Quantum Monte Carlo Determination of Electronic and Structural Properties of S<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Clusters (<i>n</i><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>≤</mml:mi></mml:math>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 $n\ensuremath{\le}7$ agree within $\ensuremath{\approx}4%$ with experiments and within $\ensuremath{\approx}2%$ when the fixed-node error is decreased by using natural orbitals. For $n\ensuremath{\ge}9$ we show that the local density approximation overbinds by $\ensuremath{\approx}25%$. 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 ${\mathrm{Si}}_{13}{}^{\ensuremath{-}}$ than the one predicted by the local density approximation.

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