The small silicon clusters Si n ( n=2–10) and their anions: structures, themochemistry, and electron affinities

Abstract

The silicon clusters structures, electron affinities, and dissociation energies of the Si n / Si n − ( n=2–10) species have been examined using seven hybrid and pure density functional theory (DFT) methods. The basis set used in this work is of double-ζ plus polarization quality with additional diffuse s- and p-type functions, denoted DZP++. The geometries are fully optimized with each DFT method independently. Four different types of energy separations presented in this work are the adiabatic electron affinity (EA ad), zero-point vibrational energies (ZPVE) corrected EA ad (EA zero), the vertical electron affinity (EA vert), and the vertical detachment energy (VDE). The first Si–Si dissociation energies D e (Si n →Si n−1 +Si) for Si n , and both D e ( Si n − → Si n − 1 + Si − ) and ( Si n − → Si n − 1 − + Si ) for Si n − species have also been reported. The most reliable adiabatic electron affinities, obtained at the DZP++ BPW91 level of theory, are 2.16 (2.15) eV for Si 2, 2.32 (2.32) eV for Si 3, 2.24 (2.25) eV for Si 4, 2.51 (2.51) eV for Si 5, 2.11 (2.12) eV for Si 6, 2.06 (2.07) eV for Si 7, 2.86 (2.85) eV for Si 8, 2.28 (2.28) eV for Si 9, 2.45 (2.46) eV for Si 10. (EA zero values are in parentheses). While BP86, B3P86 and BPW91 predict to the most reliable dissociation energies. The dissociation energies for Si n →Si n−1 +Si are predicted to be 3.26 (3.23) eV for Si 2, 3.96 (3.92) eV for Si 3, 4.39 (4.33) eV for Si 4, 3.68 (3.62) eV for Si 5, 4.12 (4.08) eV for Si 6, 4.07 (4.01) eV for Si 7, 2.76 (2.73) eV for Si 8, 4.28 (4.22) eV for Si 9, 4.33 (4.28) eV for Si 10 with error of 0.13 (0.16) eV (corrected with ZPVE in parentheses). And the dissociation energies of Si n − → Si n − 1 − + Si are predicted to be 3.95 (3.92) eV for Si 2 − , 4.14 (4.11) eV for Si 3 − , 4.29 (4.24) eV for Si 4 − , 3.98 (3.92) eV for Si 5 − , 3.72 (3.68) eV for Si 6 − , 4.01 (3.96) eV for Si 7 − , 3.59 (3.54) eV for Si 8 − , 3.69 (3.63) eV for Si 9 − , and 4.51 (4.46) eV for Si 10 − .