Real-space indicators for chemical bonding. Experimental and theoretical electron density studies of four deltahedral boranes

In an approach combining high-resolution X-ray diffraction at low temperatures with density functional theory calculations, two closo-borates, B(12)H(12)(2-) (1) and B(10)H(10)(2-) (2), and two arachno-boranes, B(10)H(12)L(2) [L = amine (3) or acetonitrile (4)], were analyzed by means of the atoms-in-molecules (AIM) theory and electron localizability indicator (ELI-D). The two-electron three-center (2e3c) bonds of the borane cages are investigated with the focus on real-space indicators for chemical bonding and electron delocalization. In compound 2, only two of the three expected bond critical points (bcp's) are found. However, a weakly populated ELI-D basin is found for this pair of adjacent B atoms and the delocalization index and the Source contributions are on the same order of magnitude as those for the other pairs. The opposite situation is found in the arachno-boranes, where no ELI-D basins are found for two types of B-B pairs, which, in turn, exhibit a bcp. However, again the delocalization index is on the same order of magnitude for this bonding interaction. The results show that an unambiguous real-space criterion for chemical bonding is not given yet for this class of compounds. The arachno-boranes carry a special B-B bond, which is the edge of the crown-shaped molecule. This bond is very long and extremely curved inward the B-B-B ring. Nevertheless, the corresponding bond ellipticity is quite small and the ELI-D value at the attractor position of the disynaptic valence basin is remarkably larger than those for all other B-B valence basins. Furthermore, the value of the ED is large in relation to the B-B bond length, so that only this bond type does not follow a linear relationship of the ED value at the bcp versus B-B bond distances, which is found for all other B-B bcp's. The results indicate that both 2e2c and 2e3c bonding play a distinct role in borane chemistry.     

硼烷分子中化学键性质的研究III. 锥型分子B3H6X的结构与成键特征

用MP2/6-31G方法, 对三角锥型分子B3H6X(X=B^2^-, C^-,N, O^+, BH^-, CH和NH^+)及其碎片B3H6和X的结构进行了abinitio研究。结果表明, 当X=NH^+, O^+和N时, B3H6基环上的端氢(Ht)朝着帽基X方向, 而当X=CH, BH^-, B^2^-和C^-时, Ht却转向帽基X的方向。这种特征可用配位原子的电负性和配位原子轨道的弥散性给以说明。我们还进一步研究了B3H6X系列化合物的结合能和稳定性。     

Exohedral multiple bonding in polyhedra. 2. Skeletal distortions in ring-stacked boranes

Ring-stacked boranes of the B(10)H(10)(2)(-) and B(12)H(12)(2)(-) type, when substituted with lone pair bearing groups such as -O, -NH, and -S at the para positions, are theoretically shown to exhibit exopolyhedral multiple bonding on oxidation. Successive removal of two and four electrons from the parent B(n)H(n)(-)(2)X(2) results in highly varied and intriguing skeletal deformations that are explained using fragment molecular theory.     

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。     

The pairing principle in tensor surface harmonic theory: Electron counts of large closo boranes

Tetratomic tetrahedral main-group clusters have four or six (but not five) skeletal pairs, an exception to the (n + 1) rule for closo clusters. A general group-theoretical criterion, based on the pairing principle in Stone's tensor surface harmonic (TSH) theory, is presented for symmetry-induced departures from the (n + 1) rule. A count of (n + 2) or n skeletal pairs is forced by symmetry for: (i) T- or T_d-clusters with an odd number of sets of four equivalent cage atoms, and (ii) C_m or C_mv (m ? 3) clusters with an odd number of cage atoms on the C_m-axis. Three such cases, B_nH_n or B_nH_n^4?, are found among the hypothetical supraicosahedral closo boranes proposed by Brown and Lipscomb (n = 16,19 or 22). Extended Hückel calculations show that the TSH pattern applies to the whole series of closo boranes (n$\text{}\text{?}$ 24). Charges of + 4, ?8 and ?2 are discussed for a very large B₃₂H₃₂^q cluster.     

Studies of delocalized electron bonding

Valence Bond calculations are made using the methane-type models, CH ₂, CH ₃, and CH ₄. The calculated proton spin-spin coupling constants are found to depend on the complexity of the model. These coupling constants are related to the exchange order and bond order, which are useful as explicit measures of the extent of delocalized electron bonding.

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Zusammenfassung An den Modellen vom Methantyp: CH ₂, CH ₃, und CH ₄ werden Valenzstrukturrechnungen ausgeführt. Es ergibt sich, daß die errechneten Spin-Spin-Kopplungskonstanten der Protonen vom Umfang des Modells abhängen. Diese Kopplungskonstanten werden mit Austausch- und Bindungsordnung verknüpft, die als explizites Maß für die delokalisierte Elektronenbindung von Nutzen sind.

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Résumé Des calculs sur les modèles du type méthane: CH ₂, CH ₃, et CH ₄ sont faits dans le cadre de la méthode de la mésomérie. On trouve que les constantes de couplage spin-spin protonique dépendent de la complexité du modèle. Ces constantes de couplage sont liées aux indices d'échange et de liaison, quantités qui peuvent servir de mesures explicites de la délocalisation de la liaison électronique.

