Quantum Monte Carlo Calculations of Nanostructure Optical Gaps: Application to Silicon Quantum Dots

Quantum Monte Carlo (QMC) calculations of the optical gaps of silicon quantum dots ranging in size from 0 to 1.5 nm are presented. These QMC results are used to examine the accuracy of density functional (DFT) and empirical pseudopotential based calculations. The $GW$ approximation combined with a solution of the Bethe-Salpeter equation performs well but is limited by its scaling with system size. Optical gaps predicted by DFT vary by 1–2 eV depending on choice of functional. Corrections introduced by the time dependent formalism are found to be minimal in these systems.

Figure 1

Size dependence of optical gaps of silicon nanoclusters, calculated using diffusion Monte Carlo (DMC), time independent (LDA) and dependent (TD-LDA) DFT, semiempirical tight binding, and pseudopotential approaches. DMC statistical error bars are smaller than the symbols.

Figure 2

Deviation of the optical gap predicted by density functional calculations based on the (a) LDA functional and (b) B3LYP hybrid functional from the DMC optical gap.