Self-consistent-field Xα scattered-wave molecular-orbital calculations have been performed for molybdenum clusters containing one, two, three, and four trimetallic triangles in a stacked configuration. The bonding interactions of the parent ${\mathrm{Mo}}_3$ layer are discussed in detail and the corresponding energy diagram is analyzed as arising mainly from the superposition of two sets of Walsh-like orbitals. In the ${\mathrm{Mo}}_6$ clusters the interlayer interactions arising from the staggered ($D_{3d}$) stacking mode, as well as the eclipsed ($D_{3h}$) alternative, are analyzed. With increasing cluster size, up to ${\mathrm{Mo}}_9$ and ${\mathrm{Mo}}_{12}$, emphasis is placed on a convergence behavior in the electronic patterns. Moreover, we could observe localized d-electron states which appear to be analogous to the surface states of the crystals. Finally, an energy-band scheme, derived from finite-cluster molecular orbitals, is presented in the case of a linear chain, arising from an infinite condensation of ${\mathrm{Mo}}_3$ layers. A high density of states occurs at the Fermi level. Moreover, it is crossed by a broad half-filled $a_2$ band (xz orbitals), giving rise to quasi-one-dimensional conductor character. These electronic factors generate an instability situation, the well-known Peierls distortion, characteristic of such pseudolinear chains. An analysis of this structural unstability is given by calculations performed on distorted ${\mathrm{Mo}}_{12}$ units constructed by the juxtaposition of two ${\mathrm{Mo}}_6$ fragments. This last study allows us (i) to elucidate the important change in the electronic structure with the occurrence of a large energy gap just above the Fermi level, and (ii) to present an alternative route to the energy-band scheme of the infinite chain.

• Received 30 July 1984

DOI:https://doi.org/10.1103/PhysRevB.31.5094