RESUMO
Planar and quasi-planar boron clusters with a disk-like shape are investigated in search of common bonding characteristics. Methods used involve molecular orbital calculations based on Density Functional Theory (DFT), and valence bond partitioning using Adaptive Natural Density Partitioning (AdNDP) analysis. For high-symmetry cases the proposed bonding schemes are confirmed using the group-theoretical induction method. The focus is on the electron occupation of delocalized in-plane 3-center and 4-center bonds. For disks consisting of concentric rings this inner electron count is found to be equal to a multiple of the vertex count of the inner polygon. For two concentric rings the multiplying factor is four, for three concentric rings it is eight. The appropriate bonding schemes are presented which explain these results. Some giant clusters with two hexagonal holes are also discussed.
RESUMO
The E â e Jahn-Teller Hamiltonian in the Bargmann-Fock representation gives rise to a system of two coupled first-order differential equations in the complex field, which may be rewritten in the Birkhoff standard form. General leapfrog recurrence relations are derived, from which the quantized solutions of these equations can be obtained. The results are compared to the analogous quantization scheme for the Rabi Hamiltonian.
RESUMO
This article presents the use of free particle models to obtain quantum rules for planar boron clusters, with nuclearities in the range from seven to twenty. The information obtained from the models is being compared with electronic structure calculations based on the DFT method. Separate rules for in-plane and out-of-plane bonding are derived. In-plane bonding is precise on the cluster boundary and forms a network of alternating triangular 3c-2e bonds on the inside. The out-of-plane bonding is strongly delocalized and only depends on the global shape and size of the cluster.
