Questioning the existence of a unique ground-state structure for Si clusters

Density functional and quantum Monte Carlo calculations challenge the existence of a unique ground-state structure for certain Si clusters. For Si clusters with more than a dozen atoms the lowest ten isomers are close in energy and for some clusters entropic effects change the energetic ordering of the configurations. Isotope pure configurations with rotational symmetry and symmetric configurations containing one additional isotope are disfavored by these effects. Comparisons with experiment are thus difficult since a mixture of configurations is to be expected at thermal equilibrium.

Figure 1

The bond length distribution averaged over various low-lying ${\mathrm{Si}}_{17}$-configurations. The six vertical lines indicate the first to sixth nearest neighbor distances in the crystal.

Figure 2

The dependence of the PBE energy interval for the lowest ten configurations on the cluster size.

Figure 3

Symmetrized geometries of low-lying ${\mathrm{Si}}_{13}$, ${\mathrm{Si}}_{16}$, ${\mathrm{Si}}_{17}$, ${\mathrm{Si}}_{18}$, and ${\mathrm{Si}}_{19}$ isomers.

Figure 4

The sum of the electronic (QMC, with errors), rotational, and vibrational (including zero point) free energy contributions for ${\mathrm{Si}}_{13a}$ (upper band) and ${\mathrm{Si}}_{13d}$ (lower band) configurations as a function of temperature with the ${\mathrm{Si}}_{13}$ free energy chosen as reference energy (solid line, set to 0). The bandlike structure indicated by the two dashed lines above and below each solid line represents the statistical error of the QMC results.

Figure 5

The configurational density of states for ${\mathrm{Si}}_{17}$.