Structural increment system for 11-vertex nido-boranes and carboranes.

An increment system forming a set of quantitative rules that govern the relative stabilities of 11-vertex nido-boranes and carboranes is presented. Density functional theory computations at the B3LYP/6-311+G//B3LYP/6-31G level with ZPE corrections were carried out for 61 different boron hydride and carborane structures from [B(11)H(14)](-) to C(4)B(7)H(11) to determine their relative stabilities. Disfavored structural features that destabilize a cluster structure relative to a hypothetical ideal situation were identified and weighted by so-called energy penalties. The latter show additive behavior and allow us to reproduce (within 5 kcal mol(-)(1)) the DFT computed relative energies. Energy penalties for four structural features, i.e., adjacent carbon atoms, CC, a hydrogen atom bridging between a carbon and a boron atom, CH-B, an endo-terminal hydrogen atom at an open face carbon atom, CH(2) and an endo-H between two carbon atoms, C(BH(2))C for the 11-vertex nido-cluster are quite similar to those reported for the 6-vertex nido-cluster, thus showing a behavior independent of the cluster size. Hydrogen structural features, however, vary strongly with the cluster size. Two unknown 11-vertex nido-carboranes were identified which are thermodynamically more stable than known positional isomers.