Electrostatic interaction schemes for evaluating the polarizability of silicon clusters.

Electrostatic interaction schemes have been applied to predict the evolution of the polarizability in Si(n) clusters of increasing size (n=3-19). Both on-site polarization and charge transfer effects have been included in the interaction scheme, of which the values have been compared to B3LYP/6-311G() and other first principles results. To reproduce the pattern of the variation of the B3LYP average polarizability per Si atom as a function of the cluster size, the atomic polarizability employed in the interaction scheme should amount to roughly 80% of the bulk atomic polarizability. However, this results in a systematic underestimation of the polarizability per Si atom by about 25%, whereas increasing the atomic polarizability value leads to excessive variations of the polarizability per Si with the cluster size. An improved agreement is obtained when incorporating a charge transfer contribution, at least for sufficiently large clusters, substantiating the fact that in large clusters electrostatic effects are dominant over quantum effects. This charge transfer atomic polarizability term has been modeled by a simple function, which evolves linearly with the difference of Cartesian coordinates between the atom and the center of mass and that has been verified using B3LYP/6-311G() calculations. In the case of the prediction of the polarizability anisotropy, a similar atomic polarizability corresponding to 80% of the bulk atomic polarizability has been shown suitable to reproduce the B3LYP results, whereas inclusion of charge transfer effects can slightly improve the agreement, provided the amount of charge transfer increases with the size of the cluster.