On the 'Atomic' Polarizabilities in Small Si-n Clusters and the Dielectric Constant of Bulk Silicon

Applying the classical discrete reaction field (DRF) approach, which includes a treatment for the solution of the many-body polarization in complex systems, we calculated the mean atomic polarizability for a Si atom from the known molecular polarizability of Si-3. With only this parameter (6.16 angstrom(3), i.e., close to the free atom value), and the geometries as input, the effective atomic mean polarizabilities and their averages ((n) = (n)/n) for the series Si-4-Si-10 were calculated and found to be in excellent agreement with theoretical and experimental values. These (n) are larger than the bulk value of 3.7 angstrom(3). We used the same input parameter for (by hand) constructed model systems up to n = 4950 with various geometries. For the larger clusters with the diamond lattice, we obtained the bulk value, implying that we "predicted" the dielectric constant of silicon almost from first principles. However, even the largest system is still too small for considering it as a real dielectric. In other lattices (primitive and face centered cubic), the (n) are significantly smaller than 3.7 angstrom(3), which we attribute to the tighter packing in these lattices in comparison with that of the diamond structure. The behavior in all these systems can be easily understood by accounting properly for the local fields and for damping the interaction between induced dipoles. We show that there is no need for additional (e.g., "charge transfer") parameters.