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

Cluster bond enthalpies, EL(BB), and orders, n̄(BB), for the structurally characterised closo anions, BnHn2− (n = 6 and 8–12), have been estimated using the logarithmic length—enthalpy and enthalpy—order relationships EL(BB) (kJ mol−1) = 1.766 × 1011 [L(BB)]−4.0 and EL(BB) (kJ mol−1) = 318.8[n̄(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, EI, have been calculated using the relationships EI(BB) = 297.9 I(BB) and EI(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 EL and Σ EL generally exceed those of EI and Σ EI by some 8% and calculated values of I generally exceed those of n̄ by a greater amount, the trends in these parameters for the series of BnHn2− 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 EI values suggest that the anions are all of comparable stability, the ΣEL values clearly show B6H62−, B10H102− and B12H122− to be more stable than B8H82−, B9H92− and B11H112−. The interatomic distances in B7H72− and in the unknown B5 H52− are estimated and used to assess their relative stabilities. The EL values suggest that B7 H72− is of comparable stability to B8H82− etc., but show B5H52− as relatively unstable. The EI values suggest that both of these anions should be relatively stable members of the series of closo anions.