Quantum Monte Carlo Determination of Electronic and Structural Properties of S${\mathrm{i}}_{\mathit{n}}$ Clusters (n $\le$ 20)

Variational and fixed-node diffusion Monte Carlo methods are applied to study the structural and valence electronic properties of ${\mathrm{Si}}_n$ clusters. Binding energies for $n\le 7$ agree within $\approx 4\%$ with experiments and within $\approx 2\%$ when the fixed-node error is decreased by using natural orbitals. For $n\ge 9$ we show that the local density approximation overbinds by $\approx 25\%$. We determined unambiguously (i) the role of correlation in the energy ordering for different structures, including our new lowest energy structure of ${\mathrm{Si}}_{20}$, and (ii) a different ground state for ${\mathrm{Si}}_{13}{}^{-}$ than the one predicted by the local density approximation.