3H8), rising to 158 in (CH3)2InB3H8 (cf. 148 in H2InB3H8).The variation in H(1,2) dip angles observed across the series can probably be attributed to the increase in size of atom M, with H(1,2) forced higher above the B(1)]M(2)]B(3) plane to relieve steric strain. The H(1,4) dip angle was found to be consistent in each series, with the only significant discrepancy of 10.68 in (CH3)2B4H8 vs. 8.48 in B4H10 explained by a H2B exo tilt of 24.48 in the former, compared with 22.48 in the latter, resulting in the higher elevation of the H(1,4) [and H(3,4)] atom in (CH3)2B4H8. Once again, the ab initio value obtained for the H(1,4) dip angle in (CH3)2GaB3H8, at just 0.28, appears to be anomalous compared with the rest of the series. However, a close scrutiny of the complete range of ab initio calculations carried out (see SUP 57391 Table 3) indicates a significant variation in this parameter from 0.2 to 2.88 which can be attributed mainly to improvements in basis set.An uncertainty of about 38 in the 6-311G**/MP2 value of 0.28 would make this parameter more consistent with the results obtained for the other members of the series.Distances and angles unchanged by atom M. The distances B(1)]H(1,4), B(4)]H(1,4) and B(1)]H(1,2) and angle H(4)endo] B(4)]H(4)exo an the butterfly angle were largely unaVected by || Wing tilts as described in GED model.2162 J. Chem. Soc., Dalton Trans., 1998, Pages 2155–2162 the identity of atom M. With reference to the corresponding hydrides, the butterfly angle for (CH3)2MB3H8 was found to be wider by ca. 48 when M = B, 38 when M = Al or Ga, and 18 when M = In. This widening can probably be attributed to reducing steric strain between the (CH3)endo group and H(4)endo. The eVect is dominant in the earlier members of the series where the distance between the two groups is smaller, resulting in a larger opening of the cage to accommodate the (CH3)endo group. (d) (CH3)2InB3H8: comparison of ab initio and X-ray diVraction molecular structures The final aspect of this work involved drawing a comparison between the molecular structure of (CH3)2InB3H8 deduced by ab initio calculations and the structure determined by X-ray diVraction (see Table 8).4 Ab initio calculations determine the molecular structure of one discrete molecule which, in the absence of GED or any other experimental structural results for the gaseous molecule, represents the closest approach to the gas-phase structure that can be achieved at the present time.A direct comparison of the geometric parameters obtained ab initio with those determined by X-ray diVraction of a single crystal is therefore expected to identify diVerences between the gas- and solid-phase structures. A word of caution should be entered, however, in making this type of comparison. DiVerences in molecular structure are to be expected as a consequence of the fundamental diVerences in the two techniques. Firstly, the definition of bond length is diVerent: ab initio methods calculate the diVerence between the positions of atomic nuclei whilst X-ray diVraction measures the diVerence between centres of electron density.Secondly, the ab initio geometry is a static, vibration-free equilibrium structure; the crystal structure, measured at 150 K,4 is subject to vibrational and librational averaging eVects. For these reasons only fairly gross structural diVerences between the two sets of results have been considered significant.The main structural diVerences, X-ray vs. ab initio, were found to centre around the indium atom, with (i) r[B(1) ? ? ? In(2)] approximately 20 pm longer, (ii) the internal cage angle H(1,2)]In(2)]H(2,3) approximately 158 narrower, and (iii) C(2)endo] In(2)]C(2)exo approximately 208 wider in the solid phase compared with the discrete structure calculated ab initio. Table 8 Comparison of some geometrical parameters for (CH3)2- InB3H8 (r/pm, angles in 8) Fragment Cage Bridge Terminal Parameter r[B(1)]B(3)] r[B(1)]B(4)] r[B(1) ? ? ? In(2)] Butterfly angle r[B(1)]H(1,4)] r[B(4)]H(1,4)] r[B(1)]H(1,2)] r[In(2)]H(1,2)] H(1,2) dip H(1,4) dip H(1,2)]In(2)]H(2,3) r[In(2)]C(2)endo] r[In(2)]C(2)exo] C(2)endo]In(2)]C(2)exo Ab initio 179.7 183.5 256.3 120.2 125.7 142.4 124.4 205.2 15.4 3.3 95.5 217.2 216.9 137.2 X-Ray diVraction (averaged values) a 178.4(8) 180.5(10) 274.4(11) 124(2) 115(4) 140(7) 112(5) 224(11) 14(3) 3(1) 81(2) 210.6(1) 210.5(1) 158.0(1) a See ref. 4. Two molecules, of C1 symmetry were located in the asymmetric unit. Parameters are averaged to Cs symmetry for direct comparison with the ab initio structure, and uncertainties are quoted to 1 s. The explanation for these structural diVerences is evident upon closer examination of the crystal structure: two neighbouring molecules interact with the indium centre through hydrogen H(1) atoms, eVectively increasing the co-ordination number of the indium centre from four to six.As a result of this change in co-ordination H(1,2)]In(2)]H(2,3) will narrow, r[B(1) ? ? ? In(2)] will lengthen to maintain the r[B(1)]B(3)] distance, and C(2)endo]In(2)]C(2)exo will widen to force the two methyl groups apart and thereby accommodate the two new co-ordinating species. In short, the changes reflect the greater ionic character of the compound in the crystal structure compared to that calculated, and the increased metallic character of the heavier Group 13 elements.Indium is characterised by adopting a high coordination number (typically six), and by forming solids with potential anionic partners manifesting increased ionic character. Acknowledgements We thank the EPSRC for the financial support of the Edinburgh Electron DiVraction Service (grant GR/K44411) and the Edinburgh ab initio facilities (grant GR/K04194). We also thank Drs. Simon Aldridge, John Dain and Simon Parsons for the parts they played in the experimental characterisation of the compounds (CH3)2MB3H8 (M = Al, Ga or In); and Dr. Lise Hedberg (Oregon State University) for providing us with a copy of the ASYM40 program. We are grateful to the Rutherford Laboratory for their generous allocation of time on the DEC Alpha 8400/300 workstation. Finally, we thank the University of Edinburgh for funding a research studentship for C. A. Morrison. References 1 A. J. Blake, P. T. Brain, H. McNab, J. Miller, C. A. Morrison, S. Parsons, D. W. H. Rankin, H. E. Robertson and B. A. Smart, J. Phys. Chem., 1996, 100, 12 280. 2 P. T. Brain, C. A. Morrison, S. Parsons and D. W. H. Rankin, J. Chem. Soc., Dalton Trans., 1996, 4589. 3 C. J. Dain, A. J. Downs and D. W. H. Rankin, J. Chem. Soc., Dalton Trans., 1981, 2465. 4 S. Aldridge, A. J. Downs and S. Parsons, Chem. Commun., 1996, 2055. 5 C. A. Morrison, B. A. Smart, P. T. Brain, C. R. Pulham, D. W. H. Rankin and A. J. Downs, preceding paper. 6 M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montogomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez and J. A. Pople, GAUSSIAN 94, Revision C.2, Gaussian, Inc., Pittsburgh, PA, 1995. 7 S. Huzinaga and M. Klobukowski, J. Mol. Struct., 1988, 167, 1. 8 L. Hedberg and I. M. Mills, ASYM40 version 3.0, update of program ASYM20, J. Mol. Spectrosc., 1993, 160, 117. 9 A. S. F. Boyd, G. S. Laurenson and D. W. H. Rankin, J. Mol. Struct., 1981, 71, 113. 10 A. W. Ross, M. Fink and R. Hilderbrandt, International Tables for Crystallography, ed. A. J. C. Wilson, Kluwer, Dordrecht, Boston and London, 1992, vol. C, p. 245. 11 D. D. Ebbing, General Chemistry, ed. M. S. Wrighton, Houghton MiZin, Boston, 1987, ch. 7. 12 C. J. Dain, A. J. Downs, G. S. Laurenson and D. W. H. Rankin, J. Chem. Soc., Dalton Trans., 1981, 472. 13 M. T. Barlow, A. J. Downs, P. D. P. Thomas and D. W. H. Rankin, J. Chem. Soc., Dalton Trans., 1979, 1793. Received 24th February 1998; Paper 8/01554F