A peculiar bonding feature of a-rhombohedral boron is found in the electron density distribution of the icosahedral B 12 cluster. The electron density distribution is obtained by using the maximum entropy method with synchrotron radiation powder data. It clearly shows the characteristic two-and three-center covalent bond network which threads through atoms on the cluster surface. Besides, two kinds of covalent bonds in intercluster space are also shown in detail: a three-center trilaterally formed bond among the three clusters and a two-center bond with a remarkable feature of a bent bond between the clusters. The obtained covalent bonding features indicate the cluster-based nature of this material.

Electron density distributions were obtained using the maximum entropy method with synchrotron radiation powder data. In the metallic Al12Re, metallic bonding was observed for the icosahedral Al12 cluster with central Re atom. In the nonmetallic alpha-AlMnSi 1/1 approximant, covalent bonds were found in the electron density distribution of the Mackay icosahedral cluster without central atom. Rather than the Hume-Rothery mechanism, the covalency of Al (Si) icosahedron and that between Al (Si) and Mn atoms is considered to be the origin of the pseudogap and nonmetallic behavior of alpha-AlMnSi.

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