Structural relationships among two vertex sharing macropolyhedral boranes

Various two vertex sharing macropolyhedral boranes were computed at the B3LYP/6-311 + G**//B3LYP/6-31G* level of theory to determine the preferred fragments for the thermodynamically most stable isomers. These are nido-10 and arachno-9 vertex fragments for neutral macropolyhedral boranes. The thermodynamically most stable isomers of the nido:nido-, arachno:nido- and arachno:arachno-macropolyhedral borane classes are structurally related to each other by the successive removal of one open face vertex as in the case of simple polyhedral boranes. For these classes, the stabilities of the thermodynamically most stable macropolyhedra relative to isomeric simple polyhedra follow similar trends with respect to the number of skeletal electrons.     

Structural paradigms in macropolyhedral boranes

Macropolyhedral borane clusters are concave polyhedra constituting fused convex simple polyhedra. They are formally obtained by condensation of simple polyhedral boranes under elimination of between one and four BH(3) or isoelectronic units. The number of eliminated vertexes from simple polyhedra equals the number of shared vertexes in macropolyhedral boranes. For each of the eight classes with general formulae ranging from B(n)H(n-4) to B(n)H(n+10), more than one structure type is possible, differing in the number of shared vertexes and in the types of the two combined cluster fragments. However, only one type of "potential structures" is represented by experimentally known examples and is found to be favored by theoretical calculations. A sophisticated system exists among the favored macropolyhedral borane structures. For each class of macropolyhedral boranes, the number of skeletal electron pairs is directly related to the general formula, the number of shared vertexes and the type of fused cluster fragments. In order to predict the distribution of vertexes among the fused fragments, we propose the concept of preferred fragments. Preferred fragments are those usually present in the thermodynamically most stable structure of a given class of macropolyhedral boranes and are also frequently observed in the experimentally known structures. This allows us to completely predict the cluster framework of the thermodynamically most stable macropolyhedral borane isomers.     

Which nido:nido-macropolyhedral boranes are most stable?

A comparison of the relative stabilities computed at RB3LYP/6-311+G(d,p)//RB3LYP/6-31G(d)+ZPE of the neutral nido-single clusters and two vertex-sharing macropolyhedral nido:nido-clusters shows single-cluster nido-boranes with up to 11 vertexes to be energetically more favorable than isomeric macropolyhedral boranes. Extra hydrogen atoms at the open face have a significant influence on the relative stabilities of the single cluster nido-boranes vs nido:nido-macropolyhedral boranes. For anionic species, a clear-cut turning point for macropolyhedral preference is shifted to no less than 17 vertexes. Thermodynamically most stable neutral and anionic nido:nido-macropolyhedral boranes usually consist of a nido-10-vertex and a nido-11-vertex unit, respectively. The relative stabilities of isomeric neutral macropolyhedra reflect the patterns exhibited by the sum of thermodynamic stabilities of the individual clusters.     

硼烷结构规则的量子化学计算

利用EHMO方法,对n=5～12的完整多面体硼烷骨架、缺一个和两个顶点以及戴一个和两个帽原子的各种异构体进行了量子化学计算。直接对硼烷的价成键轨道数公式BMO=4n-[f+3(s+1)]进行了验证。在对计算结果讨论的基础上,进一步探讨了骨架几何结构与成键轨道数之间的关系。     

Ab initio studies on isomers of macropolyhedral borane ions [B20H18]n (n = 0, -2, -4)

Various isomers of macropolyhedral borane ions [B20H18]n (n = 0, -2, -4) are investigated by using the density functional theory methods at RB3LYP/6-31+G* and RB3LYP/6-31G* levels to obtain the optimized geometries, harmonic vibrational frequencies, electron structures, and the stability order. The calculated results show that optimized bond lengths are consistent with the available experimental values and the natural populations, taking [a2 -B20H18]4- (4) as an example, are also in agreement with NMR spectra. The calculated vibrational frequencies are all real, so all of these isomers could be stable, among which [a2 -B20H18]2- (3) and [a2 -B20H18]0 (7) are considered for the first time in this paper. On the basis of the contour maps of molecular orbitals, the delocalized characteristic of molecular orbitals and the possible redox mechanism of these ions are also discussed. Moreover, the analysis on counting of skeletal bonding electrons shows that the isomers (1)-(6) obey the electronic requirement predicted by the mno rule, whereas the newly predicted isomer (7) does not match the mno rule.     

