Cluster-surface and cluster-cluster interactions: Ab initio calculations and modeling of asymptotic van der Waals forces

We present fully ab initio calculations of van der Waals coefficients for two different situations: (i) the interaction between hydrogenated silicon clusters and (ii) the interactions between these nanostructures and a nonmetallic surface (a silicon or a silicon carbide surface). The methods used are very efficient and allow the calculation of systems containing hundreds of atoms. The results obtained are further analyzed and understood with the help of simple models. These models can be of interest for molecular-dynamics simulations of silicon nanostructures on surfaces, where they can give a very fast yet sufficiently accurate determination of the van der Waals interaction at large separations.

Figure 1

(Color online) $C_6^{AB}$ Hamaker constants as a function of the square root of the product of silicon atoms in clusters $A$ and $B$. As $C_6^{AB}$ scales basically with the product between the number of (silicon) atoms in $A$ and $B$, we plot the Hamaker constants divided by this number. Values of $C_6^{AB}$ when $A$ and $B$ are the same cluster are plotted as red (dark gray) squares, otherwise they are plotted as orange (light gray) dots.

Figure 2

(Color online) London effective frequency ${\omega }_1$, blue (dark gray) crosses, and static polarizabilities per atom, red (light gray) squares, for the silicon clusters under study as a function of the number of silicon atoms.

Figure 3

(Color online) van der Waals $C_3$ coefficients between silicon nanoclusters and a silicon surface. The $C_3$ coefficients were divided by the number of silicon atoms in the cluster. The different curves were calculated using different approximations for the dielectric constant of the bulk crystal at imaginary frequencies (see the text for details).

Figure 4

(Color online) van der Waals $C_3$ coefficient between silicon nanoclusters and a silicon carbide surface. The meaning of the curves is as in Fig. 3.

Figure 5

(Color online) Dielectric function of Si along the imaginary axis as a function of the frequency in a logarithmic scale. Results obtained with different approximations for the xc kernel are compared with the curve extracted from experimental data by using Eq. (14).

Figure 6

(Color online) Dielectric function of SiC along the imaginary axis as a function of the frequency in a logarithmic scale. We compare results obtained within different approximations for the xc kernels (Ref. 17).

Figure 7

(Color online) Dielectric function of Si and SiC along the imaginary axis: the model function is compared with the curve obtained using the LRC dynamical approximation for the xc kernel, which gives the best agreement with the experiment.