Lec14 (1) - 10.675 LECTURE 14 RICK RAJTER 1. Today...

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10.675 LECTURE 14 RICK RAJTER 1. Today Introduction to Plane Wave Pseudo Potential Methods Electronic Structure of Extended Systems Bloch’s Thereom Plane Wave Basis Set Implementation of DFT Pseudo potentials 2. MOT Molecular Orbital Theory 1D con±guration of H-atoms Atoms 1 and 2 Φ 1 wave function centered around atom 1 Φ 2 wave function centered around atom 2 Bonding Φ A = Φ 1 + Φ 2 Anti-Bonding Φ B = Φ 1 Φ 2 The bonding state is energetically favorable in the band splitting that occurs. Move on to 3 atoms in a ring (1D line) 3 energy con±gurations (2 unique) Lowest, Φ 1 + Φ 2 + Φ 3 Highest Φ 1 + Φ 2 Φ 3 AND Φ 1 Φ 2 Φ 3 Date : Fall 2004. 1
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2 RICK RAJTER Every reverse of sign from neighboring atoms (1 links to 2, 2 links to 3, 3 links back to 1) is a node. Nodes are higher in energy from the band splitting. N atoms, 1 huge ring. Lowest energy is all wave functions of the same sign Highest energy is an alternating arrangement of wave functions. Each energy in between (combinations of + and -’s) creates a continuum of levels
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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Lec14 (1) - 10.675 LECTURE 14 RICK RAJTER 1. Today...

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