Studies on the structural rule of boranes

The authors discuss the structural rule of different kinds of polyhedral boranes and propose a general topological formula for calculating the number of bonding molecular orbitals. In the case of single polyhedral boranes, results obtained from the formula are the same as those from the famous Wade rule. Futhermore, the formula can also be used to calculate the number of bonding molecular orbitals of joined-type polyhedral boranes. We have also made some quantum chemistry calculations to verify the concept that the number of bonding molecular orbitals of boranes can be determined by considering only the corresponding boron polyhedral frameworks.     

Some examples of unusual skeletal bonding topologies in metallaboranes containing two or three early transition metal vertices

The metallaboranes (CpM)(2)B(n)H(n+4) (M = Cr, Mo, W; n = 4, 5; Cp = eta(5)-C(5)H(5), eta(5)-C(5)Me(5)), (CpW)(2)B(7)H(9), (CpRe)(2)B(7)H(7), and (CpW)(3)B(8)H(9) have the 2v or 2v + 2 skeletal electrons for closo or isocloso deltahedra (v = number of polyhedral vertices) if the early transition metal vertices are assumed to contribute four or more internal orbitals rather than the usual three internal orbitals for BH vertices. The polyhedra for the metallaboranes (CpM)(2)B(n)H(n+4) (M = Cr, Mo, W; n = 4, 5) are derived from (n + 1)-gonal bipyramids by removal of an equatorial vertex. The deltahedra for the larger metallaboranes (CpW)(2)B(7)H(9), (CpRe)(2)B(7)H(7), and (CpW)(3)B(8)H(9) are derived from the corresponding B(n)H(n)(2)(-) deltahedra (n = 9 and 11 in these cases) by sufficient diamond-square-diamond processes to provide vertices of degrees > or = 6 for each of the CpM vertices. Reasonable skeletal bonding topologies in accord with the availability of skeletal electrons and orbitals consist of surface 2c-2e and 3c-2e bonds supplemented by metal-metal bonding through the center of the polyhedron.     

Cluster increments for macropolyhedral boranes

Cluster increments derived for individual cluster fragments reproduce the DFT computed relative stabilities of macropolyhedral boranes usually within +/-6 kcal mol(-1). A simple summation procedure helps to select the best partner for a given cluster fragment in order to construct the thermodynamically most stable macropolyhedral borane. Cluster increments are considerably smaller for nido-cluster fragments with an even number of vertexes than for odd nido-cluster fragments pointing towards high thermodynamic stability of macropolyhedral boranes with even numbered nido-units.     

Defective vertices in arachno borane networks

Triangulated boron networks can be described in terms of the deviation of their local vertex environments from the degree 5 vertices found in ideal icosahedra. Vertices of degrees other than 5 or equivalent are considered to be defective vertices. This method, which was previously applied to deltahedral borane anions B(n)H(n)(2-) and nido-B(n)H(n+4) boranes, has now been applied to arachno boranes of the types B(n)H(n+6) and B(n)H(n+5)(-) (4 < or = n < or = 10). The known structures of the neutral arachno boranes B(4)H(10), B(8)H(14), and n-B(9)H(15) consist of triangulated boron networks with no defective vertices in accord with their higher stabilities relative to other neutral arachno boranes. In other structures of known arachno boranes, there are relatively small numbers of defective vertices, and these are isolated as far as possible from each other.     

Effects of halogen substitution on the properties of eight- and nine-vertex closo-boranes

The symmetry constrained geometries of the eight- and nine-vertex polyhedral boranes and haloboranes BnXnz (n = 8 and 9; X = H, F and Cl; z = -2, -1 and 0) were optimized at the B3LYP/6-311+G(d) level and their nucleus-independent chemical shifts (NICS) were calculated using the GIAO method with Kohn-Sham orbitals. Substitution of halogens on borane cages was found to significantly impact not only the geometric but also magnetic properties. Multiple fluorine substituents cause a deviation from the Wade-Mingos skeletal electron rules in B8F8(2-), resulting in a distortion from the expected D2d bisdisphenoid to a C2v nido type bicapped trigonal prism. However, all of the nine-vertex cages B9X9z retain the D3h tricapped trigonal prismatic structure of B9H9(2-). The presence of halogen substituents was found to enhance the three-dimensional diatropic ring currents within the dianionic borane cages B8X8(2-) and B9X9(2-). For the neutral structures the NICS values indicate BnFn to be aromatic, BnCln to be essentially non-aromatic, and BnHn to be antiaromatic (n = 8, 9).     

