Cluster bonding and energetics of the borane anions,BnHn2? (n = 5–12): A comparative study using bond length—bond enthal

Cluster bond enthalpies, E_L(BB), and orders, n?(BB), for the structurally characterised closo anions, B_nH_n^2? (n = 6 and 8–12), have been estimated using the logarithmic length—enthalpy and enthalpy—order relationships E_L(BB) (kJ mol^?1) = 1.766 × 10¹¹ L(BB)]^?4.0 and E_L(BB) (kJ mol^?1) = 318.8n?(BB)]^0.697, respectively. In a parallel study, the molecular-orbital bond index CNDO-based calculation method has been used to give BB and BH bond indices, I(BB) and I(BH), from which bond index based bond enthalpies, E_I, have been calculated using the relationships E_I(BB) = 297.9 I(BB) and E_I(BH) = 374.8I(BH) (enthalpies in kJ mol^?1; lengths in pm). From these, total skeletal bond enthalpies Σ E(BB), and total bond enthalpies, Σ E(BB) + Σ E(BH), have been calculated. Although calculated values of E_L and Σ E_L generally exceed those of E_I and Σ E_I by some 8% and calculated values of I generally exceed those of n? by a greater amount, the trends in these parameters for the series of B_nH_n^2? anions are very similar, showing the greater efficiency with which the n + 1 skeletal electron pairs are used as n increases. However, the two approaches differ in that, whereas the Σ E_I values suggest that the anions are all of comparable stability, the ΣE_L values clearly show B₆H₆^2?, B₁₀H₁₀^2? and B₁₂H₁₂^2? to be more stable than B₈H₈^2?, B₉H₉^2? and B₁₁H₁₁^2?. The interatomic distances in B₇H₇^2? and in the unknown B₅ H₅^2? are estimated and used to assess their relative stabilities. The E_L values suggest that B₇ H₇^2? is of comparable stability to B₈H₈^2? etc., but show B₅H₅^2? as relatively unstable. The E_I values suggest that both of these anions should be relatively stable members of the series of closo anions.