Structural Increment System for 11-Vertexnido-Boranes and Carboranes

Abstract

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.

Periodic trends and easy estimation of relative stabilities in 11-vertex nido-p-block-heteroboranes and -borates

“…This is to be expected when structural features behave additively. For instance, the estimated energy penalty for adjacent carbon atoms, i.e., the energy difference of 7,8-C 2 B 9 H 11 2À and 7,9-C 2 B 9 H 11 2À is 16.3 kcal mol À1 , very close to the statistically fitted value (16.0 kcal mol À1 ) derived from 20 carboranes [57][58][59]. Here, we present the relative stability order (E inc rel ¢) for 11-vertex nido-sila-, germana-, stanna-, arsa-, stiba-, thia-, selena-and tellura(carba)boranes and -borates, phosphathiaboranes and -borates and selenathiaboranes produced by E inc ¢, which are more approximate but easier to determine and are accurate enough for the interpretation of general trends which we wish to investigate in the present study.…”

“…The approach was applied to the 10-vertex nido-(carba)boranes and -borates [58], and to the 11-vertex nido-mixed hetero(carba)boranes and -borates [59] with H-C, P, H-P, N and H-N heteromoieties. Our work [56][57][58][59] quantified Williams' rules [6,54,55] by corresponding energy penalties for each heteroatom and introduced some more rules due to open-face hydrogen characteristics of the nido-cluster. These quantitative rules allow us not only to predict the thermodynamically most stable isomer but also to estimate a stability order of various isomers easily [56][57][58][59].…”

“…Our work [56][57][58][59] quantified Williams' rules [6,54,55] by corresponding energy penalties for each heteroatom and introduced some more rules due to open-face hydrogen characteristics of the nido-cluster. These quantitative rules allow us not only to predict the thermodynamically most stable isomer but also to estimate a stability order of various isomers easily [56][57][58][59]. Furthermore, these energy penalties successfully elaborate which two heteroatoms are more favorable choices for adjacent positions in the thermodynamically most stable mixed nido-heteroboranes.…”

“…In our previous work [56][57][58][59], energy penalties (E inc ) were determined by statistical fitting to a large number of structures. This procedure gives accurate values but requires extensive computations.…”

Rearrangements in icosahedral boranes and carboranes revisited

“…These compounds, which are characterized by their electron deficiencies, form nonclassical three-center two-electron bonds and have been the topic of numerous texts [10][11][12][13][14]. This leads to the very familiar deltahedron geometries for closo-CxBn−xHn−x+2 with n+1 skeletal electron pairs, nido-CxBn−xHn−x+4 with n+2 skeletal electron pairs, and arachno-C x B n−x H n−x+6 with n+3 skeletal electron pairs, determined empirically by Wade's Rules [1,2,15,16]. Although a great deal of time has been spent in comparing and contrasting carborane systems of varying size in terms of stability, rearrangement, and reactivity [7,8,[17][18][19][20][21][22][23], a special effort has been expended in understanding closo-B 12 H 12 2À , closo-C 2 B 10 H 12 , and their respective derivatives [21,[24][25][26][27][28][29], which is due primarily to their unusually high stability.…”