Ab initioconfiguration interaction calculations of the semiconductor ternary clustersGelSimCn(l+m+n<~6)

Abstract

Ground-state structures, stabilization energies, HOMO-LUMO energy gaps, and vibrational frequencies of ${\mathrm{Ge}}_{l}{\mathrm{Si}}_{m}{\mathrm{C}}_{n}$ ternary microclusters $(s=l+m+nl~6)$ have been investigated using the configuration interaction with all single and double substitutions method, and ionization potentials and vertical detachment energies of trimers and tetramers predicted utilizing the outer valence Green-function frozen-core procedure. ${\mathrm{Ge}}_{l}{\mathrm{Si}}_{m}{\mathrm{C}}_{n}$ is found to follow structural patterns similar to corresponding ${\mathrm{Si}}_{l+m}{\mathrm{C}}_{n}$ binary clusters and most ternary species possess singlet ground states except ${\mathrm{GeSiC}}_{4},$ which prefers a triplet one. Trimers, tetramers, and ${\mathrm{GeSi}}_{2}{\mathrm{C}}_{2}$ are planar, and the C-rich ${\mathrm{GeSiC}}_{3}$ and ${\mathrm{GeSiC}}_{4}$ are linear, while all the other Si-rich or Si- and Ge-rich clusters with $sg~5$ atoms prefer three-dimensional structures. Formation of strong C=C bond(s) predominates the relative stabilities of different isomers for clusters with limited numbers of C atoms, while Si=C bonds play an important role for silicon-rich species or systems with close C and Si atomic ratios. Planar and linear semiconductor clusters possess delocalized multicenter\char21{}two-electron \ensuremath{\pi} bonds (aromatic) and follow the $(4n+2)$ electron counting rule. Frequency analyses indicate that most vibrational modes of small ternary clusters are carbon dominated in terms of amplitudes, while Si atoms vibrate in medium sizes and Ge atoms vibrate very weakly.