From structure to surface tension of small silicon clusters by Quantum Monte Carlo simulations

We investigate the structural, surface and electronic properties of small silicon clusters Si${}_n$ (for $n=2$ to 15) using HF, DFT and FN-DMC calculations. We analyze the atomic configurations, surface properties and electronic structures and show that the radius and average surface area of the clusters can be modeled by a Jellium-type model. We found that the surface tension $\sigma$ of the clusters decreases with increasing cluster size in the range of the clusters under investigation. An estimate of the surface tension for bulk silicon yields ${\sigma }_{bulk}=0.88\left(3\right)$ J/m² in agreement with recent experiments. The average bond length of the clusters shows a non-monotonic behavior. Smaller clusters exhibit a high spin state influenced by electron correlation, especially during the 2D to 3D structural transition, which occurs at $n=4$ to $n=5$. We also find that the Si₄, Si₁₀ and Si₁₂ clusters exhibit enhanced stability due to electron correlation. Our results are consistent with the experiments on bond length, binding energy and dissociation energy.