Smaller particles known as clusters however are computationally feasible using

# Smaller particles known as clusters however are

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much beyond the size that we can model with DFT methods. Smaller particles, known as clusters, however are computationally feasible using electronic structure methods. In addition clusters often display much different, often useful, properties than their larger counterparts. You are to model silicon clusters, or Sin(n = 1 to 10). We will use a trick to get the geometries from PM3, but then the energies and orbital information from B3LYP (DFT). n Binding Energy (Hartree) Addition Energy (Hartree) HOMO- LUMO (au) 1 0 0 0.031 2 289.4801 -0.1512 0.018 3 289.6796 -0.1995 0.033 4 289.8828 -0.2032 0.078 5 289.9073 -0.0245 0.085 6 290.1045 -0.1972 0.097 7 290.231 -0.1265 0.086 8 290.394 -0.163 0.051 9 290.4938 -0.0998 0.025 10 290.5331 -0.0393 0.03 0 50 100 150 200 250 300 350 0 2 4 6 8 10 12 Energy n Binding Energy
The bonding energy for n=1-10 varies 289.48 to 290.53 which is a difference of 1.05. It is a flat line. The addition energy peaks at n=5. The addition energy it the lowest between n=3 and n=4. The HOMO-LUMO difference peak at n=6. The minimum of the HOMO- LUMO difference is n=2. -0.25 -0.2 -0.15 -0.1 -0.05 0 0 2 4 6 8 10 12 Energy n Addition Energy 0 0.02 0.04 0.06 0.08 0.1 0.12 0 2 4 6 8 10 12 HOMO-LUMO Difference n HOMO-LUMO

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