     

Studies of delocalized electron bonding

A calculation of the ethane barrier is made using a six-electron model in which all single exchange interactions are included. A barrier of 0.6 Kcal. per mole favoring the staggered configuration is calculated. The wave function is used to calculate the NMR proton spin-spin coupling constants, which are found to be at variance with the experimental values. The factors which influence these calculated results are discussed.

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Zusammenfassung Die Potentialschwelle für die innere Rotation des Äthans wird mit einem Sechselektronen-modell unter Einschluß aller Austauschintegrale berechnet. Man erhält eine Schwelle von 0,6 kcal/Mol zugunsten der trans-Konfiguration. Die mit der Eigenfunktion berechneten magnetischen Spin-Spin-Kopplungskonstanten der Protonen weichen von den experimentellen Werten ab. Die die berechneten Werte beeinflussenden Faktoren werden diskutiert.

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Résumé La barrière de potentiel de la rotation intramoléculaire de léthane est calculée à l'aide d'un modèle à 6 électrons et tenant compte de toutes les interactions d'échange. On la calcule à 0,6 kcal/mole en faveur de la configuration trans. Avec la fonction d'onde sont calculées les constantes de couplage magnétique des spins protoniques; elles sont en désaccord avec les valeurs expérimentales. Les facteurs influençant ces résultats sont discutés.

     

Radical reductions of alkyl halides bearing electron withdrawing groups with N-heterocyclic carbene boranes

1,3-Dimethylimidazol-2-ylidene borane and 2,4-dimethyl-1,2,4-triazol-3-ylidene borane are found to be useful reagents for the reduction of alkyl iodides and bromides bearing nearby electron withdrawing substituents. Signatures of radical chain reactions are seen in many cases, but ionic reductions may also be occurring with some substrates. The reagents are attractive because of their low molecular weight, their availability from inexpensive precursors, and their stability. Separation of the borane products from the target products is readily accomplished either with or without prior regeneration of the borane for later reuse. 2,4-Dimethyl-1,2,4-triazol-3-ylidene borane is versatile because both starting borane and its derived products can be removed by extraction with water.     

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.     

Three-dimensional aromaticity in deltahedral boranes and carboranes

Methods derived from topology and graph theory indicate that the deltahedral boranes B _n H _n ^2– and the corresponding carboranes C₂B_n–2H _n (6 n 12) may be regarded as three-dimensional delocalized aromatic systems in which surface bonding and core bonding correspond to -bonding and -bonding, respectively, in planar polygonal two-dimensional hydrocarbons CinnH _n ^(n–6)+ (n=5/7). The two extreme types of topologies which may be used to model core bonding in deltahedral boranes and carboranes are the deltahedral (D _n ) topology based on the skeleton of the underlying deltahedron and the complete (K _n ) topology based on the corresponding complete graph. Analyses of the Hoffmann-Lipscomb LCAO extended Hückel computations, the Armstrong—Perkins—Stewart self-consistent molecular orbital computations, and SCF MOab initio GAUSSIAN-82 computations on B₆H₆ ^2– indicate that the approximation of the atomic orbitals by the sum of the molecular orbitals, as is typical in modernab initio computations, leads to significantly weaker apparent core bonding approximated more closely by deltahedral (D _n ) topology than by complete (K _n ) topology.This work was presented at the Workshop The Modern Problems of Heteroorganic Chemistry sponsored by the A. N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences (May 8–13, 1993).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1353–1360, August, 1993.     

Chemical bonding effect in electron scattering by gaseous molecules

The experimental intensity of 30 keV electron small angle scattering by a gaseous molecule is much different from the calculation using usual independent atom model. This is due to the rearrangement of electron distribution in a molecule by the formation of chemical bonds, and is called chemical bonding effect (CBE). The molecules studied are mainly hydrocarbons such as methane, acetylene, ethane, etc. and some non-hydrocarbons. The measurement was carried out on both elastic and total scattering and the effect was found for not only elastic but also inelastic scattering. The effect is relatively large for hydrogen rich molecules as H₂O, NH₃ and hydrocarbons, but is essentially related to the number of atoms contained in molecules. The origin of CBE will attribute mainly to the concentration of inner atomic electrons resulting from chemical bonding.     

Cooperativity and electron correlation effects on hydrogen bonding in infinite systems

Structural and electronic properties of hydrogen-bonded infinite chains of hydrogen cyanide and formamide molecules have been investigated by the ab initio crystal orbital method using several, partly highly polarized, atomic basis sets of increasing size at the Hartree–Fock (HF ) level and by including electron correlation effects in the second order of Møller–Plesset perturbation theory. The results obtained show that hydrogen bonding in molecular crystals of the type investigated is a highly cooperative phenomenon, both from the structural and energetic points of view. Comparison with clusters of up to four monomers demonstrate how various structural parameters converge toward their limiting values in the infinite system. The results obtained for infinite HCN chains show an excellent agreement with those observed for solid HCN, whereas the infinite formamide chain proves to be a reasonable model for the corresponding liquid phase. © 1994 John Wiley & Sons, Inc.     

