The growth behavior of metal-doped silicon clusters $M{\mathrm{Si}}_n,M=\mathrm{Ti}$, Zr, and Hf and $n=8\text{–}16$ is studied using an ab initio ultrasoft pseudopotential plane wave method and the generalized gradient approximation for the exchange-correlation energy. For $n=8\text{–}12$, we find basketlike open structures to be most favorable, while for $n=13\text{–}16$, the metal atom is completely surrounded by silicon atoms. These results are in excellent agreement with the observed reactivity of these clusters. Our results suggest continuous aggregation until $n=16$, which is the optimal cage for the metal-encapsulated silicon clusters with these elements. Further calculations have been done on cation and anion clusters using the Gaussian method. The calculated electron affinities agree well with experimental results in the range of $n=12\text{–}16$ while the calculated values for smaller clusters are higher. Raman activity and infrared spectra have been calculated for selected clusters. These could help in the identification of the structures of these clusters from experiments.

• Received 23 March 2004

DOI:https://doi.org/10.1103/PhysRevB.71.075423