Cluster bonding and energetics of the borane anions, B nH n2− ( n = 5–12): A comparative study using bond length—bond enthal

Abstract

Cluster bond enthalpies, E L (BB), and orders, n̄(BB), for the structurally characterised closo anions, B n H 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 × 10 11 [ L(BB)] −4.0 and E L (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, E I , have been calculated using the relationships E I (BB) = 297.9 I(BB) and E I(BH) = 374.8 I(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 n̄ by a greater amount, the trends in these parameters for the series of B n H 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 Σ E L values clearly show B 6H 6 2−, B 10H 10 2− and B 12H 12 2− to be more stable than B 8H 8 2−, B 9H 9 2− and B 11H 11 2−. The interatomic distances in B 7H 7 2− and in the unknown B 5 H 5 2− are estimated and used to assess their relative stabilities. The E L values suggest that B 7 H 7 2− is of comparable stability to B 8H 8 2− etc., but show B 5H 5 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.