Momentum–space electron densities—localized orbitals in hydrocarbons,boranes, and transition metal complexes

Position and momentum space plots are presented for localized molecular orbitals in hydrocarbons, boranes, a carborane, and two octahedral transition metal complexes. The p-space representation proves to be valuable for visualizing such orbitals since it highlights the differences in their character from one molecule to another. Factors influencing the form of the orbitals in p space, including the oscillatory behavior caused by contributions to an orbital from more than one center, are examined in detail. © 1996 John Wiley & Sons, Inc.     

Direct preparation and structure determination of tertiary and secondary amine boranes from primary or secondary amine boranes

New secondary and tertiary amine borane derivatives were prepared in a one-pot reaction starting from primary amine boranes. The reaction involves treatment of an amine borane with 2 equivalents of s-BuLi at −78 °C. In general, mixtures of mono and di metallated products were obtained. Alkyl iodides and benzyl chloride reacted with the lithiated amine, but aldehydes and ketones were reduced. Conversion was high as determined by NMR, but moderate to low yields were obtained after chromatography, possibly due to decomposition on silica. Crystal structures were obtained for the compounds 3a, 3b and 3c.     

Synthesis and reactions of N-heterocyclic carbene boranes

Boranes are widely used Lewis acids and N-heterocyclic carbenes (NHCs) are popular Lewis bases, so it is remarkable how little was known about their derived complexes until recently. NHC-boranes are typically readily accessible and many are so stable that they can be treated like organic compounds rather than complexes. They do not exhibit "borane chemistry", but instead are proving to have a rich chemistry of their own as reactants, as reagents, as initiators, and as catalysts. They have significant potential for use in organic synthesis and in polymer chemistry. They can be used to easily make unusual complexes with a broad spectrum of functional groups not usually seen in organoboron chemistry. Many of their reactions occur through new classes of reactive intermediates including borenium cations, boryl radicals, and even boryl anions. This Review provides comprehensive coverage of the synthesis, characterization, and reactions of NHC-boranes.     

Organoboron compounds,synthesis of allyl(dialkyl)boranes and diallyl(alkyl)boranes

Highly reactive allyl(dialkyl)-, crotyl(dialkyl)-, 3,3-dimethylallyl(dialkyl)-(= prenyl(dialkyl), and diallyl(alkyl)-boranes were prepared by allylation of esters R₂BOR′, RB(OR′)₂ or thioesters R₂BSR′ (R = alkyl) using allylic derivatives of aluminium, magnesium or boron in exchange reactions.The titled compounds are stable up to 100°C and do not symmetrize even on heating at 100°C for a long time. PMR spectroscopy data show that the characteristic feature of these compounds is a permanent allyl rearrangement, the rate of which increases with an increase in temperature. For allyl(diethyl)-borane at 100°C and 125°C the rates are equal to 2500 and 5000 sec^?1 respectively; activation energy of the rearrangement amounts to 11.8±0.2 kcal mol^?1.The boronallyl bonds in unsymmetrical allyl(alkyl)boranes readily split under the action of water and alcohols, protonolysis being accompanied by allyl rearrangement, crotyl and prenyl compounds are converted into 1-butene or 3-methyl-1-butene, respectively.     

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.     

Chemical bonding in view of electron charge density and kinetic energy density descriptors

Stalke's dilemma, stating that different chemical interpretations are obtained when one and the same density is interpreted either by means of natural bond orbital (NBO) and subsequent natural resonance theory (NRT) application or by the quantum theory of atoms in molecules (QTAIM), is reinvestigated. It is shown that within the framework of QTAIM, the question as to whether for a given molecule two atoms are bonded or not is only meaningful in the context of a well‐defined reference geometry. The localized‐orbital‐locator (LOL) is applied to map out patterns in covalent bonding interaction, and produces results that are consistent for a variety of reference geometries. Furthermore, LOL interpretations are in accord with NBO/NRT, and assist in an interpretation in terms of covalent bonding. © 2008 Wiley Periodicals, Inc.J Comput Chem, 2009.     

Characterization of bonding modes in metal complexes through electron density cross-sections

Qualitative inspection of molecular orbitals (MOs) remains one of the most popular analysis tools used to describe the electronic structure and bonding properties of transition metal complexes. In symmetric coordination complexes, the use of group theory and the symmetry-adapted linear combination (SALC) of fragment orbitals allows for a very accurate and informative interpretation of MOs, but the same procedure cannot be performed for asymmetric complexes, such as Schrock and Fischer carbenes. In this work, we present a straight-forward approach for classifying and quantifying MO contributions to a particular metal–ligand interaction. Our approach utilizes the topology of MO density contributions to a cross-section of an inter-nuclear region, and is computationally inexpensive and applicable to symmetric and asymmetric complexes alike. We also apply the same approach with similar decompositions using Natural Bond Orbitals (NBO) and the recently developed Fragment, Atomic, Localized, Delocalized and Interatomic (FALDI) density decomposition scheme. In particular, FALDI analysis provides additional insights regarding the multi-centric nature of metal-carbene bonds without resorting to expensive multi-reference calculations.