Oblate deltahedra in dimetallaboranes: geometry and chemical bonding

A new series of nonspherical and very oblate deltahedra, conveniently called the oblatocloso deltahedra, is found in dimetallaboranes among which the dirhenaboranes Cp2Re2B(n-2)H(n-2) (8 相似文献   

Rules for macropolyhedral boranes

Based on extensive computational studies, rules to derive the thermodynamically most stable macropolyhedral borane for any formula between B_nH_n−4 to B_nH_n+8 were identified. Formally, the macropolyhedral boranes may be obtained by condensing regular convex borane clusters where as many BH₃ moieties are eliminated as vertexes are shared in the macropolyhedral framework. Macropolyhedral boranes consisting of two cluster fragments may be classified according to their general formulae ranging from B_nH_n−4 to B_nH_n+8. For each of these formulae, various structure types are conceivable differing in the number of shared vertexes and in the types of combined cluster fragments. However, for each general formula, only one structure type is known experimentally and this one is also computationally found to be thermodynamically preferred! For each class of macropolyhedral B_nH_m boranes, a preferred number of shared vertexes is identified, and this determines the number of skeletal electron pairs. With this knowledge, the type of fused clusters, i.e. the most favourable framework, may be predicted. The concept of preferred fragments may be applied to even predict the distribution of vertexes among the fused fragments in the thermodynamically most stable isomers. When there is at least one closo fragment it has 12-vertexes. Without any closo fragment the most stable macropolyhedral borane has a nido 10-vertex cluster fragment.     

确定硼烷的杂硼烷价成键轨道对称性的拓扑方法

本文通过对硼烷的分子轨道的定域化分析, 建立了由硼烷或杂硼烷的骨架多面体的几何性质, 确定其价成键轨道对称性的拓扑方法。从以多面体骨架的三角面和缺顶点周围的边为基约化出的不同约表示中, 按建议的能量与节面数的对应规则,选定出分子的价成键轨道所属的不可约表示。     

Graph-theoretical analysis of the bonding topology in polyhedral organic cations

It is shown that in several cases where planar delocalisation in organic cations would result in the formation of an anti-aromatic system, polyhedral delocalisation is the form of bonding actually preferred. This explains, for instance, why organic cations in such cases adopt cage-like structures. A full graph-theoretical analysis, similar to one previously published¹² for polyhedral boranes, carboranes and metal clusters, indicates that the nido structure for (CH)₅⁺ may readily be accounted for. Moreover, in the case of the dication (CH)₆²⁺ the fact that its energy minimum also corresponds to a nido structure is explained. In fact, no closo- or arachno-type structures appear to be possible for organic cations. A number of structural predictions concerning these species are given in the conclusion.     

Relative Stability of closo‐closo,closo‐nido,and nido‐nido Macropolyhedral Boranes: The Role of Orbital Compatibility

The concept of orbital compatibility is used to explain the relative energies of different macropolyhedral structural patterns such as closo‐closo, closo‐nido, and nido‐nido. A large polyhedral borane condenses preferentially with a smaller polyhedron owing to orbital compatibility. Calculations carried out at the B3LYP/6‐31G* level show that the macropolyhedron closo(12)‐closo(6) is the most preferred structural pattern among the face‐sharing closo‐closo systems. The relative stabilities of four‐shared‐atom closo‐closo, three‐shared‐atom closo‐closo, three‐shared‐atom closo‐nido, edge‐sharing closo‐nido, and edge‐sharing nido‐nido structures are in accordance with the difference in the number of vertices of the individual polyhedra of the macropolyhedra. When the difference in the number of vertices of the individual polyhedra is large, the stability of the macropolyhedra is also large. Calculations further show that the orbital compatibility plays an important role in deciding the stability of the macropolyhedral boranes with more than two polyhedral units. The dependence of the orbital compatibility on the relative stability of the macropolyhedron varies with other factors such as inherent stability of the individual polyhedron and steric factors.     

Polyhedral boranes and elemental boron: direct structural relations and diverse electronic requirements.

