REAL SP ACE AB INITIO CALCULA TIONS OF EXCIT A TION ENERGIES IN SMALL SILICON QUANTUM DOTS Aristides D. Zdetsis and C. S. Garoufalis Department of Physics, University of Patras, 26500 Patras, Gr e ece Stefan Grimme Organisch-Chemisches Institut, Westf¨lische Wilhelms Universit ¨ at, Corrensstraße 40, ¨ D-48149 Munster, Germany ¨ Abstract We report accurate ab initio calculations, performed over the last three years, of the optical gap of small silicon nanocrystals (Si dots).In these calculations the Si dangling bonds on the surface of the nanocrys- tals are passivated by hydrogen and (more recently) by hydrogen and oxygen. The actual diameters of the nanocrystals range from about 2 ˚ A (SiH4) to 25 ˚ ˚ 281H172). The results for the optical gap can be safely (judging from the quality of the fit) extrapolated up to much larger diameters. We have used a large variety of real-space theoretical tech- niques, including configuration-interaction singlets (CIS) and multi-ref- erence second-order perturbation theory (MR–MP2). The bulk of the calculations has been performed in the framework of density functional theory (DFT) using advanced methods ranging from screened Coulomb interactions and ΔSCF calculations to DFT/CIS and time-dependent DFT (TDDFT). In all DFT methods we have used the hybrid nonlocal exchange- correlation functional of Becke and Lee, Yang and Parr, which includes partially exact Hartree–Fock exchange (B3LYP). Our results are in ex- cellent agreement with accurate recent and earlier experimentaldata. We have found that the diameter of the smallest oxygen-free nanocrystal that could emit photoluminescence in the visible region of the spectrum is around 22 ˚ A, whereas the largest diameter falls in the range of 84– 85 ˚ A. The high level and the resulting high accuracy (estimated within ˚ 0.3 eV for the optical gap) of our calculations have led to the resolution of existing experimental and/or theoretical discrepancies. Our (most re- cent) results also clarify unambiguously and confirm earlier predictions about the role of oxygen on the gap size. 317 © 2005 Springer. Printed in the Netherlands. B. A. Joyce et al. (eds.), Quantum Dots: Fundamentals, Applications, and Frontiers, 317–332.