Kekulé count in capped zigzag boron-nitride nanotubes

Hemi-B16N16 capped zigzag boron-nitride nanotube is introduced, and its Kekulé count is studied. With a bond-allocating and coding scheme, recurrence formulas are established as well as for the case of a hemi-B36N36 capped zigzag nanotube. Numerical results reveal that the Kekulé counts increase exponentially with respect to the number of layers in the nanotubes concerned.     

Which electron count rules are needed for four-center three-dimensional aromaticity?

A series of charged and neutral four-center n-electron (4c-ne, n = 1-4) molecules based on the adamantane framework, but which include combinations of boron, nitrogen, and phosphorus atoms at bridgehead positions, were studied computationally at the B3LYP/6-31G* level of density functional theory (DFT). The three-dimensional aromaticity, observed earlier for the 1,3,5,7-bisdehydroadamantane dication (1), is found to be general for 4c-2e electron systems. The degree of electron delocalization, evaluated by energetic, geometric, and various magnetic criteria, is quite independent of the molecular symmetry (point groups vary from Td to Cs), the degeneracy of the orbitals, the molecular charges, and the nature of the atoms participating in the delocalized bonding. Although the multiple positive (e.g., in 1 and some of the heteroatom systems) and multiple negative charges are strongly repulsive, the rigid adamantane frameworks help hold the bridgehead atoms within bonding distances with the fewer available electrons. The corresponding 4c-1e doublets are approximately half as aromatic as the 4c-2e singlets based on the same criteria. However, the three-electron systems may either adopt distorted but still four-center delocalized structures, or alternative 3c-2e two-dimensional arrangements in which the fourth bridgehead atom is more distant. There is no need to derive special rules for each point group for 4c-ne systems. Although the three-dimensional stabilization is computed to be quite appreciable, ranging between 10 and 50 kcalmol(-1), this delocalization energy is generally not sufficient to overcome distortion due to strain in higher homologues of 1 and in analogous noncage systems. Among the various 4c-2e homoadamantanedehydro dications studied, only the 1,8-dehydrohomoadamandiyl-3,6-dication forms a three-dimensional aromatic system.     

An alternative strategy for count and storage of Kekulé and longer range resonance valence bond structures

In this paper, we suggest a simple representation for notation of Kekulé valence bond (KVB) structures and longer range resonance valence bond (RVB) structures, which is called "the adjacency bonding array". In this representation, only an N component one-dimensional array is needed for inscribing each KVB or longer range RVB structure for an N-carbon system. Based on the adjacency bonding arrays, we develop very efficient algorithms for the systematic search of KVB and RVB structures as well as evaluation of the basis set overlap and Hamiltonian matrices.     

A combination of Clar number and Kekulé count as an indicator of relative stability of fullerene isomers of C<Subscript>60</Subscript>

Kekulé count is not as useful in predicting the thermodynamic stability of fullerenes as it is for benzenoid hydrocarbons. For example, the Kekulé count of the icosahedral C₆₀, the most stable fullerene molecule, is surpassed by its 20 fullerene isomers (Austin et al. in Chem Phys Lett 228:478–484, 1994). This article investigates the role of Clar number in predicting the stability of fullerenes from Clar’s ideas in benzenoids. We find that the experimentally characterized fullerenes attain the maximum Clar numbers among their fullerene isomers. Our computations show that among the 18 fullerene isomers of C₆₀ achieving the maximum Clar number (8), the icosahedral C₆₀ has the largest Kekulé count. Hence, for fullerene isomers of C₆₀, a combination of Clar number and Kekulé count predicts the most stable isomer.     

Development of more labile low electron count Co(I) sources: mild, catalytic functionalization of activated alkanes using a [(Cp*Co)2-μ-(η4:η4-arene)] complex

Catalytic transfer dehydrogenation of silyl protected amines, requiring sp(3) C-H bond activation, is mediated by a bridging arene complex of the type [(Cp*Co)(2)-μ-(η(4):η(4)-arene)] under mild conditions. Mechanistic and qualitative rate studies establish the compound as a more reactive Co(I) source when compared to other known Cp*Co(I) complexes.