Ucdavisedutheoreticalchemistry

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Unformatted text preview: l interference filters (bu5erfly wings) which use diffrac[on to produce colors, but at electron wavelengths 5 Bonding and An[bonding Orbitals in Hydrogen (The Simplest Bandgap) Elemental Hydrogen: 1s1 Hydrogen #1: 2 states, 1 electron Hydrogen #2: 2 states, 1 electron H2: 4 states, 2 electrons Electron not located between hydrogen atoms Higher Energy Lower Energy Electron located between hydrogen atoms http://chemwiki.ucdavis.edu/Theoretical_Chemistry/ Chemical_Bonding/Molecular_Orbital_Theory 6 Energy Bands •  •  •  As atoms are brought together to form a solid, the forces of a5rac[on and repulsion between atoms will find a balance at the proper inter- atomic spacing for the crystal The discrete atomic energy levels form bands as the atoms are brought closer together. These bands become the conduc[on and valence band, separated by the forbidden gap where no electron states exist. Silicon Atom: 1s2 2s2 2p6 3s2 3p2 (missing 4 electrons to fill outer shell) –  Core: 1s2 2s2 2p6 Valence: 3s2 3p2 n=3 Available States 3S 3P Total •  2 6 8 # of Electron 2 2 4 Assuming we have N Si atoms to form a crystal, we have N x (3s2 3p2) valence electrons n=3 Available States # of Electron Total Nx8 Nx4 Conduc[on Band Nx4 0 (at 0°K) Valence Band Nx4 Nx4 (at 0°K) 7 Forma[on of Energy Bands What happens when a collection of Si atoms are brought closer together? Conduction Band Edge Valence Band Edge Smaller Lattice Spacing “p” “s” Isolated Atoms 8 Large Spacing: Weak Poten[al Individual atoms begin to “see” neighboring atoms (periodic potential), the p-orbitals no longer have degenerate energy: the interaction of the fields cause differences to develop in px, py, and pz orbitals* *Simplified picture 9 Wave Func[on Overlap Region Significant wavefunction overlap between the orbitals of adjacent atoms – electrons are freely exchanges. No sp3 hybridization yet. 10 Wavefunc[on Overlap Comparison •  If the atomic sp...
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