Details of the electronic and structural connections between macropolyhedral boranes and elemental boron are reported. The nature of electron deficiency in the beta-rhombohedral polymorph of boron is analyzed by using a molecular fragments approach with boranes as model systems. The B57H36 molecule constructed from such an approach has three more electrons than mandated by the electron-counting rules (Balakrishnarajan, M. M.; Jemmis, E. D. J. Am. Chem. Soc. 2000, 122, 456. Jemmis, E. D.; Balakrishnarajan, M. M.; Pancharatna, P. D. J. Am Chem. Soc. 2001, 123, 4313-4323.) devised for macropolyhedral boranes. This is also confirmed by electronic structure calculations at the extended Hückel and B3LYP/6-31G levels. The aromaticity of this B57H36(3+) molecule is on par with the most stable B12H12(2-) itself, as revealed by nuclear independent chemical shift calculations. The B57 skeleton can be made electron precise by adopting a nido arrangement by eliminating an atom from the closo skeleton, so that three valence electrons will be removed. The exact site of elimination, governed by thermodynamic factors, necessitates the removal of a boron atom from any of the six symmetrically equivalent B[13] sites in the unit cell. This leads to partial occupancies, which causes disorder in packing, as revealed by X-ray structure studies. The rest of the boron atoms are distributed in icosahedral B12 fragments, whose two-electron deficiency is satisfied by the capping of extra atoms, distributed statistically in the interstitial sites. These results show that the three-dimensional network of the idealized beta-rhombohedral unit cell is not stable, unlike the electron-precise carbon polymorphs such as diamond and graphite. Thus, disorder in the form of partial occupancies, interstitial atoms, alien atoms, etc., is necessary for electron sufficiency and hence for the stability of this polymorphic form. Through these ingenious steps, all components of the unit cell attain electron sufficiency, which explains the high thermodynamic stability of the polymorph. The connection established between boranes and elemental boron in terms of their structure and distribution of electrons has important implications in understanding the structure of boron-rich solids and new strategies to utilize their diverse and technologically important properties.     

Details of the reaction graphs for intramolecular isomerizations of the carboranes

From proposed mechanisms for framework reorganizations of the carboranes C₂B _n-2H _n ,n = 5–12, we present reaction graphs in which points or vertices represent individual carborane isomers, while edges or arcs correspond to the various intramolecular rearrangement processes that carry the pair of carbon heteroatoms to different positions within the same polyhedral form. Because they contain both loops and multiple edges, these graphs are actually pseudographs. Loops and multiple edges have chemical significance in several cases. Enantiomeric pairs occur among carborane isomers and among the transition state structures on pathways linking the isomers. For a carborane polyhedral structure withn vertices, each graph hasn(n -1)/2 graph edges. The degree of each graph vertex and the sum of degrees of all graph vertices are independent of the details of the isomerization mechanism. The degree of each vertex is equal to twice the number of rotationally equivalent forms of the corresponding isomer. The total of all vertex degrees is just twice the number of edges orn(n - 1). The degree of each graph vertex is related to the symmetry point group of the structure of the corresponding isomer. Enantiomeric isomer pairs are usually connected in the graph by a single edge and never by more than two edges.     

Closo-alanes (Al4H4, AlnHn+2, 4 <or= n <or= 8): a new chapter in aluminum hydride chemistry

Anion photoelectron spectroscopy and density functional theory were employed to study aluminum hydride clusters, AlnHm- (4 相似文献   

过渡金属杂硼烷结构规则的量子化学计算

用EHMO量子化学计算方法,计算了过渡金属杂硼烷骨架Fe_{nB6-n(n=0,1,…,6),验证和讨论了过渡金属杂硼烷的价成键和价非键轨道数BMO+NBMO=4n1+9n2-F。其中n1、n2和F都只与骨架的几何性质有关。}     

A "sea urchin" family of boranes and carboranes: the 6m + 2n electron rule

A new family of related borane and carborane cages has been designed computationally. These compounds obey a new electron counting rule (6m + 2n rule) rather than Wade's rule. The structures of these cages can be conceived by combining m aromatic pyramidal and n aromatic triangular units. The interstitial electrons from the m pyramids (six electrons for each unit) and the n triangles (two electrons for each unit) constitute the total 6m + 2n skeletal electrons. The greater number of skeletal electron pairs in large closo-borane cages (e.g., B32H328- or C8B24H32) achieves stabilization through the optimal occupancy of all bonding orbitals. The favorable electronic structure, the large HOMO-LUMO gaps, the large lowest positive frequencies, and the local aromaticity of the pyramidal and triangular units (as demonstrated by the large negative NICS values) of the new large closo-cages auger well for their eventual experimental realization.